Managerial Economics & Business Strategy Chapter 4 The Theory of Individual Behavior McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Overview I. Consumer Behavior Indifference Curve Analysis. Consumer Preference Ordering. II. Constraints The Budget Constraint. Changes in Income. Changes in Prices. III. Consumer Equilibrium IV. Demand Curves Individual Demand. Market Demand. 4-2
Consumer Behavior Consumer Opportunities The possible goods and services consumer can afford to consume. Consumer Preferences The goods and services consumers actually consume. Given the choice between 2 bundles of goods a consumer either: Prefers bundle A to bundle B: A B. Prefers bundle B to bundle A: A B. Is indifferent between the two: A ~ B. 4-3
Indifference Curve Analysis Indifference Curve Good Y A curve that defines the combinations of 2 or more goods that give a consumer the same level of satisfaction. I. II. III. Marginal Rate of Substitution The rate at which a consumer is willing to substitute one good for another and maintain the same satisfaction level. Good X 4-4
Consumer Preference Ordering Properties Completeness More is Better Diminishing Marginal Rate of Substitution Transitivity 4-5
Complete Preferences Completeness Property Consumer is capable of expressing preferences (or indifference) between all possible bundles. ( I don t know is NOT an option!) If the only bundles available to a consumer are A, B, and C, then the consumer Good Y I. A II. III. B w is indifferent between A and C (they are on the same indifference curve). C w will prefer B to A. w will prefer B to C. Good X 4-6
More Is Better! More Is Better Property Bundles that have at least as much of every good and more of some good are preferred to other bundles. Bundle B is preferred to A since B contains at least as much of good Y and strictly more of good X. Bundle B is also preferred to C since B contains at least as much of good X and strictly more of good Y. More generally, all bundles on IC III are preferred to bundles on IC II or IC I. And all bundles on IC II are preferred to IC I. Good Y I. 100 33.33 A II. III. B C 1 3 Good X 4-7
Diminishing MRS MRS The amount of good Y the consumer is willing to give up to maintain the same satisfaction level decreases as more of good X is acquired. The rate at which a consumer is willing to substitute one good for another and maintain the same satisfaction level. To go from consumption bundle A to B the consumer must give up 50 units of Y to get one additional unit of X. To go from consumption bundle B to C the consumer must give up 16.67 units of Y to get one additional unit of X. To go from consumption bundle C to D the consumer must give up only 8.33 units of Y to get one additional unit of X. Good Y 100 50 33.33 25 I. A II. B III. C 1 2 3 4 D Good X 4-8
Consistent Bundle Orderings Transitivity Property For the three bundles A, B, and C, the transitivity property implies that if C B and B A, then C A. Transitive preferences along with the more-is-better property imply that Good Y I. 100 75 A II. III. C indifference curves will not intersect. 50 B the consumer will not get caught in a perpetual cycle of indecision. 1 2 5 7 Good X 4-9
The Budget Constraint Opportunity Set The set of consumption bundles that are affordable. P x X + P y Y M. Budget Line The bundles of goods that exhaust a consumers income. P x X + P y Y = M. Market Rate of Substitution The slope of the budget line -P x / P y. M/P Y Y The Opportunity Set Budget Line Y = M/P Y (P X /P Y )X M/P X X 4-10
Changes in the Budget Line Changes in Income Increases lead to a parallel, outward shift in the budget line (M 1 > M 0 ). Decreases lead to a parallel, downward shift (M 2 < M 0 ). Changes in Price A decreases in the price of good X rotates the budget line counter-clockwise (P X0 > P X1 ). An increases rotates the budget line clockwise (not shown). Y M 1 /P Y M 0 /P Y M 2 /P Y Y M 0 /P Y M 2 /P X M 0 /P X M 1 /P X New Budget Line for a price decrease. X M 0 /P X0 M 0 /P X1 X 4-11
Consumer Equilibrium The equilibrium consumption bundle is the affordable bundle that yields the highest level of satisfaction. Consumer equilibrium occurs at a point where MRS = P X / P Y. Equivalently, the slope of the indifference curve equals the budget line. (Tangency condition) Y M/P Y Consumer Equilibrium I. III. II. M/P X X 4-12
Income Changes and Equilibrium Normal Goods Good X is a normal good if an increase (decrease) in income leads to an increase (decrease) in its consumption. Inferior Goods Good X is an inferior good if an increase (decrease) in income leads to a decrease (increase) in its consumption. 4-13
Normal Goods & Inferior Goods Y: An increase in income increases the consumption of normal goods. Y M 1 /Y Y 1 B X: An increase in income decreases the consumption of inferior goods. (M 0 < M 1 ). II (M 0 < M 1 ). M 0 /Y A Y 0 I 0 X 1 X 0 M 0 /X M 1 /X X 4-14
Price Changes and Equilibrium Substitution Effect: The change in the amount of a good that would be consumed as the price of that good changes, holding constant all other prices and the level of utility. Income Effect: The change in the amount of a good that a consumer would buy as purchasing power changes, holding all prices constant. 4-15
Decomposing the Income and Substitution Effects Initially, bundle A is consumed. A decrease in the price of good X expands the consumer s opportunity set. The substitution effect (SE) causes the consumer to move from bundle A to B. Y X is inferior good and Y is normal good. C A higher real income allows the consumer to achieve a higher indifference curve. A II The movement from bundle B to C represents the income effect (IE). The new equilibrium is achieved at point C. B I 0 SE IE 4-16 X
Decomposing the Income and Substitution Effects Initially, bundle A is consumed. A decrease in the price of good X expands the consumer s opportunity set. The substitution effect (SE) causes the consumer to move from bundle A to B. Y Both X and Y are normal goods. A higher real income allows the consumer to achieve a higher indifference curve. The movement from bundle B to C represents the income effect (IE). The new equilibrium is achieved at point C. A B C II I 0 SE IE X 4-17
Income and Substitution Effects Example U(x,y) = xy P x =1, P y =6, P y2 = 4, M = 48. Step 1: Old equilibrium: Bundle A MU x = y and MU y = x MU x /MU y = y/x = 1/6 6y = x 48 = P x x + P y y = x + 6y = 6y + 6y = 12y y A = 4, x A = 6y = 24, U A = xy = 24*4 = 96. 4-18
Income and Substitution Effects Example Step 2: New Equilibrium: Bundle C MU x /MU y = y/x = 1/4 so 4y = x 48 = P x x + P y2 y = x + 4y = 4y + 4y = 8y 48 = 8y y C = 6, x C = 4y = 24 Step 3: Decomposition Bundle B xy = U A = 96 & y/x = ¼ so x = 4y. Plug into U. 4y*y = 96 4y 2 = 96 y B = (24), x B = 4 (24) 4-19
Income and Substitution Effects SE for y: Example y decomposition basket y initial basket = (24) 4 = 0.9. Lower price of y increases the consumption for y. IE for y: y final basket y decomposition basket = 6 (24) = 1.1. Lower price of y leads to an increase in real income, positive IE means y is normal good. Total change in y = 6 4 = 2 (=1.1+0.9). 4-20
Application: A Classic Marketing Other goods (Y) A buy-one, getone free pizza deal. A C D E I II 0 0.5 1 2 B F Pizza (X) 4-21
Application: Joining a Club Suppose Neil spends $400 per month on golf and other things. 9 holes of golf is $16, but if Neil buys a pass for $150, 9 holes is only $8. Other goods (Y) 400 250 I A II B 0 18.75 23 25 50 Golf (X) 4-22
Individual Demand Curve Y An individual s demand curve is derived from each new equilibrium point found on the indifference curve as the price of good X is varied. $ P 0 P 1 D I II X X 0 X 1 X 4-23
Individual Demand Calculation Example U(x,y) = xy with P x, P y, and M. Step 1: MU x = y and MU y = x Step 2: MRS x,y = y/x = P x /P y è y = xp x /P y Step 3: M = P x x + P y y = P x x + P y * xp x /P y = 2P x x è x = M/2P x àdemand for x Step 4: y = xp x /P y = M/2P x * P x /P y = M/2P y è Demand for y 4-24
Market Demand The market demand curve is the horizontal summation of individual demand curves. It indicates the total quantity all consumers would purchase at each price point. $ Individual Demand Curves $ Market Demand Curve 50 40 D 1 D 2 1 2 Q 1 2 3 D M Q 4-25
Market Demand Calculation Example Suppose that Bart and Homer are the only two people who drink beer. Their inverse demand curves are respectively P = 10 4 Qb and P = 25 2 Qh. Write down market demand curve for all possible prices. Bart will only consume when the price is less than 10. Therefore his demand curve for beer is Qb = 2.5 0.25P when P <10 and zero otherwise. Homer will only consume if the price is less than 25. So his demand curve is Qh = 12.5 0.5P when P < 25 and zero otherwise. 4-26
Market Demand Calculation Example The market demand curve is Q M = 0, if P 25 Q M = 12.5 0.5P, if 10 P < 25 Q M = 15 0.75P, if P < 10 4-27
Conclusion Indifference curve properties reveal information about consumers preferences between bundles of goods. Completeness. More is better. Diminishing marginal rate of substitution. Transitivity. Indifference curves along with price changes determine individuals demand curves. Market demand is the horizontal summation of individuals demands. 4-28