The total cost function of a company is given by the equation: TC = 1 900 000 +

Question

The total cost function of a company is given by the equation:

              TC = 1 900 000 + 530 000Q.

a) Derive the company’s average variable cost and average total cost equations.

b) Derive the marginal cost and average fixed cost equations.

c) If the firm wanted to minimise the ATC of production, would it choose to be very large or very small? Explain.

d) Suppose the company borrows money and expands its factory. Its fixed cost rises by $50 000, its variable cost falls by $50 000 and each one-point increase in the interest rate raises costs by $30 000. Write the new total cost equation.

Explanation / Answer

a) Averga variable cost = 530000Q / Q = 530000

average total cost = 1900000 + 530000Q / Q

ATC = 1900000 / Q + 530000

b) MArginal cost =1900000 + 530000Q

differentitate it with respect to Q

MC = 530000

average fixed equations = 1900000 / Q

C) If firm wanted to minimise the ATC of production, the firm choose to be very large because when firm become very large its production also increases to very large, then avergae total cost declines because we know that, avergae total cost declines as the number of output increases.

D) TC = 1900000 +50000 +530000Q - 50000Q+30000i

TC = 1950000 + 480000Q + 30000i

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