ECON 2100 – Principles of (KSU, Prof. Mathews) “ Theory”

Relevant readings from the textbook:  Mankiw, Ch. 21 – “The Theory of Consumer Choice”

Suggested problems from the textbook:  Chapter 21 “Quick Quiz Multiple Choice” (Page 447): 1, 3, and 5  Chapter 21 “Questions for Review” (Page 448): 1,2 3, 4, 5, 6, and 7  Chapter 21 “Problems and Applications” (Pages 448-449): 1, 2, 4, 5, 6, and 12

Definitions and Concepts:  Budget Line – the limit on consumption bundles that a consumer can afford, given his scarce income and which he faces (“budget line” is the collection of all consumption bundles that cost an amount exactly equal to consumer’s income)  Budget Set – the set of consumption bundles that are affordable for a consumer, given his scarce income and prices which he faces (“budget set” is the collection of all consumption bundles that cost an amount less than or equal to the consumer’s income)

 Equation of budget line: p1 x1  p2 x2  I

 Equation of budget set: p1x1  p2 x2  I  Monotonic Preferences – consumer preferences such that both are desirable, so that more of either good is better

 Indifference – a consumer is indifferent between two bundles, X A  x1A , x2 A and

X B  x1B , x2B , if the two bundles are exactly equally desirable  – collection of different consumption bundles which give a consumer the exact same amount of satisfaction (i.e., collection of bundles that a consumer is indifferent between)  Marginal Rate of Substitution – the rate at which a consumer is able to trade consumption of one good for another while remaining indifferent between consumption bundles  Convexity of Preferences – consumer preferences such that if a consumer is indifferent between two bundles (A and B), then any weighted average of the two (C) is better (“averages are preferred to extremes”)  – a good for which an increase in income leads to an increase in consumption  – a good for which an increase in income leads to a decrease in consumption  Giffen good – a good for which an increase in results in an increase in quantity demanded (i.e., a good for which the “” is violated)

Graphical illustration of Budget Line and Budget Set:

x2

I/p2

Budget Line: red line

Budget Set: red line plus green shaded area

0 x1

I/p1 0

Graphical depiction and properties of Indifference Curves:

x2

E

B 30 G C 22 F D 16 53 A

28 17

0 x1 21 29 38 0 1. Indifference Curves are negatively sloped 2. Bundles on Indifference Curves to the “northeast” are more desirable 3. Indifference Curves cannot intersect (or “cross”) each other 4. Indifferences Curves are typically “bowed inward” . the slope of an indifference curve through a particular consumption bundle is equal to “minus the Marginal Rate of Substitution (of good one for good two)” at the consumption bundle => indifference curves will be “bowed inward” so long as the MRS1,2 gets closer to zero as we move down the indifference curve . this property is called “convexity of preferences” Consumer’s Optimal Choice…  Problem: Choose the consumption bundle from the Budget Set which is most desirable (i.e., on the indifference curve furthest from the origin  Solution: For preferences that satisfy monotonicity and convexity, the optimal choice is the point on the budget line where the slope of the budget line is equal to the slope of the indifference curve. Visually… x2

I/p2 E G

B 30

C 22 F D 16 53 A 28 H 17

0 x1 21 29 38 I/p1 0 Optimal consumption bundle is C=(x1,x2)=(29,22)… . B, D, E, and F are not in the budget set (i.e., not “feasible,” not “on the menu”) . A is in the budget set but does not spend all income => for monotonic preferences, there are affordable bundles (with some more of each good) that are better . G and H are not best, since consumer can adjust consumption “toward C” and instead get an affordable bundle that is better Algebraically, the optimal bundle must satisfy: (i) p1x1+p2x2 = I & (ii) – MRS1,2 = – p1/p2 Examination of “tangency condition” (–MRS1,2 = – p1/p2)…  In order to be optimizing, the consumer must be at a point where MRS1,2 = p1/p2  That is, he must be consuming at a point where… . the rate at which he is willing to decrease consumption of good two in order to increase consumption of good one by a single unit (given his preferences)… . is exactly equal to the rate at which he is able to decrease consumption of good two in order to increase consumption of good one by a single unit in the marketplace (given the prices of the goods).

Example: suppose preferences are such that MRS1,2 = x2/x1 (i) p1x1+p2x2 = I (ii) – MRS1,2 = – p1/p2  Condition (ii) becomes x2/x1 = p1/p2 => Cross multiplying, we get p1x1=p2x2  Substituting into Condition (i) yields 2p2x2 = I => Solving for x2 gives us x2* = I / 2p2  Since p1x1=p2x2 (which can be expressed as x1=p2x2/p1), x1* = I / 2p1 How does the optimal choice change as income changes?  An increase in income (with prices fixed) leads to a parallel outward shift of the budget line food

IH/pF

IL/pF

0 beer

IL/pB IH/pB 0

 Change in optimal consumption bundle:

food

IH/pF

IL/pF

B

A

0 beer

IL/pB IH/pB 0

. As depicted above, initial optimal bundle is A and final optimal bundle (after increase in income) is B . Compared to A, bundle B has more of good one and more of good two => both goods are “normal goods” for this increase in income

 Change in optimal consumption bundle if good two is an inferior good:

food

IH/pF

IL/pF

A B

0 beer

IL/pB IH/pB 0 . As depicted above, initial optimal bundle is A and final optimal bundle (after increase in income) is B . Compared to A, bundle B has more of good one but less of good two => good one is a “normal good” but good two is an “inferior good” for this increase in income

How does the optimal choice change as a price changes?  An increase in the price of good one (with the price of good two and income fixed) leads to an inward rotation of the budget line (same vertical intercept; steeper)

food

I/pF

0 beer

I/pBH I/pBL 0  Change in optimal consumption bundle:

food

I/pF

B A

0 beer

I/pBH I/pBL 0

. As depicted above, initial optimal bundle is A and final optimal bundle (after increase in p1) is B . Compared to A, bundle B has less of good one and more of good two

Why exactly does consumption of each good change?  As the price of beer is increased, there are two effects on the consumer’s purchasing behavior: 1. Substitution Effect: “Since the price of beer increased, the of beer in terms of food is now higher. Each unit of beer costs me more units of food than it did before. As a result, I should substitute some consumption of beer with increased consumption of food.” 2. Income Effect: “Since the price of beer increased, my income has less purchasing power. I am essentially poorer than I was before. Therefore, I should adjust my purchases of all goods in the same way that I would if income were to decrease.”

Two effects illustrated below:  Hypothetical consumption bundle “D” is introduced to decompose the total effect into these two distinct effects  Identify “D” by moving along the initial indifference curve to a point with MRS1,2 equal to the new price ratio  (Total Effect) = (Income Effect) + (Substitution Effect)

food

I/pF

Income D

Effect B A

Substitution Effect

0 beer

I/pBH I/pBL 0

Income Effect Substitution Effect

 Previous picture was drawn assuming both goods were “normal” (so that the income effect for the price increase led to decreased consumption of both goods).  What if the income effect for beer were “zero”? Entire change in consumption of beer is due to substitution effect…

food

Substitution I/pF Effect D

A

B Income

Effect

0 beer

I/pBH I/pBL 0

Substitution Effect

. What if beer were an inferior good (so that the effective decrease in income from the price increase induces the consumer to purchase more beer)? Total decrease in consumption of beer is less than the substitution effect (since the income effect works in the opposite direction)…

food

Substitution I/pF

Effect D

A

B

Income Effect

0 beer

I/pBH I/pBL 0

Income Effect Substitution Effect . What if beer were an inferior good (so that the effective decrease in income from the price increase induces the consumer to purchase more beer) and the income effect was “really large in magnitude”?

food

I/pF Substitution Effect D

A

Income B

Effect 0 beer

I/pBH I/pBL 0

Income Effect Substitution Effect

 As illustrated, in the graph above the income effect on beer consumption more than offsets the substitution effect, so that the total effect of the increase in the price of beer is that the consumer purchases more beer => Law of Demand is violated!!!

Multiple Choice Questions:

1. The ______refers to the rate at which a consumer is able to trade consumption of one good for another while remaining indifferent between consumption bundles. A. budget line B. price ratio C. marginal rate of substitution D. optimal consumption bundle

2. Thomas buys apples and shoes. His income is $200. Apples cost $5 per pound and shoes cost $20 per pair. Which of the following consumption bundles is within his budget set? A. 40 pounds of apples and 10 pairs of shoes. B. 12 pounds of apples and 7 pairs of shoes. C. 6 pounds of apples and 8 pairs of shoes. D. More than one of the above answers is correct.

3. Consider a consumer with preferences for which MRS 1,2  x2 . Suppose prices

and income are: p1  20 , p2  4 , and I  500 . Which of the following consumption bundles is optimal? * * A. x1  12.5 and x2  62.5. * * B. x1  15 and x2  75 . * * C. x1  19 and x2  5 . * * D. x1  20 and x2  25 .

4. If a consumer realizes an increase in income, his budget line will A. not change. B. become steeper (with the vertical intercept unchanged). C. become flatter (with the vertical intercept unchanged). D. shift outward (i.e., further from the origin) with the slope unchanged.

5. The price of pizza increases (with all other prices and income fixed). Ann changes her consumption of pizza due to both an income effect and a substitution effect. As a result of the substitution effect, she decreases her consumption of pizza by 5 units. As a result of the income effect, she decreases her consumption of pizza by 3 units. From these observations, we can infer that A. the total effect of the price change was that she decreased pizza consumption by 8 units. B. the total effect of the price change was that she decreased pizza consumption by 2 units. C. pizza is an inferior good for Ann. D. pizza is a Giffen good for Ann.

x2 6. Consider a consumer with preferences for which MRS 1,2  . This 4x1 consumer’s optimal consumption bundle (as a function of prices and income) is

* I * 4I A. x1  and x2  . 5p1 5p2

* I * I B. x1  and x2  . 2 p1 2 p2

* I * I C. x1  and x2  . p1  p2 p1  p2

* I  p2 * I  p1 D. x1  and x2  . 2 p1 2 p2

For questions 7 and 8, consider the graph below.

x2

C

B A Budget Line 1

Budget Line 2

0 x1

0

7. The change from “Budget Line 1” to “Budget Line 2” would result from A. a change in consumer preferences. B. an increase in income. C. an increase in the price of good one. D. an increase in the price of good two.

8. The Substitution Effect is illustrated by the change in consumption from ______; the Income Effect is illustrated by the change in consumption from ______. A. A to B; B to C. B. A to C; C to B. C. B to C; C to A. D. C to B; C to A.

9. Jim is indifferent between the following two consumption bundles: A  (40,10) and B  (20,60) . Suppose that his preferences over good one and good two satisfy the property of convexity. As a result, which of the following consumption bundles must be strictly preferred to bundles A and B ? A. (10,70) . B. (29,34) . C. (24,50) . D. (20,10) .

10. Which of the following statements is correct? A. “All goods are Giffen goods.” B. “All normal goods are Giffen goods.” C. “All inferior goods are Giffen goods.” D. “All Giffen goods are inferior goods.”

For questions 11 and 12, consider the graph below

x2

I/p2 A

B E

78 C 64 D 35 0 x1

I/p1 0

11. The preferences of this consumer appear to A. be monotonic and satisfy the property of convexity. B. be monotonic but violate the property of convexity. C. not be monotonic but satisfy the property of convexity. D. not be monotonic and violate the property of convexity.

12. Which consumption bundle (or bundles) is optimal for this consumer? A. Only bundle C. B. Bundles B and C are both optimal. C. Bundles A, B, C, and D are all optimal. D. Only bundle B.

Answers to Multiple Choice Questions:

1. C 2. D 3. D 4. D 5. A 6. A 7. C 8. B 9. C 10. D 11. B 12. D