Question

Assume that, in the short-run, K = 16, w = 3, r = 8, and Q = 3 4KL. Graph the Total Cost, Fixed Cost, Variable Cost, Average Total Cost, Average Variable Cost, Average Fixed Cost, and Marginal Cost curves. Label your graph carefully.

Answer 1

Answer:-

The short-run production function is as follows:

Q = (3/4)KL

where K = capital and L = Labor

In short run, capital is fixed at 16 units.

We have wage rate = $3 and Interest on capital = $8

Total Cost = Cost of capital + cost of labor = units of capital*r + units of labor*w

To find TC we must first find out the optimum level of labor.

Lets first put value of K in the production function

Q = 12L

L = Q/12

T.C in short run= 16*8 + (Q/12)*3 = 128 + Q/4

Fixed Cost = 128. ( The constant part of a total cost is fixed cost that does not vary with change in output level)

Variable Cost = Q/4 (As TC=F.C + V.C; V.C = TC-F.C)

Average Total Cost = Tc / Q = 128/Q + 1/4

Average variable Cost = AC/Q = 1/4

Average Fixed Cost = 128

Marginal Cost = Derivative of Tc w.r.t Q = 1/4

The values of each curve at different level of output are as follows:

Plotting the curves as follows: