# estimated cost function

1. Beta Industries manufactures floppy disks that consumers perceive as identical to those produced by numerous other manufacturers. Recently, Beta hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C = 20 +2Q^2. Show all work.

a. What are the firm's fixed costs?

b. What is the firm's marginal cost?

Now suppose other firms in the market sell the product at a price of $10.

c. How much should this firm charge for the product?

d. What is the optimal level of output to maximize profits?

e. How much profit will be earned?

f. In the long run, should this firm continue to operate or shut down? Why?

#### Solution Preview

a. Calculate the average product of labor when 9 units of labor are utilized.

<br>

<br>average product of labor is APl = Q/L = (K^1/2 L^1/2)/L = L^ -1/2

<br>when L=9, Apl= 9^ -1/2 = 1/3

<br>

<br>b. Calculate the marginal product of labor when 9 units of labor are utilized.

<br>

<br>marginal product of labor is MPl = dQ/dL = 1/2* L^ -1/2

<br>when L=9, MPl= 1/2 *1^1/2 * 9^ -1/2 = 1/6

<br>

<br>c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output.

<br>

<br>Profit=100*Q-10*L-Fixed Cost

<br>To maximize profit, MR=MC

<br>MR=100

<br>MC=W/MP = 10/ (1/2* L^ -1/2) = 20 L^ 1/2

<br>Then

<br>100 = 20 L^ 1/2

<br>solve for L=25

<br>then Q= L^1/2= 5

<br>

<br>d. What is the maximum price of capital at which the firm ...

#### Solution Summary

What are the firm's fixed costs? What is the firm's marginal cost?