ECON 2100 Principles of Microeconomics (Fall 2018) Consumer Choice Theory

Transcription

1 ECON 21 Principles of Microeconomics (Fall 218) Consumer Choice 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 pplications (Pages ): 1, 2, 4, 5, 6, and 12 efinitions and Concepts: udget Line the limit on consumption bundles that a consumer can afford, given his scarce income and prices which he faces ( budget line is the collection of all consumption bundles that cost an amount exactly equal to consumer s income) udget 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 p2x2 I Equation of budget set: p1 x1 p2x2 I Monotonic Preferences consumer preferences such that both goods are desirable, so that more of either good is better Indifference a consumer is indifferent between two bundles, X x, 1 x2 and X x, 1 x2, if the two bundles are exactly equally desirable Indifference Curve collection of different consumption bundles which give a consumer the exact same amount of satisfaction (ie, 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 ( and ), then any weighted average of the two (C) is better ( averages are preferred to extremes ) Normal Good a good for which an increase in income leads to an increase in consumption Inferior Good a good for which an increase in income leads to a decrease in consumption Giffen good a good for which an increase in price results in an increase in quantity demanded (ie, a good for which the Law of emand is violated)

2 Graphical illustration of udget Line and udget Set: x 2 I/p2 udget Line: red line udget Set: red line plus green shaded area I/p1 x 1 Graphical depiction and properties of Indifference Curves: x 2 E 3 G C 22 F x Indifference Curves are negatively sloped 2 undles 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

3 Consumer s Optimal Choice Problem: Choose the consumption bundle from the udget Set which is most desirable (ie, 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 x 2 I/p2 G E 3 C 22 F H 17 x I/p1 Optimal consumption bundle is C=(x1,x2)=(29,22),, E, and F are not in the budget set (ie, not feasible, not on the menu ) 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 lgebraically, 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

4 How does the optimal choice change as income changes? n increase in income (with prices fixed) leads to a parallel outward shift of the budget line IH/pF IL/pF IL/p IH/p Change in optimal consumption bundle: IH/pF IL/pF IL/p IH/p s depicted above, initial optimal bundle is and final optimal bundle (after increase in income) is Compared to, bundle has more of good one and more of good two => both goods are normal goods for this increase in income

5 Change in optimal consumption bundle if good two is an inferior good: IH/pF IL/pF IL/p IH/p s depicted above, initial optimal bundle is and final optimal bundle (after increase in income) is Compared to, bundle 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

6 How does the optimal choice change as a price changes? n 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) I/pF Change in optimal consumption bundle: I/pF I/pH I/pL I/pH I/pL s depicted above, initial optimal bundle is and final optimal bundle (after increase in p1) is Compared to, bundle has less of good one and more of good two

7 Why exactly does consumption of each good change? s the price of is increased, there are two effects on the consumer s purchasing behavior: 1 Substitution : Since the price of increased, the relative price of in terms of is now higher Each unit of costs me more units of than it did before s a result, I should substitute some consumption of with increased consumption of 2 Income : Since the price of 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 is introduced to decompose the total effect into these two distinct effects Identify by moving along the initial indifference curve to a point with MRS1,2 equal to the new price ratio (Total ) = (Income ) + (Substitution ) Income I/pF Substitution I/pH I/pL Income Substitution

8 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 were zero? Entire change in consumption of is due to substitution effect Substitution I/pF Income I/pH I/pL Substitution What if were an inferior good (so that the effective decrease in income from the price increase induces the consumer to purchase more )? Total decrease in consumption of is less than the substitution effect (since the income effect works in the opposite direction) Substitution I/pF Income I/pH I/pL Income Substitution

9 What if were an inferior good (so that the effective decrease in income from the price increase induces the consumer to purchase more ) and the income effect was really large in magnitude? Substitution I/pF Income I/pH I/pL Substitution Income s illustrated, in the graph above the income effect on consumption more than offsets the substitution effect, so that the total effect of the increase in the price of is that the consumer purchases more => Law of emand is violated!!!

10 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 budget line price ratio C marginal rate of substitution optimal consumption bundle 2 Thomas buys apples and shoes His income is $2 pples cost $5 per pound and shoes cost $2 per pair Which of the following consumption bundles is within his budget set? 4 pounds of apples and 1 pairs of shoes 12 pounds of apples and 7 pairs of shoes C 6 pounds of apples and 8 pairs of shoes 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: 1 2 p 4 2, and 5 Which of the following consumption bundles is optimal? x * * * x 1 15 and * 2 75 C x * 1 19 * 5 2 * x 2 and * If a consumer realizes an increase in income, his budget line will not change become steeper (with the vertical intercept unchanged) C become flatter (with the vertical intercept unchanged) shift outward (ie, further from the origin) with the slope unchanged 5 The price of pizza increases (with all other prices and income fixed) nn changes her consumption of pizza due to both an income effect and a substitution effect s a result of the substitution effect, she decreases her consumption of pizza by 5 units s a result of the income effect, she decreases her consumption of pizza by 3 units From these observations, we can infer that the total effect of the price change was that she decreased pizza consumption by 8 units the total effect of the price change was that she decreased pizza consumption by 2 units C pizza is an inferior good for nn pizza is a Giffen good for nn

11 6 Consider a consumer with preferences for which x 2 MRS 1,2 This 4x1 consumer s optimal consumption bundle (as a function of prices and income) is * I * 4I x1 and x2 5p1 5 p2 * I * I x1 and x2 2 p1 2 p2 C * I * I x1 and x2 p1 p2 p1 p2 * I p2 * I p1 x1 and x2 2 p 2 p For questions 7 and 8, consider the graph below x C udget Line 1 udget Line 2 x 1 7 The change from udget Line 1 to udget Line 2 would result from a change in consumer preferences an increase in income C an increase in the price of good one an increase in the price of good two 8 The Substitution is illustrated by the change in consumption from ; the Income is illustrated by the change in consumption from to ; to C to C; C to C to C; C to C to ; C to

12 9 Jim is indifferent between the following two consumption bundles: (4,1) and (2,6) Suppose that his preferences over good one and good two satisfy the property of convexity s a result, which of the following consumption bundles must be strictly preferred to bundles and? ( 1,7) ( 29,34) C ( 24,5) ( 2,1) 1 Which of the following statements is correct? ll goods are Giffen goods ll normal goods are Giffen goods C ll inferior goods are Giffen goods ll Giffen goods are inferior goods For questions 11 and 12, consider the graph below x 2 I/p2 E 11 The preferences of this consumer appear to be monotonic and satisfy the property of convexity be monotonic but violate the property of convexity C not be monotonic but satisfy the property of convexity not be monotonic and violate the property of convexity C 12 Which consumption bundle (or bundles) is optimal for this consumer? Only bundle C undles and C are both optimal C undles,, C, and are all optimal Only bundle I/p x 1

13 nswers to Multiple Choice Questions: 1 C C 8 9 C