1 Chapter 5 Consumer Comparative StaticsIntermediate Microeconomics: A Tool-Building Approach Routledge, UK © 2016 Samiran Banerjee

2 Price Consumption Curve (PCC)Keeping everything else fixed, how do the utility-maximizing bundles change as the price of one good changes? • Keep income, m, fixed • Keep price of good 2, p2, fixed • Keep preferences fixed • Suppose price of good 1 drops from p1old to p1new

3 R maximizes utility over budget BoPCC for u = min{x1, x2} Leontief R maximizes utility over budget Bo

4 PCC for u = min{x1, x2} Price of good 1 drops

5 S maximizes utility over budget BnPCC for u = min{x1, x2} S maximizes utility over budget Bn

6 T maximizes utility for an intermediate budgetPCC for u = min{x1, x2} T maximizes utility for an intermediate budget

7 As the budget goes from Bo to Bn…PCC for u = min{x1, x2} As the budget goes from Bo to Bn…

8 … it traces the PCC as the line joining R and SPCC for u = min{x1, x2} … it traces the PCC as the line joining R and S

9 R maximizes utility over budget BoPCC for u = x1x2 Cobb- Douglas R maximizes utility over budget Bo

10 PCC for u = x1x2 Price of good 1 drops

11 S maximizes utility over budget BnPCC for u = x1x2 S maximizes utility over budget Bn

12 PCC for u = x1x2 Unchanged!

13 T maximizes utility for an intermediate budgetPCC for u = x1x2 T maximizes utility for an intermediate budget

14 As the budget goes from Bo to Bn…PCC for u = x1x2 As the budget goes from Bo to Bn…

15 … it traces the PCC as the line joining R and SPCC for u = x1x2 … it traces the PCC as the line joining R and S

16 Income Consumption Curve (ICC)Keeping everything else fixed, how do the utility-maximizing bundles change as income changes? • Keep price of good 1, p1, fixed • Keep price of good 2, p2, fixed • Keep preferences fixed • Suppose income increases from mold to mnew

17 R maximizes utility over budget BoICC for u = x1x2 Cobb- Douglas R maximizes utility over budget Bo

18 Income rises from mo to mnICC for u = x1x2 Income rises from mo to mn

19 S maximizes utility over budget BnICC for u = x1x2 S maximizes utility over budget Bn

20 The ICC is the line joining R and SICC for u = x1x2 The ICC is the line joining R and S

21 R maximizes utility over budget BoICC for u = 2√x1 + x2 Quasilinear R maximizes utility over budget Bo

22 Income rises from mo to mnICC for u = 2√x1 + x2 Income rises from mo to mn

23 S maximizes utility over budget BnICC for u = 2√x1 + x2 Unchanged! S maximizes utility over budget Bn

24 The ICC is the line joining R and SICC for u = 2√x1 + x2 The ICC is the line joining R and S

25 Individual demand elasticitiesKeeping everything else fixed, what is a consumer’s demand elasticity when • its own price changes? Own-price elasticity of demand • when the price of another good changes? Cross-price elasticity of demand • when income changes? Income elasticity of demand

26 Own-price elasticitiesSuppose a consumer has demand functions for good 1 and good 2. The own price-elasticity for good 1 is The own price-elasticity for good 2 is ∂x1 ∂p1 p1 x1 . ε11 = “epsilon” ∂x2 ∂p2 p2 x2 . ε22 =

27 Cross-price elasticitiesSuppose a consumer has demand functions for good 1 and good 2. The cross price-elasticity for good 1 is The cross price-elasticity for good 2 is ∂x1 ∂p2 p2 x1 . ε12 = ∂x2 ∂p1 p1 x2 . ε21 =

28 Income elasticities Suppose a consumer has demand functions for good 1 and good 2 The income elasticity for good 1 is The income elasticity for good 2 is ∂x1 ∂m m x1 . η1 = “eta” ∂x2 ∂m m x2 . η2 =

29 Price Effect DecompositionKeeping everything else fixed, how does the quantity demanded of a good change as its price changes? Price effect (PE) = Substitution effect (SE) + Income effect (IE) Substitution effect: Consumer’s desire to purchase more of a good that is relatively cheaper Income effect: Consumer’s desire to purchase more of a good because a price drop increases purchasing power

30 Hicks-Allen DecompositionBundle A maximizes utility over budget Bo

31 Hicks-Allen DecompositionBundle C maximizes utility over budget Bn

32 Hicks-Allen DecompositionPrice effect: Movement from A to C

33 Hicks-Allen DecompositionMove Bn back until uo is barely reached at B From C, reduce m to attain old utility at new prices

34 Hicks-Allen DecompositionSubstitution effect: Movement from A to B

35 Hicks-Allen DecompositionPositive IE reinforces SE Normal good case: SE > 0, IE > 0

36 Hicks-Allen DecompositionNegative IE dampens SE “Slightly” inferior good case: SE > 0, IE < 0, PE > 0

37 Hicks-Allen DecompositionNegative IE swamps SE Giffen good “Very inferior” good case: SE > 0, IE < 0, PE < 0

38 Slutsky DecompositionBundle A maximizes utility over budget Bo

39 Slutsky DecompositionBundle C maximizes utility over budget Bn

40 Slutsky DecompositionPrice effect: Movement from A to C

41 Slutsky DecompositionMove Bn back until it passes through A From C, reduce m to attain old bundle A at new prices

42 Slutsky DecompositionFind B that maximizes utility on dashed budget

43 Slutsky DecompositionSE is movement from A to B, IE from B to C