Question

1. Assume a firm’s total cost function is:- TC=12+60Q-15Q2+Q3
Required: Suppose that the firm produces 20 units of output. Calculate
Total fixed cost (TFC),
Total variable cost (TVC),
Average total cost (ATC),
Average fixed cost (AFC),
Average variable cost (AVC), and
Marginal cost (MC).

Answer 1

Total fixed cost (TFC)

The fixed cost is the cost that remains constant regardless of the level of production. Based on the above function the total fixed cost is:

$\text{Total fixed cost}=12$

Total variable cost (TVC)

Variable cost refers to the cost that varies with the level of production. The total vriable cost is:

$\text{Total variable cost}=60Q-15Q^2+Q^3$

$\text{Total variable cost}=60\times20-15\times 20^2+20^3$

$\text{Total variable cost}=3,200$

Average total cost (ATC)

Average total cost is computed using the following formula:

$\text{Average total cost}=\dfrac{\text{Total cost}}{\text{Total Quantity}}$

$\text{Average total cost}=\dfrac{12+60Q-15Q^2+Q^3}{Q}$

$\text{Average total cost}=\dfrac{12+60 \times 20- 15\times 20^2+20^3}{20}=160.6$

Average fixed cost (AFC)

The average fixed cost is estimated using the following formula:

$\text{Average fixed cost}=\dfrac{\text{Total fixed cost}}{\text{Quantity/Output}}$

$\text{Average fixed cost}=\dfrac{12}{Q}=\dfrac{12}{20}=0.6$

Average variable cost (AVC)

The variable cost is estimated by the following formula:

$\text{Average variable cost}=\dfrac{\text{Variable cost}}{\text{Output}}$

$\text{Average variable cost}=\dfrac{3200}{20}=160$

Marginal cost (MC)

The marginal cost is the derivative of the total cost function.

$\dfrac{\Delta \text{Total cost}}{\text{Output}}=60-30Q+3Q^2$

$\text{Marginal cost}=60-30\times 20+3\times 20^2=660$

$\text{Marginal cost}=660$