Question

4. Suppose that a consumer faces the choice of how many left shoes to buy and how many right shoes to buy if the price of a shoe is $20 and the consumer has $200 to spend on shoes. (20 points in total) a. Write down the consumer's budget constraint, assuming that we will measure left shoe consumption on the X axis and right shoe consumption on the Y axis. (5 points)

Answer 1

(a)

Budget constraint: 200 = 20L + 20R where L: Number of Left shoe and R: Number of Right shoe

L + R = 10 (dividing both sides by 20)

(b)

From budget constraint, When L = 0, R = 10 (vertical intercept) and when R = 0, L = 10 (Horizontal intercept).

In graph below, AB is the budget line.

Right Allo left

(c)

Revised Budget line: 200 = 10L + 20R  

L + 2R = 20 (dividing both sides by 10)

When L = 0, R = 20/2 = 10 (vertical intercept) and when R = 0, L = 20 (Horizontal intercept).

In the graph above, AC is the new budget line.

(d)

Left and right shoes are used in conjunction (used together). Hence they are complements in consumption, representing fixed-proportion utility function. Such indifference curves are L-shaped.

In following graph, U0, U1 and U2 are three indifference curves, where U2 has higher utility than U1, and U1 has higher utility than U0.

Right