Question

The short-run cost function of a company is given by the equation TC=200+55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.
a. What is the company’s fixed cost?
b. If the company produced 100,000 units of goods, what would be its average variable cost?
c. What would be its marginal cost of production?
d. What would be its average fixed cost?
e. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1000 units. The cost of interest (i) also enters into the
equation. Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation.

Answer 1

Answer on Question #44220 – Economics – Microeconomics

The short-run cost function of a company is given by the equation $TC = 200 + 55q$, where TC is the total cost and q is the total quantity of output, both measured in thousands.

a. What is the company's fixed cost (FC)?

Total cost is the sum of fixed and variable costs ($TC = FC + VC$) and FC is constant for any quantity produced, so $FC = \$200$ thousands.

b. If the company produced 100,000 units of goods, what would be its average variable cost?

$AVC = (TC - FC)/q = 55q/q = \$55$ thousands.

c. What would be its marginal cost of production?

Marginal cost (MC) is the derivative of total cost (TC), so $MC = \$55$ thousands for any amount of quantity produced.

d. What would be its average fixed cost?

$AFC = FC/q = 200,000/100,000 = \$2$ thousands

e. Suppose the company borrows money and expands its factory. Its fixed cost rises by \$50,000, but its variable cost falls to \$45,000 per 1000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by \$3000. Write the new cost equation.

New equation will be $TC = 250 + 45q + 3000i$

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