1. Chapter 5 Consumer Comparative Statics
Intermediate 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 Bo
PCC 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 Bn
PCC for u = min{x1, x2}
S maximizes utility over budget Bn

6. T maximizes utility for an intermediate budget
PCC 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 S
PCC for u = min{x1, x2}
… it traces the PCC as the line joining R and S

9. R maximizes utility over budget Bo
PCC 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 Bn
PCC for u = x1x2
S maximizes utility over budget Bn

12. PCC for u = x1x2
Unchanged!

13. T maximizes utility for an intermediate budget
PCC 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 S
PCC 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 Bo
ICC for u = x1x2
Cobb-
Douglas
R maximizes utility over budget Bo

18. Income rises from mo to mn
ICC for u = x1x2
Income rises from mo to mn

19. S maximizes utility over budget Bn
ICC for u = x1x2
S maximizes utility over budget Bn

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

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

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

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

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

25. Individual demand elasticities
Keeping 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 elasticities
Suppose 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 elasticities
Suppose 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 Decomposition
Keeping 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 Decomposition
Bundle A maximizes utility over budget Bo

31. Hicks-Allen Decomposition
Bundle C maximizes utility over budget Bn

32. Hicks-Allen Decomposition
Price effect: Movement from A to C

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

34. Hicks-Allen Decomposition
Substitution effect: Movement from A to B

35. Hicks-Allen Decomposition
Positive IE reinforces SE
Normal good case: SE > 0, IE > 0

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

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

38. Slutsky Decomposition
Bundle A maximizes utility over budget Bo

39. Slutsky Decomposition
Bundle C maximizes utility over budget Bn

40. Slutsky Decomposition
Price effect: Movement from A to C

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

42. Slutsky Decomposition
Find B that maximizes utility on dashed budget

43. Slutsky Decomposition
SE is movement from A to B, IE from B to C