Lecture 9 Exercises: Income and Substitution Effects

Stanford University | Econ 50 | Christopher Makler

Unit II: Consumer Theory

Ex 9.1: Roses and Pho, Part I

Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by the Cobb-Douglas

utility function

u(x1, x2) = x21

x2

Minh's income is m = 24 and the price of red roses is p1 = 4. Tragically, due to higher tariffs on beef

imports, the price of pho is set to rise from p2 = 1 to p2 = 8! Note: there are a bunch of different ways

to do some parts of this question! Clearly show your approach!

(a) Find Minh's Ordinary ("Marshallian") demand functions x

1(p1, p2,m) and x

2(p1, p2,m).

These are the solutions to the utility-maximization problem, max u(x1, x2) s.t. p1x1 + p2x2 = m.

(b) Find Minh's Compensated ("Hicksian") demand functions xc

1(p1, p2,U) and xc

2(p1, p2,U).

These are the solutions to the cost-minimization problem, min p1x1 + p2x2 s.t. u(x1, x2) = U.

(c) In a budget-line/indifference curve diagram (one is provided on the next page), show the Hicks

decomposition of this price change. In particular, draw:

Minh's budget line before and after the price change, labeled BL and BL

her optimal points before and after the price change, labeled A and C

her tangency conditions before and after the price change, labeled TC and TC

her Hicks decomposition point, labeled B, showing her cost-minimizing way of achieving her

old utility at the new prices

the indifference curves passing through points A, B, and C

(d) What is the substitution effect of the price change on her consumption of roses? What is the

income effect? What does that imply about whether roses and pho are complements, substitutes,

or independent goods?