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production function

Need help solving this homework problem for study.

A firm can manufacture a porduct accouding to the porduction function:
Q = F (K,L) = K 3/4 L 1/4

a. Calculate the average product, AP L, when the level of captial is fixed at 16 units, and firm uses 16 units of labor. How does the average production of labor change when the firm uses 81 units of labor?

b. Find an expression for the marginal product of labor, MP L , when the amount of capital is fixed at 16 units, and then illustrate that mardinal producer of labor depends on the amount of of labor hired by calculating the marginal porducto of labor for 16 and 81 units of labor.?

c. Suppose capital is fixed at 16 units. IF the firm is can sell its outpurt at a price of $100.00 per unit and can hire labor at $25.00 per unit, how many units of labor should the firm gire in roder to maximize the profits?

Solution Preview

A firm can manufacture a porduct accouding to the production function:
Q = F (K,L) = K^3/4 L^1/4

a. AP L = Q/L
So we have APL = K^3/4 L^-3/4
AP L (K=16, L=16) = (16)^3/4(16)^-3/4=1
AP L (K=16, L=81) = (16)^3/4(81)^-3/4=0.296
when the level ...

Solution Summary

Apply the production function.

$2.19