Tutorial Kit (Economics-300 L)-Vol. 2.Pdf

COVENANT

UNIVERSITY

ALPHA SEMESTER TUTORIAL KIT

(VOL. 2)

PROGRAMME: ECONOMICS 300 LEVEL

DISCLAIMER

The contents of this document are intended for practice and learning purposes at the undergraduate level. The materials are from different sources including the internet and the contributors do not in any way claim authorship or ownership of them. The materials are also not to be used for any commercial purpose.

LIST OF COURSES

*ECN311: Intermediate Microeconomics I *ECN312: Intermediate Macroeconomics I ECN313: Theories of Growth and Development I ECN314: History of Economic Thought *ECN315: Public Sector Economics I ECN316: International Economics I ECN317: Project Evaluation ECN318: Introductory Econometrics I *ECN319: Operations Research I *ECN331: Monetary Economics *ECN334: Statistical Theory

*Not included

COVENANT UNIVERSITY

CANNAN LAND, KM. 10, IDIROKO ROAD P.M.B 1023, OTA, OGUN STATE, NIGERIA.

TITLE OF EXAMINATION: B.Sc. DEGREE EXAMINATION

COLLEGE: CDS DEPARTMENT: ECONOMICS & DEVPT. STUDIES

SESSION: 2014/2015 SEMESTER: ALPHA

COURSE CODE: ECN 313 COURSE TITLE: THEORIES OF ECONOMIC GROWTH & DEVELOPMENT

INSTRUCTION: ANSWER ALL QUESTIONS IN SECTION ‘A’ AND ONE (1) QUESTION EACH FROM SECTIONS ‘B’ AND ‘C’

TIME ALLOWED: 2 HOURS

SECTION A

QUESTION 1 i) . What do economic theories and models seek to explain? (3 marks) a) ...... b) ...... c) ...... ii) HDI is based on 3 indicators; (3 marks)

a) ...... b) ...... c) ...... iii) . According to Dudley Seers, the issue of economic development centres on; (3 marks) a) ...... b) ...... c) ...... iv) State Kindleberger’s (1965) definition of economic development. (1 mark) v) Highlight the various classifications of the world economies by (3 marks)

a) International Monetary Fund,

b) The World Bank,

c) United Nations Organization

3 vi) State the four elements of the concept of dualism. (2 marks)

a) b) c) d) vii) State six indicators that have been used to measure economic development. (3 marks)

a)...... b) ...... c) ...... d) ...... e) ...... f) ......

SECTION B

QUESTION 2

(a) Explain the balanced and unbalanced growth theories including their various assumptions and criticisms. (10 marks)

(b) Discuss the key points of the “Big Push” theory and its defects. (10 marks)

TOTAL (20 marks)

QUESTION 3

(a) Highlight the assumptions of the Solow growth model. Derive the determinants of change in capital per worker. (15 marks)

(b) State and explain briefly ten characteristics of developing countries. (5 marks)

TOTAL (20 marks)

SECTION C

QUESTION 4

Present and critically evaluate the relevance of the following models of economic development to today’s developing countries;

a) Rostow’s stages of growth model. (10 marks) b) Lewis’ ‘two – sector surplus labour’ theoretical model. (10 marks)

TOTAL (20 marks)

QUESTION 5

Write short notes on any four of the following: a) The concept of economic development; (5 marks) b) Economic dualism; (5 marks) c) Vicious cycle of poverty; (5 marks) d) Sustainable economic growth; and (5 marks) e) Inclusive growth (5 marks)

TOTAL (20 marks)

COVENANT UNIVERSITY CANAAN LAND, KM. 10, IDIROKO ROAD P.M.B. 1023, OTA, OGUN STATE, NIGERIA

ECN313 MARKING GUIDE2014 / 2015

1i)

 How economies develop or not over time...... (1mk)  How barriers to growth can be identified and overcome...... (1mk)  How government can induce, sustain and accelerate growth with appropriate development policies...... (1mk) ii) Longevity...... (1mk)

 Knowledge...... (1mk)  Standard of living...... (1mk) iii)

 Poverty...... (1mk)  Unemployment...... (1mk)  Inequality...... (1mk) iv) Economic development implies both more output and changes in the technology and institutional arrangements by which it is produced and distributed...... (1mk) v) a) Industrial countries; Developing countries; Transitional economies. (1mk) b) High income, middle income and low income. (1mk) c) HDI, HPI and MPI. (1mk) vi)

 Different sets of conditions coexist in a given state. (1/2 mk)  The coexistence is chronic . (1/2 mk)

 The degree of inferiority or superiority show no sign of diminishing. (1/2 mk)  The interrelationship does not improve the inferior element. (1/2 mk)

 vii) GDP, GNP/CAPITA, WELFARE, SOCIAL INDICATORS, HDI, HPI AND MPI. (3 mks)

viii)

 Describe the state of economic development of developing countries over a given period of time. (3 mks)

 Identify economic growth theories / models you know. (2 mks)

 High experiences of countries that have benefited from these theories / models. (3 mks)

 Identify reasons why these theories and models have not worked for some countries. (2 mks)

 Suggest the way forward. (2 mks)

SECTION B

QUESTION 2

a. Explain the balanced and unbalanced growth theories including their various assumptions and criticisms.

Solution Theory of Balanced Growth Balanced growth doctrine has been described differently.To some, it is investing in a laggard industry to bring it to speed with other industries.To others, it is investment taking place simultaneously in all industries at once.It also means balanced development of the manufacturing and agriculture industries.Jhingan (2012) stated that balanced

7 growth requires balance between different consumer and capital goods industries.It implies balance between domestic and export sector.It further entails balance between social and economic overheads, directly productive investments and verticals and horizontal external economies.This theory is advocated by Paul Rosenstein-Rodan, RagnarNurkse and Arthur Lewis.Rosenstein-Rodan was the first economist that propounded the theory in his 1943 article, though did not use these words.

The theory states that “there should be simultaneous development in all inter-related sectors which help in increasing the supply of goods”.It includes the simultaneous and harmonious development of intermediate goods, raw materials, power, agriculture, irrigation, transport, etc, including all industries producing goods.The theory proposes that the government of any underdeveloped country needs to make large investments in a number of industries simultaneously.This is expected to enlarge the market size, increase productivity, and provide an incentive for the private sector to invest.It is the systematic and equal prioritization for all sectors and regions of the economy. It focuses on balanced type of investment and capital mobilization to make the growth more balanced and distributed.Thus, the main objectives of balanced growth are to make the growth of all sectors in a balanced way at the same time.

Criticisms 1. Rise in costs; simultaneous establishment of industries is likely to raise production costs. 2. No attention to reducing costs; no possibility of reducing cost in existing industries. 3. It is likely to create other problems. New industries can reduce demand for existing industries and make them unprofitable. 4. It fails as a theory of development according to Hirschman. 5. It is beyond the capabilities of underdeveloped countries. This is also according to Hirschman. 6. Disproportionality in factors; the difference in abundance or otherwise of factors of production in underdeveloped countries is another problem. (5marks for discussing the assumptions and criticisms)

Theory of Unbalanced Growth The unbalanced growth approaches seems to be the alternative of balanced growth approaches.Economists such as Hirschman, Dr. Singer, Paul Streeten, Rostow, Kindleberger, etc, are associated with this theory.Hirschman’s argument is often popularized.His contention is that deliberately unbalancing the economy as a pre- designed strategy is the best way to achieve economic growth in an underdeveloped country.

Assumptions The theory state that investment should be made in selected sectors rather than simultaneously in all sectors.With this, the economy gradually moves from path of unbalanced to that of balanced growth.The best way to achieve development in developing countries is the unbalanced growth. This means that unbalancing the economy makes the growth faster and easier.The unbalance of economy is made by the unequal investment patterns. This means the investment is concentrated at the potential and selective sector only. Another version is that Hirschman does not believe the issue with underdeveloped economies is lack of capital but lack of entrepreneurial abilities.According to Hirschman, not a balanced growth should be aimed at, but rather existing imbalances must be maintained.Investments should not be spread evenly but concentrated in such projects in which they cause additional investments because of their backward and forward linkages without being too demanding on entrepreneurial abilities.Manufacturing industries and import substitutions are relevant examples. These first investments initiate further investments which are made by less qualified entrepreneurs.

Limitations 1. Inadequate attention to the composition, direction and timing of unbalanced growth. 2. It neglects resistances. 3. Also beyond the capabilities of underdeveloped countries. 4. Lack of basic facilities. 5. Lack of factor mobility. 6. Emergence of Inflationary Pressures. 7. Linkage effects explained is not based on data. (5marks for discussing the assumptions and criticisms)

b. Discuss the key points of the “Big push” theory and its defects.

Solution The Key Points of the “Big Push” theory The theory is associated with Prof. Paul N. Rosenstein-Rodan.It states that “a big push or large comprehensive programme is needed in the form of a high minimum amount of investment to overcome the obstacles to development in an undeveloped economy and to launch it on the path of progress”.It argues that proceeding “bit by bit” will not launch the economy successfully on the development path, rather a minimum amount of investment is a necessary condition. It necessitates the obtaining of external economies that arise from the simultaneous establishment of technically interdependent industries.

Thus, indivisibilities and external economies flowing from a minimum quantum of investment are prerequisite for launching economic development successfully.He also distinguished between three different kinds of indivisibilities and external economies. 1. Indivisibilities in Production Function; Indivisibilities in inputs, outputs or processes leads to increasing returns. 2. Indivisibility of Demand; this requires simultaneous setting up of interdependent industries in underdeveloped countries. 3. Indivisibility in the Supply of Savings; a high minimum size of investment requires a high volume of savings. (5 marks for explanation)

Defects 1. Negligible economies from investment in export and import substitutes. 2. Negligible economies even from cost-reducing investments. 3. Neglects investments in the agricultural sector. 4. Generates Inflationary Pressures. 5. Low investment leads to large increase in output. (5 marks for the defects)

QUESTION 3

a. Highlight the assumptions of the Solow growth model. Derive the determinants of change in capital per worker.

Solution • Prof. Robert. M. Solow built the model as an alternative to the H-D model.The Solow model is a modification of the Harrod-Domar model. The key modification is that the Solow model allows for the substitution between factors of production, i.e. labor and capital.It is without H-D’s assumption of fixed proportions in production. Capital-output and capital-labor ratios are not fixed Assumptions • The model assumes that there is diminishing returns to the use of labor and capital. • The model provides the basic framework for the study of convergence across countries. • One composite commodity is produced. • Output is regarded as net output after making allowance for depreciation of capital. • Constant returns to scale. i.e. production function is homogenous of degree 1. • Two factors of production, labour and capital are paid according to their marginal physical productivities. • Prices and wages are flexible. • There is perpetual full employment of labour. • Full employment of available stock of capital

• Labour and capital are substitutes for each other. • Neutral technical progress. • The saving ratio is constant. (1mk for any five correct answers)

Deriving the determinants of change in capital per worker; • Recall from the H-D model that

K  sY  dK k K L    K Y k K L   s  d K K Re arranging: But K k L    K k  K k L L But L  n L By substitution: k K Y  n   s  d k K K

k Y   s  n  d k K

Y  K   k  s    nk  dk K  L  K Note: k  L  k  sy  nk  dk  k  sy  (n  d)k

(8mks)

Thus change in capital per worker is determined by three things:(2 mks)

1. It’s positively related to saving (investment) per worker 2. It’s negatively related to population growth. There should always be new investments to match increases in the labor force 3. Depreciation erodes the capital stock.

b. State and explain briefly ten characteristics of developing countries.

Solution

1. Low living standards (ie low real income per capita) associated with high income inequality, poor health and inadequate education and limited life expectancy. 2. Low levels of productivity possibly because of limited resources; unskilled labour; weak complementary factors and management practices and backward technology. 3. High population growth rate due to falling death rate resulting in significant dependency burdens. 4. Large-scale unemployment and underemployment. 5. A small industrial sector with outdated technology unable to employ large numbers of poorly educated workers.

6. Large but neglected agricultural sector and outward migration from rural to urban areas. 7. Market imperfections. In many developing economies markets may not existeg financial market. 8. Limited technology, infrastructure, and social and political institutions. 9. Low social capital and social cohesion. 10. Developing countries generally have a colonial past.

(1/2 mk each for any 10 correct answer)

SECTION C

QUESTION 4

Solution

The Rostow’s stages of growth model presented five stages that a nation goes through to reach development. These stages include; traditional society, preconditions for take-off, take-off, drive to maturity and the age of mass consumption.

i. Traditional society; this is the early stage of economic development where the society is still at the traditional stage. It is defined as one whose structure is developed within limited production functions based on pre-Newtonian science and technology and as pre- Newtonian attitudes towards the physical world. The societies does not lack inventiveness and innovation, but lack tools and outlook toward the physical world of post-Newtonian era(1mark)

ii. Preconditions for take-off; this is the second stage in Rostow’s linear stages of economic development. It presents a number of conditions that must be in place in preparedness for the take-off of the development of the society. It is a transitional era in which the preconditions for sustained growth are created. The pre-conditions for take-off were encouraged by four forces;The New learning or Renaissance, New Monarchy, the New World and the New Religion or Reformation. Pre-conditions for sustained industrialization according to Rostow, requires radical changes in three non-industrial sectors;Firstly, build up of social overhead cost especially in transport to enlarge extent of the market to exploit resources productively and allow state to rule effectively. Secondly, technological revolution in agriculture for agricultural productivity to increase to meet the requirements of a rising general and urban population.Thirdly, expansion of imports including capital imports financed by efficient production and marketing of natural resources for exports.(1mark) iii. The take-off Stage; Rostow defines this stage as an industrial revolution tied directly to radical changes in the methods of production, having their decisive consequence over a relatively short period of time.This stage is supposed to be short lasting for about two decades. (1mark) iv. Drive to Maturity; Rostow defined this stage as the period when a society has effectively applied the range of modern technology to the bulk of its resources.It is a period of long sustained economic growth extending well over four decades. At this stage, new production techniques take the place of the old ones with new leading sectors created. Also, rate of net investment is high, well above 10% of national income and the economy is able to withstand unexpected shocks. (1mark) v. Age of Mass Consumption; This is the final stage of the linear stage model and is characterized by the migration to suburbia, extensive use of the automobile, the durable consumers’ goods and household gadgets.In this stage, attention of society shifts from supply to demand, problems of production to problems of consumption and of welfare in the widest sense.(1mark)

Relevance to Developing Countries. i. According to Rostow, one of the important conditions for take-off is the raising of savings and investing ratio from 5% or less to over 10% of national income and maintaining it for two or more decades. It is a critical transitional stage of self- sustained growth. So ensuring increase in savings and rate of investment is essential for the economic development of developing countries. (2.5 marks) ii. The second condition for take-off which is the development of one or more leading sectors in the economy is equally relevant for the developing nations. They must strive to develop the agricultural, industrial and tertiary sectors considerably. (2.5 marks)

Lewis’ two-sector surplus labour model: This model was formulated by Nobel Laureate, W. Arthur Lewis in the mid-1950s. It became the general theory of development process in surplus labour third World countries during the 1960s and 1970s. The model posits that the underdeveloped economy consists of two sectors: traditional overpopulated rural subsistence sector characterized by zero marginal labour productivity.According to Lewis, the surplus labour in this sector can be withdrawn from the agricultural sector without any loss of output thus the zero marginal labour productivity. On the other hand is the high-productivity modern urban industrial sector into which labour from the subsistence sector is gradually transferred.Primary focus of the model is on process of labour transfer and growth of output and employment in the modern sector. (6marks)

Relevance to Developing Countries.

The lewis theory is applicable to overpopulated underdeveloped countries under certain set conditions. Its applicability is, therefore circumscribed by its assumptions which are the bases of criticisms some of which are discussed below;

1. Assumption of rate of labour transfer and employment creation in the modern sector is proportional to rate of modern sector capital accumulation. Not valid if capitalist reinvests profits in sophisticated labour-saving equipments. 2. Notion that surplus labour exists in the rural areas while there is full employment in the urban areas was found not to be valid as contemporary research indicates little general surplus labour in rural locations. 3. Notion of competitive modern-sector labour market that guarantees constant real urban wages was not valid as well, as institutional factors tend to negate competitive forces in LDCs 4. A final concern of the lewis model is its assumption of diminishing returns in the modern industrial sector, as there is much evidence that increasing returns prevail in that sector posing special problems for development policymaking. (4marks)

QUESTION 5

Concept of Development: Economic development is both a policy objective and a means to achieving other policy goals such as full employment, poverty alleviation, egalitarialism and social program. Economic development is both growth in GDP accompanied by relevant social and institutional changes by which that growth can be sustained. These changes include reduction in absolute poverty, a better quality of life, high literacy level, improved productivity of labour. (5marks)

Economic Dualism: This is defined as the stratification of the economy into two main sectors; one which is modern and industrial where the rate of growth is faster, and the other, which is traditional or subsistent where growth is slower or rather stagnant. The various descriptions of economic dualism include, capital dualism, social dualism, technological dualism and financial dualism. The elements of dualism are different sets of condition coexist; the coexistence is chronic; the difference shows no sign of diminishing, no mutual benefit. (5marks)

Inclusive Growth: We need economic growth to pay for the things we need in life such as education, health, housing, roads, etc. Inclusive growth ensures that growth benefits everyone, without further widening inequality and poverty. (5marks)

Vicious Cycle of Poverty: Due to low income, the capacity to save is low. Low income is a result of low productivity which is in turn due to lack of capital which is as a result of low saving capacity. (present this in a circular diagram form). (5marks)

Sustainable Economic Growth (SEG): SEG means a rate of growth which can be maintained without creating other significant economic problems, especially for future generation. There is a trade-off between rapid economic growth today and growth in the future. Rapid growth today may exhaust resources and create environmental problems for future generations including the depletion of oil and fish stock and global warming. (5marks)

COVENANT UNIVERSITY CANAANLAND, KM 10, IDIROKO ROAD P.M.B 1023, OTA, OGUN STATE, NIGERIA. TITLE OF EXAMINATION: BSc Economics EXAMINATION COLLEGE: College of Business & Social Sciences SCHOOL: Social Sciences DEPARTMENT: Economics & Development Studies SESSION: 2014/2015 SEMESTER: Omega COURSE CODE: ECN 324 CREDIT UNIT: 2 COURSE TITLE: History of Economic Thought II TIME: 2 HOURS INSTRUCTION: Answer Three Questions in all and Section A is Compulsory. Answer two other questions-one must be from section B and the other from section C.

Section A: Compulsory Question (30 marks)

1. Carl Menger, W.S Jevons and Leon Walras simultaneously but independently introduced ………………. into economics. 2. Smith, Ricardo and Mill belong to the ……………………school of economic thought. 3. Whereas Alfred Marshall advocated …………………..analysis, Leon Walras advocated …………..analysis. 4. …………………….is a group of economists who believe that the wealth of nations depends on the amount of gold and silver a nation possesses. 5. ………………….is the major component of monetarism. 6. Absolute advantage is to Adam Smith as comparative advantage is to ………………… 7. ………………was born in 1835 and in 1854 left school to take a job as an assayer in an Australian Mint. 8. …………………..is a foremost English economist known for his book “Principles of Economics” published in 1890. 9. ……………….ideas formed the foundation of the theory and practice of modern macroeconomics. 10. Milton Friedman won the Nobel Prize in Economics Sciences in the year ………. 11. Keynes agree with Classical economics that an economy is always at full employment (True/False). 12. According to Smith, the higher is capital accumulation, the more an economy grows (True/False). 13. Monetarists agree with Keynes that government should intervene in the economy by injecting funds that will stimulate aggregate demand (True/False). 14. According to Ricardo, wages vary with the price of food (True/False).

15. In Smith’s opinion, labour is the real measure of the worth of a good (True/False).

Section B: Answer ONE Question from this Section

2a. Describe the essential elements of Leon Walras’ General Equilibrium Theory (14 marks) 2b. How does this theory compare with Alfred Marshall’s Partial Equilibrium Theory? (6 marks)

3a. Compare and Contrast Adam Smith’s economic ideas with that of David Ricardo (15 marks) 3b. How does the central ideology of Adam Smith resonate in modern economic reality? (5 marks)

Section C: Answer ONE Question from this Section

4a. Discuss the role of “Time” in the theory of value as explained by Marshall (10 marks)

4b. Itemize some of the characteristics of Alfred Marshall’s “Representative Firm”. (10 marks)

5a. Differentiate between the ideas of Keynes and the Classicals (10 marks)

5b. Discuss some of the criticisms of the Keynes’ theory (10 marks)

COVENANT UNIVERSITY CANAAN LAND, KM. 10, IDIROKO ROAD P.M.B. 1023, OTA, OGUN STATE, NIGERIA TITLE OF EXAMINATION: B.Sc. Degree Examination COLLEGE: Development Studies DEPARTMENT: Economics  Development Studies SESSION: 2014/2015 SEMESTER: Alpha COURSE CODE: ECN 314 COURSE TITLE: History of Economic Thought I TIME ALLOWED: 2 hours DATE: November, 2014 INSTRUCTION: Answer three questions in all. Question 1 is compulsory

MARKING GUIDE

This section requires short answers to questions asked.

Section A (Compulsory)

1. Marginalism/Marginal Analysis 2. Classical 3. Partial equilibrium; general equilibrium 4. Mercantilist 5. Milton Friedman 6. David Ricardo 7. W.S Jevons 8. Alfred Marshall 9. John Maynard Keynes 10. 1976 11. False 12. True 13. False 14. True 15. True (2 marks each for 15 questions. Total is 30 marks)

SECTION B

2a. Describe the essential elements of Leon Walras’ General Equilibrium Theory

Solution

First define the concept General EquilibriumTheory (2 Marks):

• General equilibrium theory is an analysis of the economy in which all sectors are considered simultaneously

Then, State the major assumptions of the General Equilibrium Theory (12 marks),

2 marks each for at least 6 points.

General equilibrium assumes:

• a household sector with given tastes or preferences of individuals who demands goods

• a firm sector with technology available for producing goods that supplies goods • A perfectly competitive market where demanders and suppliers of goods and services are free to engage in processes of bargaining in the markets, which will equalise supply and demand of these goods and services • A set of equilibrium price where consumers maximize utility, firms maximize their profit and the market clears- solution to his model • Etc

2 (b) How does this theory compare with Alfred Marshall’s Partial Equilibrium Theory

 More factors are assumed to be held constant in partial equilibrium analysis than in general equilibrium analysis

• partial equilibrium models, following the tradition of Alfred Marshall, limit themselves to the analysis of a particular household, firm, or industry

• General equilibrium models are more complex than the manageable partial equilibrium models

• Partial equilibrium consider equilibrium in quantity while general equilibrium considers equilibrium in prices

(6 marks @ 2marks for at least three points)

*Full marks awarded to students who demonstrate better knowledge than what they were taught in class and also students who do not just list and explain concisely their points

3a. Compare and contrast Adam Smith’s economic ideas with that of David Ricardo (15 marks)

Solution

This question requires that students point the similarities and differences in the thoughts of Adam Smith and David Ricardo. 2 marks are awarded for vivid explanation of at least 7 points

Similarities

• Both are classicals and believed in free trade

Differences

Smith’s main preoccupation was on engine of growth and for Ricardo, his main focus was on distribution of wealth among landowners, workers and capitalists

On trade, Smith talked about absolute advantage, while Ricardo focused on comparative advantage

On labor theory of value, Smith believed that labor is the true measure of the value of a commodity, for Ricardo labor (direct and indirect) is the real measure of the value of a good

Ricardo thinking was deductive, he applied abstract thinking and modeling

3b.How does the central ideology of Adam Smith resonate in modern economic reality (5 marks)

Solution

The central ideology of Adam Smith hinges on freedom, laissez faire, natural order. In our contemporary economic thinking and order, this central ideology takes root in economic policies such as deregulation, privatization, free trade and globalization, private property etc

Ability to outline Smith central ideology (ies) attract 1 mark

Explaining Smith’s idea as relevant to contemporary times attracts 4 marks

*Full marks awarded to students who demonstrate better knowledge than what they were taught in class and also students who do not just list but concisely explained their points

4a. Discuss the role of “Time” in the theory of value as explained by Marshall.

Theory of Value and Time Element

On the theory on value, Marshall was of the opinion that both supply (cost of production) as concluded by the classicals, and demand (based on marginal utility) as propounded by the marginalist school determined value. According to Marshall, the forces behind both supply and demand determine value and this theory of value combines marginal utility with subjective real cost. The Marshallian theory of value owing to its emphasis on both supply and demand as forces governing value, is known as the Dual theory of value. It is important to note that the theory emphasizes the role of margin. Value is determined by the forces of demand and supply at the margin. On the basis of time element, Marshall classified value into four kinds; market value, short period value, long period value and secular value. The market price of a commodity is the price ruling at a particular period and in this case, supply is fixed while price depends mainly on demand. In the short period case, it is defined as that period during which the variable inputs can be increased or decreased but the fixed plant cannot be changed. Thus, under this scenario, both demand and supply determine the price. In the case of the long period, supply means what can be produced by plant which itself can be remuneratively produced and supplied within the given time”. In the long run, the cost of production is the most important determinant of price. Marshall’s introduction of time element in economic analysis was one of his many significant contributions to economic thinking. In classifying market broadly into short and long period, his objective was to “trace a continuous thread running through and connecting the applications of the general theory of equilibrium of demand and supply of different periods of time”. (10 marks)

4b. Itemize some of the characteristics of Alfred Marshall’s “Representative Firm”.

Representative Firm

Alfred Marshall defined a representative firm as one “which has had a fairly long life and fair success, which is managed with normal ability and which has normal access to the economies, external and internal, which belong to that aggregate volume of production, the conditions of marketing them and the economic environment generally”. His representative firm is in a sense, an average firm. It is neither old nor new, neither very efficient nor inefficient, neither earning super normal profits nor incurring losses, neither developing fast nor decaying. This type of firm cannot be chosen easily. Marshall stated that “the firms rise and fall but the representative firm remains always of the same size as does the representative tree of virgin forest”. He asserted that the representative firm will have the following characteristics:

i. Representative firm will be an average firm. It has a fair amount of internal and external economies.

ii. It is neither declining nor increasing. iii. Its management is neither very efficient nor inefficient. iv. It is neither old nor new. v. It is neither earning super normal profits nor incurring losses. vi. There can be more than one such firm.

However, Marshall’s representative firm was severely criticized by the later economists as the whole concept was regarded as unrealistic. The following were the main criticisms against the concept:

i. If the law of increasing returns operates in a firm, then the firm will be enjoying profits. On the other hand, if the firm is subject to the operation of decreasing returns, it will be incurring losses. ii. Robbins stated that even the clearest statement provided by Marshall about his representative firm does not make it clear whether it is a representative plant or a technical production unit or a representative business unit. iii. Representative firm is also criticized as an illusory and unnecessary one. iv. Robertson pointed out that in practice, it is not so easy to locate a representative firm. A firm which may be representative now may not be in future. v. Also, following the assumption that the representative firm is neither increasing nor decaying, in practice however, it is near impossible to find a firm that will be happy in this position. vi. Kaldor regards the representative firm as a state of mind rather than a concrete analysis.

In conclusion, even with these criticisms, some economists attempted to identify a representative firm. For example, Chapman and Taussig tried locating a representative firm in 1914 in England, Prof. J. K. Mehta had also tried to prove that the concept is not entirely incorrect.

(Note: 2 marks for any 5 correct characteristic and criticism)

5a. Differentiate between the ideas of Keynes and the Classicals.

Keynes versus Classicals

Keynes differs from the classical school in almost all ideals and has severely criticized each and every concept.

1. The Classicals believed in laissez faire policy, but Keynes believed that free enterprise system leads to fluctuations in trade cycles, so government intervention is a must. 2. The Classicals assumed full employment and no deviation from full employment. Whereas Keynes stated that under employment equilibrium is in the reality and full employment is

a distant goal. The achievement of full employment is very difficult and its maintenance on a permanent basis is more difficult. 3. The Classicals said that there exists in the economy a state of perfect competition which allocates resources ideally and ensures maximization of output and welfare. But Keynes argued that perfect competition is a myth. Today’s market structure is characterized by imperfect market which restricts output. This leads to wastage of resources and exploitation of consumers. 4. The Classicals believed in invisible hand or flexible price mechanism which ensures maximization in all market and also in allocation of resources and distribution of resources and national income. Keynes said that private motives do not coincide with public welfare, there are no invisible hands or automatic price mechanism which ensures the welfare of one and all in the society. 5. According to the Classicals, there is automatic self-adjusting character of the economy. There is no such automatic system in Keynesian economics. If such a force is there, depressions and booms can be easily avoided and fluctuations averted. 6. The Classical contributions constitute the core of “micro economics”. The classicals assumed a fixed quantity of resources and concentrated on ideal allocation among firms, industries and individual units in the economy. They studied micro problems and believed that the principles that govern the micro problems are completely valid for macro problems also. Therefore no separate theory is required for macro problems. Keynesian contribution relates to macro problems and according to him, micro problems require one set of policies and for macro problems, another set of policy is required. The same policy tools or instruments cannot be applied for both, macro is not a mere addition of micro elements as the nature and magnitude of the latter differs from that of the former. 7. Wage-price flexibility is advocated by classicals for solving unemployment problem. According to Keynes, wage flexibility is not found in the modern economy, especially downward flexibility of wages. Modern trade unions never accept wage cut for solving disequilibrium. 8. The Classical school believed in the flexibility of interest rate in bringing about equilibrium between savings and investment. However, Keynes explained that neither savings nor investment is a function of interest rate. Savings depend on the capacity of people to save and this capacity is determined by income. Thus savings is a function of income and not interest rate. Also, it is the rate of return or profit that determines investment. 9. Money plays a passive role for classicals, as it performs only one function, medium of exchange. The store of value function of money was not given due attention. According to Keynes, money is demanded for three motives; transaction, precautionary and speculative. No asset is as liquid as cash. 10. The Classicals did not integrate the theory of value with the theory of prices or money. However, Keynes successfully integrated the theory of value with the theory of prices by inventing the concept of speculative demand for money. Also, the Classicals considered

only real variables like MPP, real profit, real wage and real sacrifice. Keynes considered monetary variables and at the same time connected them with real variables. (2 marks each for any five correct answers = 10 marks)

5b. Discuss some of the criticisms of the Keynes’ theory.

 Borrowing causes Higher Interest Rates and crowding out. Keynesian economics advocated increasing a budget deficit in a recession. However, it is argued this causes crowding out. To borrow more, the interest rate on bonds rises. Also it means that the private sector have less to invest on private projects.  Inflation. A problem of fiscal expansion is that it often comes too late when economy is recovering anyway and therefore, it causes inflation.  Difficulty of predicting Output gap. An assumption of keynesian economics is that it is possible to know how much demand needs to be increased to deal with output gap.  Encourages big government. In a recession governments increase spending, but, after recession government spending remains leading to high tax and spend regimes.  Time Lags. It takes a long time to change aggregate demand by the time AD increases it may be too late and it leads to inflation.  Short run focus. The Keynesian policy advocates focus primarily on the short run framework with no regard for the future implications of current events. They assume that all economic decision makers do the same.  Not evidence-based. Some empirical studies have argued that Keynesianism is not an evidence-based model of how the economy works. This disregard for evidence is reflected in their advocacy for more stimulus spending in the face of the obvious failure of what has already been spent.

(2 marks each for any five correct answers = 10 marks)

COVENANT UNIVERSITY CANAANLAND, KM. 10, IDIROKO ROAD PMB 1023, OTA, OGUN STATE, NIGERIA

TITLE OF EXAMINATION: B.Sc Degree Examination COLLEGE: Business & Social Sciences DEPARTMENT: Economics & Development Studies SESSION: 2014/2015 SEMESTER: Alpha Semester COURSE CODE: ECN 316 COURSE TITLE: International Economics (I) TIME ALLOWED: 2HRS DATE: November, 2014 INSTRUCTION: Answer question one and two other questions. Use diagrams for illustrations

Question One a) What are the differences and similarities between the Ricardian trade theory and the factor endowment theories of international trade? (5marks) b) Use the framework of increasing opportunity cost to show the effect of specialisation and trade in an economy (5marks) c) With the aid of a diagram, distinguish between gains from exchange and gains from specialisation. (5marks) d) Distinguish between factor endowment in terms of factor prices and factor endowment in terms of physical volume. (5marks)

e) Consider two hypothetical economies A and B, with production function given as: 푄퐴 = 푓(퐾, 퐿), and 푄퐵 = 푓(퐾, 퐿) respectively. Assume also that the various factor prices 푟 and 푤 are given as 50 and 25 respectively for country A, and 15 and 20 respectively for country B. i) Determine the factor abundance for countries A and B (5marks) ii) Assume also that there are two commodities X and Y that can be produced by A and B, if the following holds for both commodities : (퐾) < (퐾) . If country A exports commodity X and 퐿 푌 퐿 푋 country B exports commodity Y, does the H-O proposition hold? Give reasons for your conclusion. (5marks) Total [30 marks] Question Two a) Distinguish between the Absolute and comparative advantage theories of trade (10 marks) b) Write short note on the following analytical tools of international trade and explain their usefulness i) Community indifference curves (5 marks) ii) Trade offer curve (TOC) (5 marks) Total [20 marks]

Question Three a) Discuss the Leontief Paradox and provide the possible explanations for the paradox (10 marks) b) Write short notes on the following i) Immiserising growth (4 marks) ii) Hecksher-Ohlin Trade Theory (6 marks) Total [20 marks]

Question Four With the aid of a diagram, show the effects of growth on the trade using the following:

i) The size of the foreign trade sector relative to the National output (10 marks) ii) The consumption possibilities frontier (10 marks) Total [20 marks]

Question Five a) Discuss the various forms of preferential trading arrangements. (10 marks) b) Distinguish between trade creation and trade diversion as it relates to the theory of customs union. (10 marks) Total [20 marks]

ECN 316

Marking Guide

Question One (a)

What are the differences and similarities between the Ricardian trade theory and the factor endowment theories of international trade?

Note:

Here, students are to distinguish the two theories by the assumptions and also itemise the similarities in the assumptions of both theories

Question One (b)

Use the framework of increasing opportunity cost to show the effect of specialisation and trade in an economy

Question One (c)

With the aid of a diagram, distinguish between gains from exchange and gains from specialisation.

Question One (d)

Distinguish between factor endowment in terms of factor prices and factor endowment in terms of physical volume

Factor endowment in terms of factor prices looks at the ratio of factor prices in both countries to determine the abundance of factors in both countries.

For example, if there are two countries – A and B, a country say country A can be said to be capital abundant in terms of factor prices if the following condition holds:

푟 푟 푤 푤 ( ) < ( ) 표푟 ( ) > ( ) 푤 퐴 푤 퐵 푟 퐴 푟 퐵

On the other hand, in terms of physical volumes, factor abundance can be determined by the ratio of the physical quantities of both factors in the country. In terms of physical volume, country A could be said to be capital abundant if:

퐾 퐾 퐿 퐿 ( ) > ( ) or ( ) < ( ) 퐿 퐴 퐿 퐵 퐾 퐴 퐾 퐵

Question One (e(i))

For countries A and B, 푄 = 푓(퐾, 퐿).

푇ℎ푒 푝푟𝑖푐푒푠 표푓 푙푎푏표푢푟 (푤)푎푛푑 푐푎푝𝑖푡푎푙 (푟) 𝑖푛 퐶표푢푛푡푟𝑖푒푠 퐴 푎푛푑 퐵 푎푟푒 푔𝑖푣푒푛 푎푠 푓표푙푙표푤푠:

퐹푂푅 퐶푂푈푁푇푅푌 (퐴): 푟퐴 = 50; 푎푛푑 푤퐴 = 25

퐹푂푅 퐶푂푈푁푇푅푌 (퐵): 푟퐵 = 15; 푎푛푑 푤퐵 = 20

The ratio of factor prices in both countries would be given as:

푟 50 푤 25 ( ) = ( ) = 2 ; and ( ) = ( ) = 0.5 푤 퐴 25 푟 퐴 50

푟 15 푤 20 ( ) = ( )= 0.75; and ( ) = ( ) = 1.33 푤 퐵 20 푟 퐵 15

푟 푟 푤 푤 From the above, since ( ) > ( ) 푎푛푑 ( ) < ( ) ; we conclude therefore that country A is 푤 퐴 푤 퐵 푟 퐴 푟 퐵 labour abundant

푟 푟 푤 푤 Similarly, since ( ) < ( ) 푎푛푑 ( ) > ( ) ; we conclude therefore that country B is capital 푤 퐵 푤 퐴 푟 퐵 푟 퐴 abundant

Question One (e(ii))

(퐾) < (퐾) implies that commodity Y is labour intensive and X is capital intensive. If country A exports 퐿 푌 퐿 푋 commodity X, then H-O proposition does not hold. This is because, from H-O proposition, country A is labour abundant and should therefore export the labour intensive good Y and not X.

Question Two (a)

Absolute advantage theory was propounded by Adam Smith and it places more emphasis on absolute cost advantage. Comparative advantage on the other hand, was based on the works of Eli Hecksher and Bertil Ohlin. It emphasizes the importance of opportunity costs, stating that countries should specialise in producing and exporting that commodity in which she has the least comparative (opportunity cost).

Question Two (b)

Community Indifference Curves A CIC is a geometric locus of all alternative combinations of, say, commodities X and Y which enable the consumers of a nation to attain a given level of social satisfaction or utility. Each CIC

29 corresponds to a certain level of satisfaction and the collection of all the CICs forms the community indifference map.

Trade offer curves Trade offer curve is another tool of analysis in international economics formalized by Alfred Marshall but originated by John Stuart Mill. A trade offer curve (TOC) shows the quantity of imports that a country desires to purchase at various TOT and the quantity of exports it will have to provide in order to obtain those imports at those prices. Hence, TOT reflects both demand and supply conditions within the country in question.

In offer curve analysis, TOT between two traded goods is represented as the slope of a ray from the origin. See the figure below.

(Imports) Y

1 TOT4 (2X = 1Y)

TOCA L TOT3 (3X = 1Y) 1 K TOT2 (4X = 1Y) 8

5 TOT1 (5X = 1Y)

I X 10 20 30 40 (Exports) 30

Question Three (a)

The empirical test of the Hecksher-Ohlin Trade theory produced a reverse of the original H-O proposition. Discuss and provide alternative explanations for the results. Leontief used the 1947 I-O table of the U.S. economy. He aggregated industries into 50 sectors 30 of which traded their products directly on the national market. The factors of production were grouped into two categories labour, L and capital, K. The result is as shown below:

Exports Imports

K (in 1947 current $) 2,550,780 3,091,339 L (in man-years) 182,313 170,004 13,911 K/L ($ per man-year) 18,185

Leontief’s findings, as given in the above table, reveals that import-competing products are relatively more K-intensive than the export products. This is just the reverse of the H-O trade theory prediction. Hence it is called the Leontief paradox. There are however, possible explanations as to why the paradox exists. Some of these explanations are enumerated below:

i) Consumption Pattern ii) Effectiveness of U.S. Labour iii) Natural Resources iv) Labour Skills v) Research and Development vi) Factor Intensity Reversal vii) U.S. Trade Policy

Question Three (b)

Immiserizing growth

This is the case in which a country ends up having a lower real income after growth because the loss due to deteriorating TOT has outweighed the gain due to increased production.

If the TOT deteriorates as a consequence of growth, it is natural to ask whether the deterioration can outweigh the direct benefit of growth. If this is possible, it is a case of immiserizing growth. This is the case with the LDCs.

Hecksher-Ohlin Trade Model

The Hecksher ohlin trade model attempts to determine how domestic factor endowment could be an explanation for the pattern of comparative advantage. Hecksher Ohlin model concludes that a country (say country A) would have comparative advantage in the production and export of that commodity that is intensive in its relatively abundant factor. It implies that suppose country A is abundant in capital, then country A would have comparative advantage in production and export of commodities that are capital intensive. 5marks

Assumptions

The Hecksher-Ohlin model is based on the following assumptions:

i) It is 2 * 2 * 2 model meaning that there are two countries, two commodities and two factors of production. ii) L and K are in-elastically supplied iii) L and K are fully mobile iv) Pure competition reigns in both product and factor markets v) Non-reversibility and different factor intensity vi) Identical production functions vii) Linear homogenous production function in both countries viii) Absence of externalities, factor indifference between uses and identical factor qualities between countries ix) Countries A and B are alike in all respects, except in the endowment of factors L and K

Question Four (a)

We can classify the growth pattern of a country by using the relative size of foreign trade sector as a yardstick:

These are:

1. Neutral economic growth 2. Pro-trade biased economic growth 3. ultra-trade biased economic growth 4. anti-trade biased economic growth

5. ultra-anti-trade biased economic growth The size of a country’s foreign trade is measured by the size of imports to the national income.

1. Neutral Econ. Growth

The size of the foreign trade in relation to total national output remains the same.

2. Pro-Trade

There is increase in the size of foreign trade in relation to total national output.

3. Ultra Pro-Trade

There is an increase in, not only relative but also, absolute size of foreign trade sector more than the increase in total national income. “The whole income is spent on import”.

4. Anti-Trade Bias

There is decrease in the size of foreign trade relative to the national income.

5. Ultra anti-trade Bias

There is an absolute decrease in the foreign trade sector concomitant to economic growth. This will happen if the imported good is an inferior commodity. b) The graph/figure below illustrates the types of growth in terms of the familiar diagram of consumption- possibilities frontier CPF,

Types of growth and the classification of the consumption effect

Before growth, the economy products at PA and consumes at C. After growth, the economy products at P2 and the consumption point can lie anywhere on the new consumption possibilities frontier Z2 P2.

If C moves along vector ON then growth is Neutral

If C moves along the region HJ then: growth as pro-trade biased

If C moves along the region Z2 H then: growth as Ultra protrades

If C moves along the region JW then: growth as Anti- trade

If C moves along the region WP2 then: growth as Ultra–anti-pro-trade

(importables) Y

P N

c Y o c

Question Five (a)

Form of PTAs (i) Preferential Trading Club: Two or more countries form a preferential trading club when they reduce their respective import duties on imports of all goods (except the service of capital) from each other. The member countries retain their original tariffs against the outside world. A good example of a preferential trading club is the commonwealth preference system. (ii) Free-trade area (or association): Two or more countries form a FTA, when they abolish all import duties (and all quantitative restrictions) on their mutual trade in all goods (except the services of capital) but retain their original tariffs against the rest of the world. An example of a FTA is the former European Free Trade Area (EFTA) which consists of the “Outer Seven:” Austria, Denmark, Norway, Portugal, Sweden Switzerland, and the United Kingdom. (iii) Customs Union: Two or more countries form a customs union when they abolish all import duties on their mutual trade in all goods (except the service of capital), and in addition they adopt a common external tariff schedule on the imports of goods (except the services of capital) from the rest of theworld. (iv) Common Market: Two or more countries form a common market if they form a custom union and , in addition, allow free movement of all factors of production between the member countries. An example of a common market is the former European Economic Community (EEC) which is composed of Belgium, Denmark, France, Germany, Ireland, Ireland, Luxembourg, Netherlands and the UK. (v) Economic Union (EU): Two or more countries form an economic union when they form a common market and, in addition, proceed to unify their fiscal, monetary, and socioeconomic policies. A good example of an economic union is the European Union (EU). Another example is the Benelux which was the economic union formed by Belgium, the Netherlands, and Luxembourg (the term Benelux and made up of the first letters in each country’s name).

Question Five (b)

Trade Creation and Trade Diversion

Trade Creation

Trade creation refers to the case where the shift in production is from a higher-cost source to a lower-cost source abstracting from duty elements in money costs. Such a shift tends to create trade and it is a step toward the free-trade position. Here the shift in production to a lower-cost producer in a partner country constitutes trade creation.This is a shift which the free trade proponents properly approves.

Trade Diversion

On the contrary, trade diversion refers to the case where the shift in production is from a lower- cost source to a higher-cost source, again, abstracting from duty elements in money costs. In this case the shift diverts trade from the free-trade position. Here, the shift in production is from a lower-cost producer in the rest of the world to a higher producer in a partner country. This constitutes trade diversion. This is the shift which the protectionist approves.

Generaly speaking, trade creation is good and tends to increase welfare, while trade diversion is bad and tends to decrease welfare. The fundamental notion behind these statements is that ordinary trade increases welfare by reducing costs or, alternatively, by increasing world income. It is in this sense that trade creation is concerned to be beneficial, and trade diversion detrimental to welfare.

COVENANT UNIVERSITY DEPARTMENT OF ECONOMICS AND DEVELOPMENT STUDIES B.Sc. DEGREE EXAMINATIONS (ALPHA) DEPARTMENT: ECONOMICS AND DEVELOPMENT STUDIES COURSE CODE: ECN 317 COURSE TITLE: PROJECT EVALUATION SESSION: 2014/2015 TIME ALLOWED: 2 HOURS INSTRUCTIONS: ANSWER ALL QUESTION IN SECTION A AND ANY OTHER TWO (2) QUESTIONS FROM SECTION B

SECTION A No. 1. (3 marks each). a. We essentially use the same method when evaluating risks and uncertainties in Project Analysis. b. The approach to a financial or commercial analysis is the same for Economic Efficiency Analysis. c. The concept “Capital” and “Investment” are basic to the process of project evaluation and they mean the same thing to all professionals. d. Existence of basic infrastructural facilities is the most critical of all factors determining the location of a project. e. There are essentially two broad groups of benefits of a project, which can be viewed from different perspectives. f. The Pay Back Method is superior to the Average Profit Method as undiscounted measure of project worth. g. The Project Cycle is a necessary, but not sufficient condition for the success of a project. h. In estimating the cost of a project, we consider mainly the pre-production and production expenditure. i. Econometric Analysis is the only method used in estimating both the benefit and cost of a project. j. Compounding and discounting factors are used interchangeably in Project Evaluation. Total: 30 Marks

SECTION B 2. Explain briefly a. Why: i. Plans have failed in most developing countries. (5 marks) ii. There is a need for Post-Implementation Evaluation. (5 marks) b. Discuss with relevant examples; i. Traditional and modern method of Evaluating a Project. (5 marks) ii. The Problem encountered in using these methods. (5 marks)

Total: 20 marks 3. Answer all questions: a. Explain briefly the use of the following concepts in Project Evaluation. i. Incremental Rate of Returns (IRR). ii. Net Present Value Index (NPP Index) iii. Risks and Uncertainties.

b. An entrepreneur is to make a choice between two investment Projects A nand B, with the following financial information:

Project A has an initial investment cost of #3,784,800 and an annual benefit of #714,945; #1,382,585; #2,050,509; #1,998,124 and #1,964,656 in each of its five years of operation.

Project B has an initial investment cost of #6,000,000 and an annual net benefit of #2,004,200; #2,793,600; #3,507 000; #2,675,600 and #2,584,190 in each of its five year operating period.

Using the Net Present Value (NPV) and Internal Rate of Returns (IRR) methods, which of these two projects would you choose if the cost of capital is 20%? And Why? (11 marks) Will your decision change if government pegs discount rate to 15% (3 marks) Total: 20 marks 4. Compare and contrast the use of Net Present Value (NPV) and Internal Rate of Returns (IRR) in Project Analysis; especially in ranking of projects, choice between mutually exclusive projects and choice of discount rate. (9 marks) b. A company is to make a choice between a large (A) plant and small plant (B);

Plant A, has an initial investment cost of #4,000,000 and annual net benefit of #500,000; #800,00; #1,200,000; #1,500,000 and #1,800,000 in the first , second, third, fourth and fifth years of production respectively.

Plant B has an initial investment cost of #1,600,000, with an annual benefit of #270,000; #380,000; #500,000; #720,000 and #900,000 in the first, second, third, fourth and fifth years of production respectively.

Which of there two plants will you choose if the cost of capital is 15%? And why?

Will your decision change if the cost of Plant B increases by 20%? (11 marks) Total: 20 marks

5. Distinguish between Economic and Financial analysis showing the conceptual area of differences and similarities. (8 marks)

b. Consider two projects X and Y with the following cash flow Year Net Cash Flow (X) Net Cash Flow (Y)

(#) (#)

1 -3,000,000 -10,000,000

2 -2,000,000 2,750,000

3 1,100,000 2,750,000

4 900,000 2,750,000

5 900,000 2,750,000

6-20 1,320,000 2,750,000

Which of these two projects would you choose if the discounted rate is 15%?

Will your decision change if the Net Cash Flow for X and Y increases by 20% and 50% respectively? (11 marks) Total: 20 marks

ANSWERS TO ALL QUESTIONS

SECTION A No. 1. (3 marks each). k. We essentially use the same method when evaluating risks and uncertainties in Project Analysis. TRUE and FALSE: Apart from the Traditional Method, other method are available e.g. Decision Theory Approach, Certainty Equivalence, Decision Theory Approach l. The approach to a financial or commercial analysis is the same for Economic Efficiency Analysis. FALSE: Financial Analysis is aimed at Profitability; While Economic Efficiency Analysis combines Profitability with unaccounted externalities of negative and positive effects of the Project after completion. m. The concept “Capital” and “Investment” are basic to the process of project evaluation and they mean the same thing to all professionals. FASLE: Capital to the accountant is the structure of equity, loan and working funds. To the economist, capital is a physical asset. Investment to the accountant is a form of physical asset or intangible asset like stock, shares and bonds. To the economist, this is the acquisition of physical landed property or asset. n. Existence of basic infrastructural facilities is the most critical of all factors determining the location of a project. FALSE: Location of a project is determined amongst other by availability of raw materials, proximity to market, public policies and infrastructural facilities. o. There are essentially two broad groups of benefits of a project, which can be viewed from different perspectives. TRUE: Benefits are either quantitative or non-quantitative/qualitative. p. The Pay Back Method is superior to the Average Profit Method as undiscounted measure of project worth. FASLE: Pay Back Method signifies the duration of time of return on investment while Average Profit Method determines the average amount of returns over the entire years of the project. q. The Project Cycle is a necessary, but not sufficient condition for the success of a project. TRUE: The Project Cycle is the ideal stage every project is expected to go through before full operation. It however does not entirely guarantee the success of any project.

40 r. In estimating the cost of a project, we consider mainly the pre-production and production expenditure. TRUE: The pre-production and production expenditure makes up the combined cost of the any project s. Econometric Analysis is the only method used in estimating both the benefit and cost of a project. FALSE: Other methods exists; e.g. Estimation Demands, Projection of Demands and Cost of a Projects e.t.c. t. Compounding and discounting factors are used interchangeably in Project Evaluation. FASLE: Compounding and discounting factors reveals the value of the local currency presently and at a particular date i in the future. Total: 30 Marks

SECTION B 6. Explain briefly c. Why: iii. Plans have failed in most developing countries. (5 marks)  Multiplicity of objectives in the plan  Inadequate information and data during plan formation  Wrongful project identification  Neglect of one or more of the stages in the project cycle  Poor management iv. There is a need for Post-Implementation Evaluation. (5 marks)  Possibility of engineering failure  Possibility of economic failure  Possibility of market failure  Possibility of management failure  Possibility of external failure d. Discuss with relevant examples; iii. Traditional and modern method of Evaluating a Project. (5 marks) Traditional Methods are essentially undiscounted measures of project worth which includes:  Ranking by inspection  Payback Method  Peak Profit Method  Average Profit Method Modern Methods are essentially discounted measures of project worth which includes:  Net Present Value Method  Internal Rate of Returns Methods  Benefit Cost Ratio Method

iv. The Problem encountered in using these methods. (5 marks)

Total: 20 marks 7. Answer all questions: a. Explain briefly the use of the following concepts in Project Evaluation. i. Incremental Rate of Returns (IRR): used instead of Internal Rate of Return when dealing with mutually exclusive projects ii. Net Present Value Index (NPV Index): used when there are difficulties in ranking alternatives projects which have different patterns of investments. The project with the higher NPV Index value is chosen. iii. Risks and Uncertainties: Theses are assumed to have possibilities of occurrence and cannot be predicted including change in taste, government policies. There are several methods and approaches of dealing with such risks.

b. An entrepreneur is to make a choice between two investment Projects A nand B, with the following financial information:

Project A has an initial investment cost of #3,784,800 and an annual benefit of #714,945; #1,382,585; #2,050,509; #1,998,124 and #1,964,656 in each of its five years of operation.

Project B has an initial investment cost of #6,000,000 and an annual net benefit of #2,004,200; #2,793,600; #3,507 000; #2,675,600 and #2,584,190 in each of its five year operating period.

1 2 3 4

Discounted Net Discounted Net Net Benefit Net Benefit Discounted Year Benefit Benefit (Project (Project A) (Project B) Factor 20% (Project A) B)

0 (3,784,800) (6,000,000) 1.000 -3,784,800.000 -6,000,000

1 714,945 2,004,200 0.833 595,549.185 1,669,498

2 1,382,585 2,793,600 0.694 959,513.990 1,938,750

3 2,050,509 3,507 000 0.579 1,187,244.711 2,030,550

4 1,998,124 2,675,600 0.482 963,095.768 1,289,639

5 1,964,656 2,584,190 0.402 789,791.712 1,038,844

Total +710,395.366 1,967,293

1 2 3 4

Discounted Net Discounted Net Net Benefit Net Benefit Discounted Year Benefit (Project Benefit (Project A) (Project B) Factor 25% A) (Project B)

0 (3,784,800) (6,000,000) 1.000 (3,784,800.000) -6,000,000

1 714,945 2,004,200 0.800 571,956.000 1,603,360

2 1,382,585 2,793,600 0.640 884,854.000 1,787,900

3 2,050,509 3,507 000 0.512 1,049,860.608 1,795,584

4 1,998,124 2,675,600 0.410 819,230.840 1,096,996

5 1,964,656 2,584,190 0.328 644,407.168 847,614

Total 185,509.016 1,131,458

1 2 3 4

Discounted Net Discounted Net Net Benefit Net Benefit Discounted Year Benefit (Project Benefit (Project A) (Project B) Factor 20% A) (Project B)

0 (3,784,800) (6,000,000) 1.000 (-3,784,800.000) -6,000,000

1 714,945 2,004,200 0.769 549,792.705 1,541,229

2 1,382,585 2,793,600 0.592 818,490.320 1,653,811

3 2,050,509 3,507 000 0.455 932,981.595 1,595,600

4 1,998,124 2,675,600 0.350 699,343.400 936,460

5 1,964,656 2,584,190 0.269 528,492.464 695,147

Total (255,699.516) +422,300

IRR for Project A= 25 +5 ퟏퟖퟓ, ퟓퟎퟗ ( ) ퟏퟖퟓ, ퟓퟎퟗ − (−ퟐퟓퟓ, ퟔퟗퟗ) ퟏퟖퟓ,ퟓퟎퟗ =25 +5( ) ퟒퟒퟏ,ퟐퟎퟖ =25+5(ퟎ. ퟒퟐ) =25+2.10 =27.10%

Recall that the IRR for Project B =30%

DECISION: Accept both Projects. Project A at 27.10% and Project B at over 30% because the IRR value are both above the cost of capital at 20%.

However Project be has better IRR.

8. Compare and contrast the use of Net Present Value (NPV) and Internal Rate of Returns (IRR) in Project Analysis; especially in ranking of projects, choice between mutually exclusive projects and choice of discount rate. (9 marks) c. A company is to make a choice between a large (A) plant and small plant (B);

Plant A, has an initial investment cost of #4,000,000 and annual net benefit of #500,000; #800,000; #1,200,000; #1,500,000 and #1,800,000 in the first , second, third, fourth and fifth years of production respectively.

Which of there two plants will you choose if the cost of capital is 15%? And why?

Will your decision change if the cost of Plant B increases by 20%? (11 marks) Total: 20 marks

1 2 3 4

Discounted Net Discounted Net Net Benefit Net Benefit Discounted Year Benefit Benefit (Project (Project A) (Project B) Factor 15% (Project A) B)

0 (4,000,000) (1,600,000) 1.000 (4,000,000) (1,600,000)

1 500,000 270,000 0.870 435,000 234,900

2 800,000 380,000 0.756 604,800 287,280

3 1,200,000 500,000 0.658 789,600 329,000

4 1,500,000 720,000 0.572 858,000 411,840

5 1,800,000 900,000 0.497 894,600 447,300

Total -418,000 110,320

1 2 3 4

Discounted Net Net Benefit Net Benefit Discounted Year Benefit (Project (Project A) (Project B) Factor 20% B)

0 (4,000,000) (1,600,000) 1.000 (1,600,000)

1 500,000 270,000 0.833 224,910

2 800,000 380,000 0.694 263,720

3 1,200,000 500,000 0.579 289,500

4 1,500,000 720,000 0.482 347,040

5 1,800,000 900,000 0.402 361,800

Total 113,030

ퟏퟏퟎ,ퟑퟐퟎ IRR for Project B= 15 +5( ) ퟏퟏퟎ,ퟑퟐퟎ−(−ퟏퟏퟑ,ퟎퟑퟎ)

ퟏퟏퟎ,ퟑퟐퟎ =15 +5( ) ퟐퟐퟑ,ퟑퟓퟎ =15+2.4696 =17.4696%

1 2 4

Discounted Net Net Benefit Discounted Year Benefit (Project (Project A) Factor 10% A)

0 (4,000,000) 1.000 (4,000,000)

1 500,000 0.909 454,500

2 800,000 0.826 606,800

3 1,200,000 0.751 901,200

4 1,500,000 0.683 1,024,500

5 1,800,000 0.621 1,117,800

Total 158,800

ퟏퟓퟖ,ퟖퟎퟎ IRR for Project A= 10 +5( ) ퟏퟓퟖ,ퟖퟎퟎ−(−ퟒퟏퟖ,ퟎퟎퟎ) ퟏퟓퟖ,ퟖퟎퟎ =10 +5( ) ퟓퟕퟔ,ퟖퟎퟎ =10+5(ퟎ. ퟐퟕ) =10+1.37 =11.37%

Recall that the IRR for Project B =17.4696%

DECISION: Accept Project B with IRR of 17.4696% which is greater than the cost of capital. Reject Project A with an IRR value of 11.37%which is lower than the cost of capital of 15%.

However Project be has better IRR.

9. Distinguish between Economic and Financial analysis showing the conceptual area of differences and similarities. (8 marks) ECONOMIC ANALYSIS: Certain prices may be adjusted to reflect better the social and economic values by the consideration of the intangible benefits or cost or externalities.  Interest rate value is not deducted from capital as it is assumed to be part of the total return to the society.  Taxes and subsidies are treated as transfer payments.

FINANCIAL ANALYSIS: Market prices are used, which also includes taxes and subsidies.  Taxes are treated as costs and subsidies as benefits to the project

c. Consider two projects X and Y with the following cash flow Year Net Cash Flow (X) Net Cash Flow (Y)

(#) (#)

1 -3,000,000 -10,000,000

2 -2,000,000 2,750,000

3 1,100,000 2,750,000

4 900,000 2,750,000

5 900,000 2,750,000

6-20 1,320,000 2,750,000

Which of these two projects would you choose if the discounted rate is 15%?

Will your decision change if the Net Cash Flow for X and Y increases by 20% and 50% respectively? (11 marks) Total: 20 marks

1 2 3 4

Net Cash Net Cash Discounted Net Discounted Net Discounted Year Flow Flow Cash Flow Cash Flow Factor 15% (Project X) (Project Y) (Project X) (Project Y)

1 -3,000,000 -10,000,000 0.870 -2,160,000 -10,000,000

2 -2,000,000 2,750,000 0.756 1,512,000

3 1,100,000 2,750,000 0.658 723,800

4 900,000 2,750,000 0.572 514,800

5 900,000 2,750,000 0.497 447,300

6-20 1,320,000 2,750,000 0.432 3,837,240 20,208,750

Total 1,401,140 10,208,750

At 15%

Annuity factor Year 5 = 3.352 Annuity factor Year 20 =6.259 Annuity factor (Year 20 minus Year 5) = 6.259 - 3.352 = 2.907× 1,320,000 = 383,724

Annuity factor Year 1 = 0.870 Annuity factor Year 20 = 6.259 Annuity factor (Year 20 minus Year 5) = 6.259 - 0.870 = 5.389 × 2,750,000 = 20,208,750

COVENANT UNIVERSITY

CANAANLAND, KM 10, IDIROKO ROAD P.M.B 1023, OTA, OGUN STATE, NIGERIA.

TITLE OF EXAMINATION: B.Sc. EXAMINATION

COLLEGE: BUSINESS AND SOCIAL SCIENCES

SCHOOL: SOCIAL SCIENCES

DEPARTMENT: ECONOMICS AND DEVELOPMENT STUDIES SESSION: 2014/2015 SEMESTER: ALPHA

COURSE CODE: ECN318 CREDIT UNIT: 2

COURSE TITLE: INTRODUCTORY ECONOMETRICS I

INSTRUCTION: Answer question one and any other two questions TIME: 2 HOURS

1. Suppose the regression results below show the role of human capital development in the Nigerian economy. Dependent Variable: LRGDP

Method: Least Squares

Date: 11/29/11 Time: 21:08

Sample (adjusted): 1970 2005

Included observations: 36 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

LEDUC 0.365747 0.230304 1.588104 0.1224

LGFCF 0.125586 0.305920 0.410518 0.6842

LHEALTH 0.211797 0.249382 0.849284 0.4022

LSOCEXP 0.231855 0.173144 1.339090 0.1903

C 8.262758 0.796515 10.37364 0.0000

R-squared 0.740819 Mean dependent var 11.63761

Adjusted R-squared 0.707376 S.D. dependent var 1.490476

S.E. of regression 0.806269 Akaike info criterion 2.535447

Sum squared resid 20.15215 Schwarz criterion 2.755380

Log likelihood -40.63805 F-statistic 22.15185

Durbin-Watson stat 0.295253 Prob(F-statistic) 0.000000

Where LRGDP is log of real GDP, LEDUC is log of investment in education, LGFCF is log of gross fixed capital formation (capital), LHEALTH is log of government expenditure on health, SOCEXP is log of social expenditure, and C is the constant term. Now, take a few minutes to examine the main regression results and answer the following questions.

i. Interpret the results completely paying attention to the impact of each explanatory variable on the log of real gross domestic product (RGDP) and the relevant summary statistics. [10 marks] ii. Suppose the variables are not in logarithms. Using your knowledge of the effects of human capital development on the economy, examine and explain the implication of the signs and magnitude of the coefficients. [10 marks] iii. How reliable are these results? Justify your position(s). [5 marks] iv. Discuss possible remedies for any observed shortcoming(s) in the results. [5 marks]

TOTAL [30 MARKS]

2. Based on a sample of 10 observations, the following results were obtained:

Yi  1110

 X i  1700

 X iYi  205500 2  X i  322000 2 Yi  132100

With coefficient of correlation r = 0.9758. But on re-checking these calculations, it was found that two pairs of observations were recorded:

Y X Y X Instead of 90 120 80 110

140 220 150 210

i. Obtain the correct r (4 decimal places) and comment on the effect of this error on the true r [10 marks] ii. State any two properties of the coefficient of correlation r. [10 marks] TOTAL [20 MARKS]

3. i. Outline and briefly discuss three problems of regression analysis. [5 marks] ii. Using a hypothetical model, show the difference between a perfect and less than perfect multicollinearity. [5 marks] iii. Discuss five sources and consequences of multicollinearity as a problem in economic modeling. [5 marks] iv. Explain the remedial measures for addressing a case of multicollinearity in a model. . [5 marks] TOTAL [20 MARKS]

4. i. Discuss the BLUE properties of the ordinary least squares (OLS) estimators [8 marks] ii. Explain the four computational properties of OLS estimators? [6 marks] iii. Distinguish between the small sample properties and asymptotic properties of the OLS estimators [6 marks] TOTAL [20 MARKS] 5. i. With the aid of a diagram, explain what you understand about the following a. Total sum of squares [4 marks] b. Explained sum of squares [4 marks] c. Residual sum of squares [4 marks]

ii. What do you understand by the goodness of fit? [8 marks]

TOTAL [20 MARKS]

COVENANT UNIVERSITY

CANAANLAND, KM 10, IDIROKO ROAD P.M.B 1023, OTA, OGUN STATE, NIGERIA.

TITLE OF EXAMINATION: B.Sc. EXAMINATION

COLLEGE: BUSINESS AND SOCIAL SCIENCES

SCHOOL: SOCIAL SCIENCES

DEPARTMENT: ECONOMICS AND DEVELOPMENT STUDIES SESSION: 2014/2015 SEMESTER: ALPHA

COURSE CODE: ECN318 CREDIT UNIT: 2

COURSE TITLE: INTRODUCTORY ECONOMETRICS I

INSTRUCTION: Answer question one and any other two questions TIME: 2 HOURS

MARKING GUIDE

QUESTION 1 TOTAL [30 MARKS]

Presentation of Results

퐿푅퐺퐷푃 =∝̂1+∝̂2 퐿퐸퐷푈퐶 +∝̂3 퐿퐺퐹퐶퐹 +∝̂4 퐿퐻퐸퐴퐿푇퐻 +∝̂5 퐿푆푂퐶퐸푋푃 (1)

퐿푅퐺퐷푃 = 8.26 + 0.37퐿퐸퐷푈퐶 + 0.13퐿퐺퐹퐶퐹 + 0.21퐿퐻퐸퐴퐿푇퐻 + 0.23퐿푆푂퐶퐸푋푃 (2) (10.37) (1.59) (0.41) (0.85) (1.34) The t-stats are reported in parenthesis below each coefficient estimate

R2 = 0.74

푅̅2 = 0.71

DW-Stat. = 0.295

F-Stat. = 22.15

Prob(F-Stat) = 0.0000

Interpretation of Results

1. Impact of explanatory variable on the dependent variable

The above results represent a case of double-log function which requires that each estimated coefficient be interpreted as elasticity in the usual interpretation of elasticity which compels us to ignore the signs since elasticity coefficient lies between o and +∞. [2 marks]

The coefficient of LEDUC is 0.37 which is less than 1 and fairly inelastic. What this means is that the Nigerian economy is less sensitive to variations in investment in education. A possible explanation for this is the lag between investment in education and return on such investment.

[2 marks]

The coefficient of 푳푮푭푪푭 is 0,13 which also is less than 1 or fairly inelastic. It can therefore be remarked here that the Nigerian economy is less sensitive to changes in capital stock. This result is theoretically plausible and the explanation will be the issue of factor intensity of the Nigerian economy. The logic of this result makes sense for an economy that is labour intensive. [2 marks]

The coefficient of 푳푯푬푨푳푻푯 is 0.21 or fairly inelastic meaning that the Nigerian economy is less sensitive to changes in government expenditure on health. This is theoretically unexpected and a possible explanation here will be the issue of corruption or leakages in the system which creates a huge gap between what is reported as heath expenditure outlay and what actually gets to this sector.

[2 marks]

The coefficient of 푳푺푶푪푬푿푷 is 0.23 and as in previous cases, fairly inelastic. The Nigerian economy is less sensitive to changes in government expenditure on social amenities. This result also is theoretically unexpected but not surprising. Interestingly, the huge burden of corruption in the country will always leave a significant gap between the reported expenditure on social amenities and what was actually expended. [2 marks]

2. Interpretation of signs and magnitude of the coefficient estimates (i.e. without the logs)

It is first noted here that while the signs of the coefficient estimates simply refer to the theoretical or a priori expectation for each explanatory variable, the magnitude of each coefficient estimate refers to the relative importance of each explanatory variable as can be judged by its level of statistical significance.

Investments in education (EDUC) impact positively on the Nigerian economy. Precisely, a 100 percent increase in investment in education will lead to about 37 percent increase in real GDP. Investments in education is positively sloped which is expected theoretically; but it is statistically insignificant even at the 10 percent traditional level. This can be seen from the t-statistic of 1.58 and a probability value of 0.1224. This leaves the variable EDUC a relatively less important explanatory factor in current year GDP in Nigeria over time. [2 marks]

Gross fixed capital formation (GFCF) also impacts positively on real GDP in Nigeria. Precisely, a 100 percent increase in gross fixed capital formation will lead to about 13 percent increase in real GDP. Gross fixed capital formation is positively sloped and this is also is expected theoretically since increases in stock of capital should lead to increases in aggregate output. The variable GFCF is however statistically insignificant even at the 10 percent traditional level. This can be seen from the t-statistic of 0.41 and a probability value of 0.6842. [2 marks]

Government expenditure on health (HEALTH) impacts positively on real GDP Nigeria. In more specific terms, a 100 percent increase in government expenditure on health will lead to about 21 percent increase in real GDP. Government expenditure on health is positively sloped which is expected theoretically. The variable HEALTH is statistically insignificant even at the 10 percent traditional level. This can be seen from the t-statistic of 0.85 and a probability value of 0.4022. This makes HEALTH a relatively less important explanatory factor in the variations of real GDP in Nigeria over time. [2 marks]

Social expenditure (SOCEXP) impacts positively on real GDP in Nigeria. Precisely, a 100 percent increase in Social expenditure will lead to about 23 percent increase in real GDP. Social expenditure is positively sloped and this of course is expected theoretically. It is however statistically insignificant even at the 10 percent traditional level. This can be seen from the t-statistic of 1.34 and a probability value of 0.1903. [2 marks]

Finally, the constant term is positive indicating that in the absence of all the explanatory variables included in this model, gross domestic product in Nigeria will still be positive. The constant term is statistically significant at the 1 percent traditional level as can be seen from the t-statistic of 10.37 and a probability value of 0.000. This leaves the constant term relatively very important in explaining the variations in real GDP in Nigeria over time. [2 marks]

3. Reliability of results

The reliability of the regression results can be determined by examining the summary statistics. At first, these statistics suggest a very impressive result.

The R2 = 0.74 shows that the overall fit of the model is good as the explanatory variables jointly explain about 74 percent of the systematic variations in the dependent variable over the period covered by the study. This result is further validated by the adjusted R2 0.71. [1 mark]

The F-statistic of 22.15 and the related probability of 0.000 reveal the explanatory variables are jointly significant at the 1 percent level. [1 mark]

However, a look at the DW-statistic of 0.295 strongly suggests the presence of some positive autocorrelation which is a violation of a key assumption of OLS. [1 mark]

Therefore, the regression results cannot be considered reliable. This is because of the violation of the assumption of no serial correlation which is one major assumption of OLS. [1 mark]

The presence of positive autocorrelation makes the coefficient estimates inefficient. In this situation, although the coefficient estimates are still unbiased, the results obtained here are likely to be very misleading. Here, OLS is no longer BLUE. [1 mark]

4. Possible remedies for observed shortcomings

Given the shortcoming discussed in 3 above, possible remedies will include the use of generalized least squares GLS. This is however on the condition that the form of autocorrelation is known.

[3 marks]

Otherwise, the Cochrane-Orcutt procedure may be employed to deal with the observed problem of autocorrelation provided it is of the first order autoregressive process. [2 marks]

QUESTION 2 TOTAL [20 MARKS]

(a) Obtain the correct r (4 decimal places), interpret the correct r and comment on the effect of this error on the true r

Required Adjustments

Y X XY Y2 X2

Correct Values

80 110 8800 6400 12100

150 210 31500 22500 44100

Correct Total 230 320 40300 28900 56200

Wrong Values

90 120 10800 8100 14400

140 220 30800 19600 48400

Wrong Total 230 340 41600 27700 62800

Difference in Totals

230 320 40300 28900 56200

230 340 41600 27700 62800

Net Errors 0 -20 -1300 1200 -6600

Wrong Summation 1110 1700 205500 132100 322000

Correct Summation 1110 1680 204200 133300 315400

2 2 ∑ 푌푖 = 1110; ∑ 푋푖 = 1680; ∑ 푋푖푌푖 = 204200; ∑ 푋푖 = 315400; 푎푛푑 ∑ 푌푖 = 133300

푛 ∑ 푥푦 − ∑ 푥 ∑ 푦 푟 = [ퟑ 퐦퐚퐫퐤퐬] √[푛(∑ 푥2) − (∑ 푥)2] [푛(∑ 푦2) − (∑ 푦)2]

10(204200) − 1680(1110) 푟 = √[10(315400) − (1680)2] [10(133300) − (1110)2]

2042000 − 1864800 푟 = √[3154000 − 2822400] [1333000 − 1232100]

177200 푟 = [ퟑ 퐦퐚퐫퐤퐬] √[331600] [100900]

177200 푟 = √33458440000

177200 푟 = 182916.484

풓 = ퟎ. ퟗퟔퟖퟕ [ퟒ 퐦퐚퐫퐤퐬]

iii. State any two properties of the coefficient of correlation r.

The following are the basic features or properties of the coefficient of correlation r.

i. The coefficient of correlation is unit free ii. It ranges between -1 and 1 iii. The closer to -1, the stronger the negative linear relationship iv. The closer to 1, the stronger the positive linear relationship v. The closer to 0, the weaker the linear relationship

[5 marks each for any two correct properties listed]

QUESTION 3 TOTAL [20 MARKS]

QUESTION 3 (i)

Three problems in regression analysis includes: (i) Multicollinearity (ii) Heteroscedasticity (iii) Model Specification bias.

Explanation

Multicollinearity: One of the assumptions of classical linear regression model is that there is no multicollinearity among the explanatory variables. Many of the explanatory variables used in regression analysis are often collinear. This term simply implies the existence of a “perfect” or exact, linear relationship among some or all explanatory variables of a regression model. When this is experienced in regression analysis, it can become a problem as the regression coefficients of the X variables become indeterminate with the standard errors infinite. If the multicollinearity is less than perfect, even though the regression coefficients would be determinate, they will possess large standard errors. This means that the coefficients cannot be estimated with great precision and accuracy. [2 marks]

Heteroscedasticity: Another important assumption of CLR model is that the variance of each disturbance term conditional on the chosen values of the explanatory variables, is some constant number equal to σ2. This is the assumption of homoscedasticity, or equal (homo) spread (scedasticity) meaning equal variance. The violation of this assumption is called heteroscedasticity. It does not destroy the unbiasedness and consistency properties of OLS estimators, but these estimators will no longer be minimum variance or efficient. That is, they are not BLUE. This problem in regression analysis can arise due to a number of problems such as following a error-learning model, improvement in data collecting techniques, presence of outliners, model mis-specification, among others. A number of methods are however available in addressing or correcting the problem. [2 marks]

Model Specification bias: If a regression model is not correctly specified, we encounter the problem of model specification error or model specification bias. In developing an empirical model, one is likely to commit one or more of the following specification errors: omission of relevant variable(s), inclusion of an unnecessary variable(s), adoption of the wrong functional form, errors of measurement, incorrect specification of the stochastic error term and assuming the error term is normally distributed. Incorrect specification of a model have their consequences and when legitimate variables are omitted from a

59 model, the problem could be serious. The consequences of including an irrelevant variable are fortunately less serious. [1 mark]

QUESTION 3 (ii)

For a k-variable regression involving explanatory variables

푋1, 푋2, … , 푋푘 , an exact linear relationship is said to exist if the following condition is satisfied;

휆1푋1 + 휆2푋2 + ⋯ + 휆푘푋푘 = 0 … (1)

푤ℎ푒푟푒 휆1, 휆2, … , 휆푘 are constants such that not all of them are zero simultaneously. [2 marks]

However, the term is today used more widely in a broader sense to include where X variables are intercorrelated but not perfectly. This yields; 휆1푋1 + 휆2푋2 + ⋯ + 휆푘푋푘 + 푣푖 = 0 … (2)

Where 푣푖 is a stochastic term. [1 mark]

To see the difference between perfect and less than perfect multicollinearity, we assume 훽2 ≠ 0 and divide through by 휆2 , equ 2 becomes;

휆1 휆3 휆푘 푋2푖 = − 푋1푖 − 푋3푖 − ⋯ − 푋푘푖 … (3) 휆2 휆2 휆2

This shows how 푋2 is exactly linearly related to other variables or how it can be derived from a linear combination of other X variables. In this situation, the coefficient of correlation between the variable 푋2 and the linear combination on the RHS is bound to be unity. [1 mark]

Similarly, if 휆2 = 0, equ 2 becomes;

휆1 휆3 휆푘 1 푋2푖 = 푋1푖 − 푋3푖 − ⋯ − 푋푘푖 − 푣푖 … (4) 휆2 휆2 휆2 휆2

This shows that 푋2 is not an exact linear combination of other X’s as it is also determined by the stochastic term 푣푖 [1 mark]

QUESTION 3 (iii)

Sources of Multicollinearity

1. Data collection method employed. E.g. sampling over a limited range of values taken by the regressors in the population.

2. Constraints on the model or in the population being sampled.

3. Model specification.This could for example adding polynomial terms to a regression model especially when the range of the X variable is small.

4. An over-determined model. This happens when the model has more explanatory variables than the number of observations.

5. Additional reason could be that the regressors included in the model share a common trend, i.e. they all increase or decrease over time.

[1 mark each for any three correct sources listed]

Consequences

1. Although BLUE, OLS estimators have large variances and co-variances making precise estimation difficult.

2. Due to 1 above, confidence interval tend to be much wider, leading to the acceptance of the “zero null hypothesis” more readily.

3. Also, t-ratio of one or more co-efficients tends to be statistically insignificant as a result of the large variance.

The larger the standard error, the smaller/insignificant the t-stat become.

4. Although the t-ratio of one or more of the co-efficients is insignificant, 푅2 which is the overall measure of goodness of fit can be very high.

5. OLS estimators and there standard errors can be sensitive to small changes in the data.

[1 mark each for any two correct consequences listed]

QUESTION 3 (iv)

Remedial measures in addressing a case of Multicollinearity

Two choices; Do nothing or follow some rules of thumb. [1 mark]

Multicollinearity is usually a data deficiency problem and often times do not have control over data used for empirical analysis. Moreover even if some of the co-efficient estimates cannot be estimated with precision, a linear combination of them can be estimated relatively efficiently. [1 mark]

Rule of thumb

1. A priori Information.

2. Combining cross-sectional and time series data. This is known as pooling the data.

3. Specification bias. This could involve dropping some variable(s).

4. Transformation of the variable. Differencing the regression model can reduce the severity of multicollinearity.

5. Use of additional or new data. Since multicollinearity is a sample feature, it is possible that in another sample involving the same variables, collinearity may not be so serious as in the first sample.

6. Reducing collinearity in polynomial regression. Sometimes simply increasing the size of the sample (if possible) may reduce the collinearity problem.

[1 mark each for any three correct rules of thumb listed]

QUESTION 4 TOTAL [20 MARKS]

2. i. Discuss the BLUE properties of the ordinary least squares (OLS) estimators [8 marks] iv. Explain the four computational properties of OLS estimators? [6 marks] v. Distinguish between the small sample properties and asymptotic properties of the OLS estimators [6 marks] TOTAL [20 MARKS]

QUESTION 4 (i)

The Gauss-Markov Theorem states that “Given the assumption of the classical linear regression model (CLRM), the ordinary least squares (OLS) estimators in the class of unbiased linear estimators, have minimum variance” meaning that it is Best, Linear, Unbiased Estimators (BLUE). [2 marks]

An estimator, say the OLS estimator 훽̂푖 is said to be a best linear unbiased estimator (BLUE) with respect to 훽푖 if the following hold:

 It is linear, that is, linearity in parameters where a linear function of a random variable is such

that 푌 = 훽̂1 + 훽̂2푋 + 푈̂ [2 marks]

 It is unbiased, that is, its average or expected value, 퐸(훽̂2) is equal to the actual value 훽2 [2 marks]  It has minimum variance meaning that in the class of linear, unbiased estimators with the least squares variance known as an efficient estimator [2 marks]

QUESTION 4 (ii)

The computational or statistical properties of the OLS estimators include the following:

PROPERTY 1: Linearity of 훽̂1

The OLS coefficient estimator 훽̂1 can be written as a linear function of the sample values of Y, the 푌푖 (i = 1, 2,…, N). [2 marks]

PROPERTY 2: Unbiasedness of 훽̂1 and 훽̂0 [2 marks]

The OLS coefficient estimator 훽̂1 is unbiased, meaning that 퐸(훽̂1) = 훽1

The OLS coefficient estimator 훽̂0 is unbiased, meaning that 퐸(훽̂0) = 훽0

PROPERTY 3: Variance of 훽̂1 (slope coefficient)

The variance of the OLS slope coefficient estimator 훽̂1 is defined as:

2 푉푎푟(훽̂1) = {[훽̂1 − 퐸(훽̂1)] }

or 휎2 ̂ 푉푎푟(훽1) = 2 ∑푖 푋푖

[1 mark for either property 3 or 4]

PROPERTY 4: Variance of 훽̂0 (intercept coefficient)

The variance of the OLS intercept coefficient estimator 훽̂0 is:

2 2 2 2 휎 ∑푖 푋 휎 ∑푖 푋 푉푎푟(훽̂ ) = 푖 = 푖 0 2 ̅ 2 푁 ∑푖 푋푖 푁(푋푖 − 푋)

The standard error of 훽̂0 is the square root of the variance: i.e.,

1 휎2 ∑ 푋2 2 ̂ ̂ 푖 푖 푠푒(훽0) = √푉푎푟(훽0) = ( 2 ) 푁 ∑푖 푋푖

PROPERTY 5: Covariance of 훽̂0 푎푛푑 훽̂1 [1 mark]

The covariance of the OLS coefficient estimators 훽̂0 푎푛푑 훽̂1 is defined as

퐶표푣(훽̂0, 훽̂1) = 퐸{[훽̂0 − 퐸(훽̂0)][훽̂1 − 퐸(훽̂1)]} QUESTION 4 (iii)

Small Sample Properties: Unbiasedness

The coefficient estimator is unbiased if and only if 퐸(훽̂1) = 훽1; i.e., its mean or expectation is equal to the true coefficient. [2 marks]

Asymptotic Properties: Consistency

Consistency (instead of unbiasedness)

First, we need to define consistency. Suppose 푊푛 is an estimator of 휽 on a sample of 푌1, 푌2, … . 푌푛 of size n. Then, W is a consistent estimator of 휽 if for every e > 0,

푷(|푾풏 − 휽| > 풆) → ퟎ 풂풔 풏 → ∞ [2 marks]

This says that the probability that the absolute difference between W and θ being larger than e goes to zero as n gets bigger. Which means that this probability could be non-zero while n is not large.

Under the small (finite) - sample properties, we say that 푊푛 is unbiased, E(푊푛) = θ. Under the asymptotic properties, we say that 푊푛 is consistent because 푊푛 converges to θ as n gets larger.

[2 marks]

QUESTION 5 (i) TOTAL [20 MARKS] i. With the aid of a diagram, explain what you understand about the following

d. Total sum of squares [4 marks] e. Explained sum of squares [4 marks] f. Residual sum of squares [4 marks]

a. SST = Total sum of squares: This measures the variation of the values of the dependent variable (yi) around their mean (푦̅) [2 marks] b. SSE = Explained sum of squares: This is a measure of the explained variation attributable to the relationship between x and y [2 marks]

64 c. SSR = Residual sum of squares: This measures the variation attributable to factors other than the relationship between x and y [2 marks]

SSR: Unexplained variation

Y 풀̂풊 = 휶̂ + 휷̂푿풊 SST: Total variation

SSE: Explained variation

푌̅

[ퟔ 풎풂풓풌풔]

0 푋푖 X

QUESTION 5 (ii)

What do you understand by the goodness of fit? [8 marks]

The goodness of fit shows how well the estimated regression line fits the actual data. The coefficient of determination, 푅2 is a measure of the goodness of fit. [4 marks]

The 푅2 is the portion of the total variation in the dependent variable that is explained by variation in the independent variable. [4 marks]

COVENANT UNIVERSITY

CANAANLAND, KM 10, IDIROKO ROAD P.M.B 1023, OTA, OGUN STATE, NIGERIA.

TITLE OF EXAMINATION: B.Sc EXAMINATION

COLLEGE: CBSS

SCHOOL: SOCIAL SCIENCES

DEPARTMENT: ECONOMICS AND DEVELOPMENT STUDIES

SESSION: 2014/2015 SEMESTER: ALPHA

COURSE CODE: ECN 319 CREDIT UNIT: 2

COURSE TITLE: OPERATIONS RESEARCH I

INSTRUCTION: ANSWER QUESTION 1 AND ANY OTHER TWO. TIME: 2 HOURS

______

1. (a) What is Operations Research? (4marks) (b)State three each of its importance and limitations. (6marks) (c)The Blue Belt Organization is using the assignment model to determine the most efficient allocation of jobs to machines. The machines work on hourly basis at the cost of N25 per hour. Any job for which a machine is not available for any reason is marked X to denote impossible task. All estimates are in hours.

Machine Job/ 1 2 3 4 5

A 35 X 37 36 38

B 37 35 38 34 39

C 45 40 X 37 X

D 36 33 40 33 38

(i) Determine the most efficient allocation for the company. (8 marks) (ii) If the fifth job is added that can only be undertaken by machines 1, 2 and 5 as shown in the table below, how would this affect your assignment? (8 marks). (Hint: Use the Branch and Bound method)

Machine 1 2 3 4 5

Job E 35 35 X X 35

(d) What is the total cost to Blue Belt Organization in each case i & ii above, briefly comment on your answers. (4 marks) Total = 30marks

2. (a) What is a decision tree? (2 marks) (b)Draw a decision tree of the table below:

DECISION LOW p=0.4 MEDIUM p=0.3 HIGH p=0.3 ALTERNATIVES

Manufacture 2,000 -1,200 3,000

Import -6,000 3,000 12,000

Purchase Locally -4,800 4,500 6,000

(5marks)

(4marks)

(d) What is the difference between a balanced and an unbalanced transportation problem? Illustrate with examples. (6 marks)

(e) Give two practical examples each of: (i) mental models (ii) iconic models (iii) verbal models. (3marks) Total = 20marks

3. (a) List ten instances where assignment model can be used. (5marks)

(b) The table below shows the transportation of tubers of yam from four locations in the Northern part of Nigeria to five locations in the South, with the unit cost of transportation shown in the box. Determine the initial feasible solution by finding the minimum cost of transportation using the North West Corner method.

LOCATIONS DUTSE KATSINA JALINGO DAMATURU SUPPLY

BENIN 180 120 135 105 2000

OWO 90 140 130 140 8000

ABA 120 100 120 150 7000

WARRI 180 140 200 162 3000

ILESA 110 130 100 160 2500

DEMAND 1000 4000 8500 4500

(15marks) Total = 20marks

4. Dumpier Nigeria Plc., makers of Fan drink are planning for the next financial year. The major decision before the operations and marketing Directors is the determination of the size of the product to sell to the market. As a matter of fact, the company has the large size (ls), medium size (ms) and small size (ss) that may be sold to the market depending on the state of nature i.e. the economy. The economy can either be good or bad. When the economy is good, it is expected that ls, ms and ss Fan drink will fetch N10,000, N7,000 and N2,000 monthly respectively. On the other hand, when the economy is bad, it is expected that ms Fan drink would fetch a loss of N2,000 while ls and ss Fan drink would fetch N2,000 and N5,000 profit respectively. Required:

Advise DN Plc. as to which size of the product to plan for in the next financial year using:

i. The maximax criterion ii. The minimax regret criterion

iii. The Laplace criterion

iv. Assuming that the chances of having a good economy is estimated at 55% likely, how would you advise DN Plc. using the Hurwicz criterion.

v. The Wald criterion (4 marks each). Total = 20marks