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.
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2. Can a consumer have a perfectly inelastic income elasticity for every good they consume? Explain.
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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
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(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
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∂L/∂Q = ∂Q/∂L = M P1L .
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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?
