What is the optimal combination of labor and capital?

Suppose a firm’s technology is described by a production function where the quantity produced is equal to the square root of capital times labor (that is, Q = √(L●K)

a. Using graph paper, draw the isoquant for output = 8 units.

b. Suppose the firm has $128 to spend on its variable inputs and the price of L and K is $8. On the same graph on which you drew the isoquant, draw the isocost line. What is the optimal combination of labor and capital?

c. Suppose the price of labor increases to $16 and the price of capital decreases to $4. draw the new isocost line and determine the new optimal combination of labor and capital.

d. Repeat c) for price of labor at $4 and capital at $16.

 
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