A firm has a fixed production cost of \(5000 and a constant marginal cost of production of \)500 per unit produced.

1. What is the firm’s total cost function? Average cost?

2. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.

The total cost function is the fixed cost plus variable cost.

The total variable cost is the product of variable cost per unit (marginal cost) and the total number of units.

Suppose the total units are Q. The total variable cost is:

TVC = MC × Q

TVC = $500Q

The total cost function is:

Total Cost = Total Fixed Cost + Total Variable Cost

Total Cost = 5000 + 500Q

The following formula gives the average cost function:

$$\begin{gathered} \mathit{A}\mathit{T}\mathit{C}\mathbf{=}\frac{\mathbf{T}\mathbf{C}}{\mathbf{Q}} \\ ATC=\frac{5000+500Q}{Q} \\ ATC=\frac{5000}{Q}+500 \end{gathered}$$

The total output has to be as maximum as possible to minimize the total cost.The maximum output will reduce the average fixed cost equal to zero.A negligible average fixed cost will result in the average total cost equal to 500, that is, the marginal cost.

Thus, the firm will choose to be maximum to minimize the average total cost.