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# maximum price of capital

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The manager of a national retailing outlet recently hired an economist to estimate the firm's production function. Based on the economist's report, the manager now knows that the firm's production function is given by Q = K^1/2L^1/2 and that capital is fixed at 1unit.

a. Calculate the average product of labor when 9 units of labor are utilized.
b. Calculate the marginal product of labor when 9 units of labor are utilized.
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.
d. What is the maximum price of capital at which the firm will still make non-negative profits?

https://brainmass.com/economics/production-function/maximum-price-of-capital-18156

#### 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. ...

#### Solution Summary

What is the maximum price of capital at which the firm will still make non-negative profits?

\$2.49