Can a consumer have a perfectly inelastic income elasticity for every good they consume? Explain.

Draw the budget constraints, indifference curves

Draw the budget constraints, indifference curves

Question
 1
. Draw the budget constraints, indifference curves, and the income consumption curve

for a good (bagels) that has an income elasticity that is perfectly inelastic on horizontal

axis, and another normal good on (salads) on the vertical axis
.

2
. Can a consumer have a perfectly inelastic income elasticity for every good they consume? Explain
.

2

Problem Set 4

3
. Koichiro and Sylvia are starting a new high-volume Sushi restaurant, called Robo Sushi

in Davis
. While Koichiro plans to manage the business himself, he needs to employ

some combination of workers and “sushi-bots” (sushi-making robots) to produce the

sushi
. He estimates his production function as

q = 100L0
.5 K 0
.5

where q is the number of Sushi rolls, L is worker hours and K is sushi-bot hours
.

Workers cost $10/hour and the amortized cost of sushi-bots is equivalent to $40/hr
.

(a) Derive Koichiro’s marginal product of labor as a function of output level q and

labor quantity L
.

(b) Koichiro needs to produce 5000 sushi-rolls per day or corporate headquarters

will fire him
. Using the substitution method, what combination of Labor and

Sushi-bots should he employ to minimize his cost? What will be hist total cost

of making 5000 rolls?

Problem Set 4

3

(c) Suppose that a surge in lunch-time demand forces Koichiro to increase his output

of Sushi quickly
. He can only add worker-hours, and does not have time to

add sushi-bots
. What is his short-run marginal cost of sushi? Hint: think of

1

∂L/∂Q = ∂Q/∂L = M P1L 
.

4

Problem Set 4

4
. You are considering setting up a business manufacturing and selling giant foam hands

(with fingers making the #1 gesture)
. The market for giant foam fingers is very

competitive and the cost of one firm is given by C (q) = q 2 − 10q + 64
. All firms are

identical and firms are free to enter or to exit the industry
. Assume that the price for

foam fingers is $10
.

(a) What are the average total cost, average variable cost, and marginal cost functions

for a single firm?

(b) Suppose you are already operating
. If the market price for foam fingers were $10,

how many would you produce to maximize your profit?

Draw the budget constraints, indifference curves

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