Question

Suppose it is possible to buy left shoes for a price of $35/shoe and right shoes for a price of $45/shoe. Alex has an annual budget of $1600 for buying shoes, and she has, like most people two feet.

a. Draw Alex’s budget line between left shoes (on the horizontal axis) and right shoes (on the vertical axis). Draw a few of her indifference curves, and show her optimal choice. How many left shoes and how many right shoes does she buy?

b. Now suppose the price of right shoes increases to $65/shoe.

Draw (on the same diagram you used to answer question 8!) her new budget line. What is her optimal choice? How many left shoes and how many right shoes will she buy?

c. Show (on the same diagram you used to answer question 8 and 9!) the income effect and the substitution effect caused by the fall in the price of right shoes on her consumption of left shoes.

d. True or False. Left shoes are an inferior good for Alex.

Answer 1

(a) Budget line: 1600 = 35L + 45R

If L = 0, R = 35.56 (vertical intercept) and if R = 0, L = 45.71 (horizontal intercept).

Since it's a fixed-proportion Utility function with the form: U = min{L, R}, the indifference curves are L-shaped.

Utility is maximized with this function when L = R.

Substituting in budget line,

1600 = 35L + 45L

1600 = 80L

L = 20

R = 20

In following graph, OC) and IC1 are two indifference curves that are drawn. Initially, utility is maximized at point X where indifference curve IC0 is tangent to initial budget line AB. Utility maximizing combination is (L0, R0) = (20, 20).

(b)

New budget line: 1600 = 35L + 65R

If L = 0, R = 24.62 (vertical intercept) and if R = 0, L = 45.71 (horizontal intercept).

Utility is maximized when L = R.

Substituting in new budget line,

1600 = 35L + 65L

1600 = 100L

L = 16

R = 16

In abovegraph, utility is maximized at point Y where new indifference curve IC0 is tangent to new budget line CB. New utility maximizing combination is (L1, R1) = (20, 20).

(c)

For perfect complements, there is no substitutability between the goods when price of one good changes. Hence substitution effect is zero. So total effect (TE) is identical to income effect (IE).

In the graph,

For Left shoes,

TE = IE = Movement from point X to point Y = L1 - L0 = 16 - 20 = - 4

For Right shoes,

TE = IE = Movement from point X to point Y = R1 - R0 = 16 - 20 = - 4

(d)

The statement is False.

For perfect complements, if one good is inferior, it means the other good also must be inferior to satisfy the utility-maximizing condition (L = R). Since both goods cannot be inferior in a two-good model, left shoes cannot be inferior.