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?

... do you feel best estimates cost functions for both ...costs could be appropriately estimated using the ... any other methods of estimating cost functions other than ...

... Notice that the linear cost function estimated using the regression ... method that can result in better estimates of cost... can be easily used to estimate a variety ...

... 1. Using the high-low method, estimate the linear ... the coming year, what should its estimated operating budget ... 10-22 Estimating a cost function, high-low method ...

... How would you determine the most important cost driver when estimating cost functions in the ... explains how to determine the cost driver and cost function for a ...

... be indifferent about hiring decision if benefit equals cost. ... S, A, and R to estimate the following ... director is comfortable using parameter estimates that are ...

... 1. Run the appropriate regression to estimate the average ... the algebraic signs of the three parameter estimates. ... answer in 1, show the estimated total variable ...

... The problem set deals with estimating total cost...costs of Sunday openings are estimated at $24,960 ... Sunnybrook estimates that 60% of its potential Sunday sales to ...

... are interested in estimating past cost... Industrial engineering method : Estimates cost functions by analyzing ... Conference method: Estimates cost function on the ...

... Recently, Beta hired an econometrician to estimate its cost... The estimated cost function is C = 20 +2Q2 ... Based on the estimates provided by a consultant, you know ...

... originally estimated at $15 million, is going to be ... Good sense suggests pro- ject estimates should come from ... people most knowledgeable about the estimate needed ...