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 a... nd “sushi-bots” (sushi-making robots) to produce the
sushi. He estimates his production function as
q = 10L
0.5K
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) Koichiro wants to produce the maximum number of sushi-rolls possible while
spending no more than $3,000/hr. Using the substitution method, what combination of Labor and Sushi-bots should he employ to maximize his output? How
many sushi rolls can he make?
(b) 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
∂L/∂Q =
1
∂Q/∂L =
1
MPL
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