1. An economist estimated that the cost function of a single-product firm is: TC

Question

1. An economist estimated that the cost function of a single-product firm is:
TC = Q2 — 5Q + 64
Based on this information, determine:
i. The average cost (AC) function ii. The marginal cost function
iii. The fixed cost of producing 10 units of output
iv. The variable cost of producing 10 units of output
v. The total cost of producing 10 units of output
vi. The average fixed cost of producing 10 units of output vii. The average variable of producing 10 units of output viii. The average total cost of producing 10 units of output

Explanation / Answer

The cost function of a single-product firm is:
TC = Q2 - 5Q + 64
Based on this information, determine:
i. The average cost (AC) function: This is given by TC/Q. Hence AC = Q - 5 + 64/Q

ii. The marginal cost function. This is the derivative of TC so MC = 2Q - 5

iii. The fixed cost of producing 10 units of output. Fixed cost is fixed at 64. Hence for Q = 0 or Q = 10 FC is 64

iv. The variable cost of producing 10 units of output. VC = Q2 - 5Q = 10*10 - 5*10 = 50

v. The total cost of producing 10 units of output: FC + VC = 64 + 50 = 114

vi. The average fixed cost of producing 10 units of output: AFC = FC/Q = 64/10 = 6.4

vii. The average variable of producing 10 units of output: AVC = VC/Q = 50/10 = 5

viii. The average total cost of producing 10 units of output: ATC = TC/Q = Q - 5 + 64/Q. ATC = 10 - 5 + 64/10 = 11.4

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