Answer:
a) We have:
The firms total cost function: TC = 5,000 + 500Q
Average cost: ATC = (5,000 / Q) + 500
b)The firm would choose to be very large if it wanted to minimize the average total cost.
Explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
A firm has a fixed production cost of 5,000 and a constant marginal cost of production of 500 per unit produced.
a) What is the firms total cost function? Average total cost?
b) If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
The explanation of the answer is now provided as follows:
a) What is the firms total cost function? Average total cost?
Let Q represents quantity of output produced by the firm.
Since the marginal cost of production is constant, this implies:
VC = Variable cost = 500 * Q = 500Q
Also, we have:
FC = Fixed production cost = 5,000
Since TC = FC + VC, the total cost function (TC) can then be obtained as follows:
TC = 5,000 + 500Q
Since ATC = TC / Q, the average cost (ATC), can also be obtained as follows:
ATC = (5,000 / Q) + (50Q/Q)
ATC = (5,000 / Q) + 500
Therefore, we have:
The firms total cost function: TC = 5,000 + 500Q
Average cost: ATC = (5,000 / Q) + 500
b) If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
The firm would choose to be very large if it wanted to minimize the average total cost.
Because fixed expenses dominate total costs at low levels of output, average total cost starts out high. In terms of Mathematics, the denominator is so tiny that average total cost is huge. As fixed costs are spread over a larger quantity of output, the average total cost decreases. Therefore, the firm would choose to be very large if it wanted to minimize the average total cost.
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