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Question about Maximum profit

At the deli counter, during the busy lunch hour (12-1 pm), the amount of sandwiches (Q) that can be made is determined by the number of workers (L). Suppose each worker makes $6 per hour and sandwiches sell for $4. Further, you have observed the number of workers and quantity of sandwiches over several days and have estimated the following production function:

Q = 4L - 0:25L2

a. How many workers should Kashian employ during the lunch hour to maximize profits?
(consider the value of the marginal product of labor and the marginal revenue product are the same)

b. Compute the maximum profit at Kashian.
(consider that profit involves Total Revenue and Total Costs)

c. Compute the marginal revenue product of the sixth worker. Explain why it is or is not
profit maximizing to hire a sixth worker.

d. Suppose instead that Kashian wants to keep the lines as short as possible by maximizing
production. How many workers should Kashian employ during the lunch hour?

e. This is an important equation. The United States constantly faces the challenge of outsourcing and imported products. What does this equation tell us about our options in combating outsourcing?

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Solution Preview

Q = 4L - 0.25L^2

A) First, you should observe that a worker is paid $6/hour and each sandwich he makes sells for $4. This means that he needs to make at least 1.5 sandwiches to breakeven (i.e. the marginal productivity of a last unit of labour is $6 and the marginal cost of the last unit of labour is also $6).

Marginal productivity = dQ/dL = 4 - 0.5L = 1.5

solve for L and get L = 5 (i.e. the 5th worker produces 1.5 sandwiches, which equals his wage, further hiring will result in a loss)

Therefore, at lunch time, the deli should hire 5 units of labour.

B) total output when L = 5 is Q = ...