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Consumer Choice Theory” ECON 2100 – Principles of Microeconomics (KSU, Prof. Mathews) “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 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 prices 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 goods 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 Indifference Curve – 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”) 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 (i.e., a good for which the “Law of Demand” 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 relative price 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.
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