A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4 . The price of output is $12 and the factor price is $3. The amount of the factor that the firm demands is
A)64
B)16
C)60
D)8
E) None of the above.

Question

A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4  . The price of output is $12 and the factor price is $3. The amount of the factor that the firm demands is
A)64 
B)16 
C)60 
D)8 
E) None of the above.

Quizplus · Accepted Answer

To maximize profit, the firm will choose the quantity of input such that the marginal revenue product (MRP) of the input is equal to the factor price ($3 in this case).

The MRP of the input is given by the marginal product of the input (MP) times the price of the output (P):

MRP = MP x P

The marginal product of the input in this case is:

MP = dQ/dx = 44x^(3/4)

So, the MRP of the input is:

MRP = 44x^(3/4) x $12 = $528x^(3/4)

Setting this equal to $3 and solving for x:

$528x^(3/4) = $3

x^(3/4) = $3/$528 = 1/($176)

x = (1/($176))^4 = 64

So, the firm demands 64 units of the input to maximize profit. Therefore, the correct choice is A) 64.

A Profit-Maximizing Competitive Firm Uses Just One Input, X