Question

A firm needs exactly 4 units of capital and 3 units of labor to produce each unit of output, Q.
Assume the price of capital is P_K a unit and the price of labor is $P_L a unit.
a. If the firm needs Q1 units of output, what are the firm’s conditional factor demands?
b. Find the firm’s total cost function.

Answer 1

a. A firm's conditional factor demand is the combination of inputs required to produce a specified amount of output at a minimum cost. Such a thing is possible when the proportion of inputs can be altered in response to their marginal product and relative costs. In this case, however, the factor proportions are already fixed at 4 units of capital and 3 units of labor for each unit of output. Hence the factor demand for Q1 units of output would be:

4*Q1 units of capital

3*Q1 units of labor

b. The firm's total cost function is as follows for a quantity Q of output:

Cost = $P_K*4*Q + $P_L*3*Q

where $P_K is the price per unit of capital and $P_L the price of each unit of labor. Q is the variable which specifies the number of units of output