1. Consider the Following Preferences Over Three Goods: �~� �~� �~� � ≽ �

Total Page:16

File Type:pdf, Size:1020Kb

1. Consider the Following Preferences Over Three Goods: �~� �~� �~� � ≽ � 1. Consider the following preferences over three goods: �~� �~� �~� � ≽ � a. Are these preferences complete? Yes, we have relationship defined between x and y, y and z, and x and z. b. Are these preferences transitive? Yes, if �~� then � ≽ �. If �~� then � ≽ �. If �~� then �~� and � ≽ �. Thus the preferences are transitive. c. Are these preferences reflexive? No, we would need � ≽ � � ≽ � 2. Write a series of preference relations over x, y, and z that are reflexive and complete, but not transitive. � ≽ � � ≽ � � ≽ � � ≽ � � ≽ � � ≻ � We know this is not transitive if � ≽ � and � ≽ � then � ≽ �. But � ≻ �, which would contradict transitivity. 3. Illustrate graphically a set of indifference curves where x is a neutral good and y is a good that the person likes: We know that this person finds x to be a neutral good because adding more x while keeping y constant (such as moving from bundle A to D, or from B to E), the person is indifferent between the new bundle with more x and the old bundle with less x. We know this person likes y because adding more y while keeping x constant (such as moving from bundle A to B, or from D to E), the person is strictly prefers the new bundle with more y than the old bundle with less y. 4. Draw the contour map for a set of preferences when x and y are perfect substitutes. Are these well-behaved? Explain why or why not. We know these are perfect substitutes because they are linear (the MRS is constant) We know they are strictly monotonic because adding Y while keeping X constant (moving from bundle A to bundle B), leads to a strictly preferred bundle (� ≻ �). However, they are not strictly convex because the bundle D which is the bundle containing the averages of bundles B and C is not strictly preferred to B and C. Thus the preferences are not well behaved because they do not satisfy both montonicity and convexity. 5. Suppose the utility function over x, y, and z is: 0 0 0 � �, �, � = �1�2�2 The price of x is 2, the price of y is 4, the price of z is 6. Income is 100. a. Write the utility maximization problem for this consumer: 0 0 0 ��� �1�2�2 �. �. �� + �� + �� = ��� We know this is the problem, as we are trying to maximize our utility subject to a budget constraint. b. Using the Lagrangian method, solve this problem for the optimal bundle. 0 0 0 � �, �, � = �1�2�2 − �(2� + 4� + 6� − 100) The optimal bundle will satisfy the following first order conditions: K K K 0 J 1. � = 0: � L�M�M − 2� = 0 H 1 K O K 0 J 2. � = 0: �L� M�M − 4� = 0 N 2 K K O 0 J 3. � = 0: �L�M� M − 6� = 0 P 2 4. �Q = 0: 2� + 4� + 6� − 100 = 0 The best way to solve this is to use condition (1) and (2) to find y=f(x) and conditions (1) and (3) to find z=f(x). We want to do this so that we can substitute into condition (4) to solve for x. Condition (1) becomes: 0 0 0 1 J � 1�2�2 = 2� 2 Condition (2) becomes: 0 R 0 1 J �1� 2�2 = 4� 4 Dividing (1) by (2) lets us cancel out z, so that what is left is a relationship between x and y. 5 � 2 = . 25 � 4 2 1 � = � = � 8 4 Dividing (1) by (3) lets us cancel out y, so that what is left is a relationship between z and x. 5 � 2 = . 25 � 6 2 1 � = � = � 12 6 Now we can use our last constraint to find x: 1 1 2� + 4 � + 6 � = 100 4 6 2� + � + � = 100 4� = 100 �∗ = 25 Then we can use our previous conditions to find �∗ and �∗: 1 1 �∗ = �∗ = 25 = 6.25 4 4 1 1 �∗ = �∗ = 25 = 4.17 6 6 The optimal bundle is �∗, �∗, �∗ = (25,6.25,4.17) Note: you could find the demand for x, y, and z by replacing making prices unknown and income unknown. 6. Consider the following optimization problem: ��� 2� + 4� �. �. 4� + 2� = 8 a. Illustrate this problem graphically. This is a case of perfect substitutes because U(x,y) = 2x+4y. All perfect substitutes have this linear form U(x,y) = ax+by. Before I go further, I want to find the slope of the indifference curves (the MRS) so that I can plot them: � 2 ��� = − H = − �N 4 I also want to find the slope of the budget constraint: �H 4 − = − �N 2 Now, I can observe that the magnitude of the MRS is less than the magnitude of the slope of the budget constraint: �H 1 4 �H = < = �N 2 2 �N I’ll keep this in mind when I plot them. First: the budget constraint. * The y-intercept is when we buy only y and zero x 4 0 + 2� = 8 8 � = = 4 2 * The x-intercept is when we buy only x and zero y 4� + 2(0) = 8 8 � = = 2 4 Now plot: Now we need to add the contour map of the utility function over the top of the budget constraint. We know one thing: the curves are less steep than the budget constraint. The utility of consuming only y is U(0,4) = 16. The utility of consuming only x is U(2,0)=4 The best bundle is to consume only y at bundle A. Note: this example walks through all the steps. An answer with just the graph is perfectly acceptable. b. Illustrate the income offer curve for this problem. The income offer curve maps out all the best bundles in the (X,Y) coordinate plane as m changes. Lets start with the best bundle and indifference curve from our last problem: I am going to decrease m and see what happens: When income decreases, the budget constraint shifts to the left. The new best bundle will be be bundle B. If we keep doing this, we will see that each bundle follows the y-axis. Connecting the dots, we get the I-O curve: c. Illustrate the Engel curve for x and y. As income decreases, x doesn’t change. As income decreases, y decreases. 7. Suppose that good x is an inferior good and good y is a normal good. Illustrate an income offer curve which would show this. If income goes up, we would expect x to go down. If income goes up, we would expect y to go up: As income goes up, we move from B1 to B2 to B3 to B4. The best bundles go from A to B to C to D. The income offer curve is down ward sloping when x is inferior and y is normal. 8. Explain what a Giffen good is. A Giffen good is a good where a person demands more of it when the price of it goes up. The demand curve for a Giffen good is upward sloping. 9. Illustrate the income, substitution, and total effects when x is a Giffen good and y is a normal good. Let the price of x decrease. The budget constraint under the original higher price is B1. The budget constraint under the new lower price is B2. If X is a Giffen good, then we know that the total effect will be a movement from A to C (x3-x1). The substitution effect is when we hold purchasing power constant and rotate budget curve B1 around bundle A to reflect the new price ratio. The new best bundle is bundle B and the substitution effect is x2-x1. The income effect occurs when purchasing power increases from this price decrease. The new bundle would be bundle C and the income effect would be x3-x2. The income effect here is sufficiently negative so that x3<x1. You can think of a Giffen good as an extremely responsive inferior good. 10. Suppose we have a utility function � �, � = min {��, ��}. a. Set up a utility maximization problem for this consumer. ��� ��� ��, �� �. �. ��� + ��� = � b. Find the demand for good x and good y. This is the case of perfect complemnets. We know what the utility function of perfect complements always takes the form U(x,y) = min{ax,by}. They are “L- shaped” utility curves with the joint where ax=by. We CANNOT use the Lagrange method here because this minimum function is not differentiable. Instead we are going to use the fact that the best bundle always lands on the joint, so �� = �� � � = � � We can substitute this into the budget constraint: � � � + � � = � H N � � � � � + � � = � � H � N �� + �� H N � = � � � �(�H, �N, �) = � ��H + ��N And we can use the fact that y = (a/b)x to solve for y: � � � � � �H, �N, � = � = � = � � � ��H + ��N ��H + ��N c. Let � = � = 1. Suppose that the initial price of x is �H = 2, the price of y is �N = 1 and income is � = 12. Find the income and substitution effects if price n increases to �H = 3. First lets find the initial demand for x: 1 � � , � , � = � 2,1,12 = 12 = 4 H N 2 + 1 If price were to increase, then income would have to increase to compensate for this and make x=4 still affordable. We can find how much income has to increase by looking at: n ∆� = ∆� ∗ � �H, �N, � = �H − �H � �H, �N, � = 3 − 2 4 = 4 Income would have to go up by 4. So the compensated income would be: �n = � + ∆� = 12 + 4 = 16 The quantity demanded at the new price and compensated income is 1 � �n , � , �n = 16 = 4 H N 3 + 1 So the demand did not change.
Recommended publications
  • Labour Supply
    7/30/2009 Chapter 2 Labour Supply McGraw-Hill/Irwin Labor Economics, 4th edition Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved. 2- 2 Introduction to Labour Supply • This chapter: The static theory of labour supply (LS), i. e. how workers allocate their time at a point in time, plus some extensions beyond the static model (labour supply over the life cycle; household fertility decisions). • The ‘neoclassical model of labour-leisure choice’. - Basic idea: Individuals seek to maximise well -being by consuming both goods and leisure. Most people have to work to earn money to buy goods. Therefore, there is a trade-off between hours worked and leisure. 1 7/30/2009 2- 3 2.1 Measuring the Labour Force • The US de finit io ns in t his sect io n a re s imila r to t hose in N Z. - However, you have to know the NZ definitions (see, for example, chapter 14 of the New Zealand Official Yearbook 2008, and the explanatory notes in Labour Market Statistics 2008, which were both handed out in class). • Labour Force (LF) = Employed (E) + Unemployed (U). - Any person in the working -age population who is neither employed nor unemployed is “not in the labour force”. - Who counts as ‘employed’? Size of LF does not tell us about “intensity” of work (hours worked) because someone working ONE hour per week counts as employed. - Full-time workers are those working 30 hours or more per week. 2- 4 Measuring the Labour Force • Labor Force Participation Rate: LFPR = LF/P - Fraction of the working-age population P that is in the labour force.
    [Show full text]
  • Chapter 8 8 Slutsky Equation
    Chapter 8 Slutsky Equation Effects of a Price Change What happens when a commodity’s price decreases? – Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other commodities. Effects of a Price Change – Income effect: the consumer’s budget of $y can purchase more than before, as if the consumer’s income rose, with consequent income effects on quantities demanded. Effects of a Price Change Consumer’s budget is $y. x2 y Original choice p2 x1 Effects of a Price Change Consumer’s budget is $y. x 2 Lower price for commodity 1 y pivots the constraint outwards. p2 x1 Effects of a Price Change Consumer’s budget is $y. x 2 Lower price for commodity 1 y pivots the constraint outwards. p2 Now only $y’ are needed to buy the y' original bundle at the new prices , as if the consumer’s income has p2 increased by $y - $y’. x1 Effects of a Price Change Changes to quantities demanded due to this ‘extra’ income are the income effect of the price change. Effects of a Price Change Slutskyyg discovered that changes to demand from a price change are always the sum of a pure substitution effect and an income effect. Real Income Changes Slutsky asserted that if, at the new pp,rices, – less income is needed to buy the original bundle then “real income ” is increased – more income is needed to buy the original bundle then “real income ” is decreased Real Income Changes x2 Original budget constraint and choice x1 Real Income Changes x2 Original budget constraint and choice New budget constraint
    [Show full text]
  • Unit 4. Consumer Behavior
    UNIT 4. CONSUMER BEHAVIOR J. Alberto Molina – J. I. Giménez Nadal UNIT 4. CONSUMER BEHAVIOR 4.1 Consumer equilibrium (Pindyck → 3.3, 3.5 and T.4) Graphical analysis. Analytical solution. 4.2 Individual demand function (Pindyck → 4.1) Derivation of the individual Marshallian demand Properties of the individual Marshallian demand 4.3 Individual demand curves and Engel curves (Pindyck → 4.1) Ordinary demand curves Crossed demand curves Engel curves 4.4 Price and income elasticities (Pindyck → 2.4, 4.1 and 4.3) Price elasticity of demand Crossed price elasticity Income elasticity 4.5 Classification of goods and demands (Pindyck → 2.4, 4.1 and 4.3) APPENDIX: Relation between expenditure and elasticities Unit 4 – Pg. 1 4.1 Consumer equilibrium Consumer equilibrium: • We proceed to analyze how the consumer chooses the quantity to buy of each good or service (market basket), given his/her: – Preferences – Budget constraint • We shall assume that the decision is made rationally: Select the quantities of goods to purchase in order to maximize the satisfaction from consumption given the available budget • We shall conclude that this market basket maximizes the utility function: – The chosen market basket must be the preferred combination of goods or services from all the available baskets and, particularly, – It is on the budget line since we do not consider the possibility of saving money for future consumption and due to the non‐satiation axiom Unit 4 – Pg. 2 4.1 Consumer equilibrium Graphical analysis • The equilibrium is the point where an indifference curve intersects the budget line, with this being the upper frontier of the budget set, which gives the highest utility, that is to say, where the indifference curve is tangent to the budget line q2 * q2 U3 U2 U1 * q1 q1 Unit 4 – Pg.
    [Show full text]
  • Evidence from a Laboratory Experiment on Impure Public Goods
    MPRA Munich Personal RePEc Archive Green goods: are they good or bad news for the environment? Evidence from a laboratory experiment on impure public goods Munro, Alistair and Valente, Marieta National Graduate Institute for Policy Studies, Tokyo, Japan, NIMA { Applied Microeconomics Research Unit, University of Minho, Portugal, Department of Economics, Royal Holloway University of London, UK 30. October 2008 Online at http://mpra.ub.uni-muenchen.de/13024/ MPRA Paper No. 13024, posted 27. January 2009 / 03:02 Green goods: are they good or bad news for the environment? Evidence from a laboratory experiment on impure public goods (Version January-2009) Alistair Munro Department of Economics, Royal Holloway University of London, UK National Graduate Institute for Policy Studies Tokyo, Japan and Marieta Valente (corresponding author: email to [email protected] ) Department of Economics, Royal Holloway University of London, UK NIMA – Applied Microeconomics Research Unit, University of Minho, Portugal The authors thank Dirk Engelmann for helpful comments and suggestions as well as participants at the Research Strategy Seminar at RHUL 2007, IMEBE 2008, Experimental Economics Days 2008 in Dijon, EAERE 2008 meeting, European ESA 2008 meeting. Also, we thank Claire Blackman for her help in recruiting subjects. Marieta Valente acknowledges the financial support of Fundação para a Ciência e a Tecnologia. Abstract An impure public good is a commodity that combines public and private characteristics in fixed proportions. Green goods such as dolphin-friendly tuna or green electricity programs provide increasings popular examples of impure goods. We design an experiment to test how the presence of impure public goods affects pro-social behaviour.
    [Show full text]
  • Demand Demand and Supply Are the Two Words Most Used in Economics and for Good Reason. Supply and Demand Are the Forces That Make Market Economies Work
    LC Economics www.thebusinessguys.ie© Demand Demand and Supply are the two words most used in economics and for good reason. Supply and Demand are the forces that make market economies work. They determine the quan@ty of each good produced and the price that it is sold. If you want to know how an event or policy will affect the economy, you must think first about how it will affect supply and demand. This note introduces the theory of demand. Later we will see that when demand is joined with Supply they form what is known as Market Equilibrium. Market Equilibrium decides the quan@ty and price of each good sold and in turn we see how prices allocate the economy’s scarce resources. The quan@ty demanded of any good is the amount of that good that buyers are willing and able to purchase. The word able is very important. In economics we say that you only demand something at a certain price if you buy the good at that price. If you are willing to pay the price being asked but cannot afford to pay that price, then you don’t demand it. Therefore, when we are trying to measure the level of demand at each price, all we do is add up the total amount that is bought at each price. Effec0ve Demand: refers to the desire for goods and services supported by the necessary purchasing power. So when we are speaking of demand in economics we are referring to effec@ve demand. Before we look further into demand we make ourselves aware of certain economic laws that help explain consumer’s behaviour when buying goods.
    [Show full text]
  • Mathematical Economics
    Mathematical Economics Dr Wioletta Nowak, room 205 C [email protected] http://prawo.uni.wroc.pl/user/12141/students-resources Syllabus Mathematical Theory of Demand Utility Maximization Problem Expenditure Minimization Problem Mathematical Theory of Production Profit Maximization Problem Cost Minimization Problem General Equilibrium Theory Neoclassical Growth Models Models of Endogenous Growth Theory Dynamic Optimization Syllabus Mathematical Theory of Demand • Budget Constraint • Consumer Preferences • Utility Function • Utility Maximization Problem • Optimal Choice • Properties of Demand Function • Indirect Utility Function and its Properties • Roy’s Identity Syllabus Mathematical Theory of Demand • Expenditure Minimization Problem • Expenditure Function and its Properties • Shephard's Lemma • Properties of Hicksian Demand Function • The Compensated Law of Demand • Relationship between Utility Maximization and Expenditure Minimization Problem Syllabus Mathematical Theory of Production • Production Functions and Their Properties • Perfectly Competitive Firms • Profit Function and Profit Maximization Problem • Properties of Input Demand and Output Supply Syllabus Mathematical Theory of Production • Cost Minimization Problem • Definition and Properties of Conditional Factor Demand and Cost Function • Profit Maximization with Cost Function • Long and Short Run Equilibrium • Total Costs, Average Costs, Marginal Costs, Long-run Costs, Short-run Costs, Cost Curves, Long-run and Short-run Cost Curves Syllabus Mathematical Theory of Production Monopoly Oligopoly • Cournot Equilibrium • Quantity Leadership – Slackelberg Model Syllabus General Equilibrium Theory • Exchange • Market Equilibrium Syllabus Neoclassical Growth Model • The Solow Growth Model • Introduction to Dynamic Optimization • The Ramsey-Cass-Koopmans Growth Model Models of Endogenous Growth Theory Convergence to the Balance Growth Path Recommended Reading • Chiang A.C., Wainwright K., Fundamental Methods of Mathematical Economics, McGraw-Hill/Irwin, Boston, Mass., (4th edition) 2005.
    [Show full text]
  • IS EFFICIENCY BIASED? Zachary Liscow* August 2017 ABSTRACT: the Most Common Underpinning of Economic Analysis of the Law Has
    IS EFFICIENCY BIASED? Zachary Liscow* August 2017 ABSTRACT: The most common underpinning of economic analysis of the law has long been the goal of efficiency (i.e., choosing policies that maximize people’s willingness to pay), as reflected in economic analysis of administrative rulemaking, judicial rules, and proposed legislation. Current thinking is divided on the question whether efficient policies are biased against the poor, which is remarkable given the question’s fundamental nature. Some say yes; others, no. I show that both views are supportable and that the correct answer depends upon the political and economic context and upon the definition of neutrality. Across policies, efficiency-oriented analysis places a strong thumb on the scale in favor of distributing more legal entitlements to the rich than to the poor. Basing analysis on willingness to pay tilts policies toward benefitting the rich over the poor, since the rich tend to be willing to pay more due to their greater resources. But I also categorize different types of polices and show where vigilance against anti-poor bias is warranted and where it is not, with potentially far-reaching implications for the policies that judges, policymakers, and voters should support. Table of Contents Introduction ................................................................................................................. 2 I. Social Welfare ..................................................................................................... 7 II. Efficiency .........................................................................................................
    [Show full text]
  • Chapter 4 Individual and Market Demand
    Chapter 4: Individual and Market Demand CHAPTER 4 INDIVIDUAL AND MARKET DEMAND EXERCISES 1. The ACME corporation determines that at current prices the demand for its computer chips has a price elasticity of -2 in the short run, while the price elasticity for its disk drives is -1. a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its sales? To its sales revenue? We know the formula for the elasticity of demand is: %DQ E = . P %DP For computer chips, EP = -2, so a 10 percent increase in price will reduce the quantity sold by 20 percent. For disk drives, EP = -1, so a 10 percent increase in price will reduce sales by 10 percent. Sales revenue is equal to price times quantity sold. Let TR1 = P1Q1 be revenue before the price change and TR2 = P2Q2 be revenue after the price change. For computer chips: DTRcc = P2Q2 - P1Q1 DTRcc = (1.1P1 )(0.8Q1 ) - P1Q1 = -0.12P1Q1, or a 12 percent decline. For disk drives: DTRdd = P2Q2 - P1Q1 DTRdd = (1.1P1 )(0.9Q1 ) - P1Q1 = -0.01P1Q1, or a 1 percent decline. Therefore, sales revenue from computer chips decreases substantially, -12 percent, while the sales revenue from disk drives is almost unchanged, -1 percent. Note that at the point on the demand curve where demand is unit elastic, total revenue is maximized. b. Can you tell from the available information which product will generate the most revenue for the firm? If yes, why? If not, what additional information would you need? No.
    [Show full text]
  • Chapter 3—Supply and Demand: Theory
    Chapter 3—Supply and Demand: Theory MULTIPLE CHOICE 1. The law of demand states that price and quantity demanded are a. directly related, ceteris paribus. b. inversely related, ceteris paribus. c. independent. d. positively related, ceteris paribus. ANS: B PTS: 1 DIF: Difficulty: Easy NAT: BUSPROG: Analytic LOC: DISC: Supply and demand KEY: Bloom's: Knowledge 2. Which of the following illustrates the law of demand? a. Jorge buys fewer pencils at $2 per pencil than at $1 per pencil, ceteris paribus. b. Chen buys more ice cream at $4 per half-gallon than at $3 per half gallon, ceteris paribus. c. Karissa buys fewer sweaters at $50 each than at $35 each, ceteris paribus. d. a, b, and c e. a and c ANS: E PTS: 1 DIF: Difficulty: Moderate NAT: BUSPROG: Analytic LOC: DISC: Supply and demand KEY: Bloom's: Application 3. At a price of $15 each, Marta buys 4 books per month. When the price increases to $20, Marta buys 3 books per month. Luz says that Marta's demand for books has decreased. Is Luz correct? a. Yes, Luz is correct. b. No, Luz is incorrect. Marta's demand has increased. c. No, Luz is incorrect. Marta's quantity demanded has decreased, but her demand has stayed the same. d. No, Luz is incorrect. Marta's quantity demanded has increased, but her demand has stayed the same. e. No, Luz is incorrect. Marta's quantity demanded has decreased and her demand has increased. ANS: C PTS: 1 DIF: Difficulty: Challenging NAT: BUSPROG: Analytic LOC: DISC: Supply and demand KEY: Bloom's: Application 4.
    [Show full text]
  • An Analysis of the Supply of Open Government Data
    future internet Article An Analysis of the Supply of Open Government Data Alan Ponce 1,* and Raul Alberto Ponce Rodriguez 2 1 Institute of Engineering and Technology, Autonomous University of Cd Juarez (UACJ), Cd Juárez 32315, Mexico 2 Institute of Social Sciences and Administration, Autonomous University of Cd Juarez (UACJ), Cd Juárez 32315, Mexico; [email protected] * Correspondence: [email protected] Received: 17 September 2020; Accepted: 26 October 2020; Published: 29 October 2020 Abstract: An index of the release of open government data, published in 2016 by the Open Knowledge Foundation, shows that there is significant variability in the country’s supply of this public good. What explains these cross-country differences? Adopting an interdisciplinary approach based on data science and economic theory, we developed the following research workflow. First, we gather, clean, and merge different datasets released by institutions such as the Open Knowledge Foundation, World Bank, United Nations, World Economic Forum, Transparency International, Economist Intelligence Unit, and International Telecommunication Union. Then, we conduct feature extraction and variable selection founded on economic domain knowledge. Next, we perform several linear regression models, testing whether cross-country differences in the supply of open government data can be explained by differences in the country’s economic, social, and institutional structures. Our analysis provides evidence that the country’s civil liberties, government transparency, quality of democracy, efficiency of government intervention, economies of scale in the provision of public goods, and the size of the economy are statistically significant to explain the cross-country differences in the supply of open government data. Our analysis also suggests that political participation, sociodemographic characteristics, and demographic and global income distribution dummies do not help to explain the country’s supply of open government data.
    [Show full text]
  • 1 Economics 100A: Microeconomic Analysis Fall 2001 Problem Set 4
    Economics 100A: Microeconomic Analysis Fall 2001 Problem Set 4 (Due the week of September 24) Answers 1. An inferior good is defined as one of which an individual demands less when his or her income rises and more when his or her income falls. A normal good is defined as one of which an individual demands more when his or her income increases and less when his or her income falls. A luxury good is defined as one for which its demand increases by a greater proportion than income. A necessary is defined as one for which its demand increases by a lesser proportion than income. The same good can be both normal and inferior. For instance, a good can be normal up to some level of income beyond which it becomes inferior. Such a good would have a backward-bending Engel curve. 2. (a) Table 2. Percentage Allocation of Family Budget Income Groups A B C D E Food Prepared at Home 26.1 21.5 20.8 18.6 13.0 Food Away from Home 3.8 4.7 4.1 5.2 6.1 Housing 35.1 30.0 29.2 27.6 29.6 Clothing 6.7 9.0 9.8 11.2 12.3 Transportation 7.8 14.3 16.0 16.5 14.4 (b) All of them. (c) Food away from home, clothing and transportation. (d) Food prepared at home and housing. (e) The graph below depicts the Engel curve for food away from home (a luxury good). (f) The graph below depicts the Engel curve for food prepared at home (a necessity good).
    [Show full text]
  • Unlocking Amenities: Estimating Public Good Complementarity
    Unlocking Amenities: Estimating Public Good Complementarity June 9, 2018 Abstract Research on public goods generally considers the value of individual public goods in isolation, when in fact there may be strong complementarities between them. This study examines the implications of public goods complementarities for economic val- uation and efficient public investment, using the setting of public safety and open space in inner cities. Cross-sectional, difference-in-difference, and instrumental- variable estimates from Chicago, New York, and Philadelphia all indicate that local crime lowers the amenity value of public parks to nearby residents. Public safety improvements \unlock" the value of open-space amenities, and could raise the value that properties receive from adjacent parks from $22 billion to $31 billion in those three cities. Ignoring these complementarities risks over-estimating benefits in dangerous areas, under-estimating benefits in poor areas or conflating reduced amenity value with the preferences of local populations, and under-estimating ben- efits overall. While safety is more fundamental in a hierarchy of amenities, open spaces are not a luxury. Key words: public goods, complements, amenities, crime, environmental amenities, parks, urban development JEL Classification: H41, Q51, Q56 1 Introduction Economic theory leans heavily on the concept that goods may be complements in con- sumption. While the joint demand of private goods, purchased directly in markets, has been studied extensively, little has been said on the joint demand for public goods. Study- ing the joint demand for public goods is difficult since they cannot be purchased directly, but only indirectly, such as access through the housing market.1 To our knowledge, no prior study has priced relationships between public goods in a well-identified causal frame- work.
    [Show full text]