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

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

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

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

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

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

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

… 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

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

PCC for u = x1x2 Price of good 1 drops

S maximizes utility over budget Bn PCC for u = x1x2 S maximizes utility over budget Bn

PCC for u = x1x2 Unchanged!

T maximizes utility for an intermediate budget PCC for u = x1x2 T maximizes utility for an intermediate budget

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

… 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

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

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

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

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

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

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

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

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

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

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

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 =

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 =

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 =

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

Hicks-Allen Decomposition Bundle A maximizes utility over budget Bo

Hicks-Allen Decomposition Bundle C maximizes utility over budget Bn

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

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

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

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

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

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

Slutsky Decomposition Bundle A maximizes utility over budget Bo

Slutsky Decomposition Bundle C maximizes utility over budget Bn

Slutsky Decomposition Price effect: Movement from A to C

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

Slutsky Decomposition Find B that maximizes utility on dashed budget

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