Economics: Production of Function Estimates

You are a consultant for Smith Restaurants.

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 Smith employ during the lunch
hour to maximize profits?

(note—consider the value of the marginal product of labor
and the marginal revenue product are the same)

b. Compute the maximum profit at Smith.

(note—consider that profit involves Total Revenue and Total

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 Smith wants to keep the lines as
short as possible by maximizing

production. How many workers should Smith 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?