An economist estimated that the cost function of a single-product firm is: C(Q)

Question

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

C(Q) = 100 + 20Q + 15Q2 + 10Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output. $

b. The variable cost of producing 10 units of output. $

c. The total cost of producing 10 units of output. $

d. The average fixed cost of producing 10 units of output. $

e. The average variable cost of producing 10 units of output. $

f. The average total cost of producing 10 units of output. $

g. The marginal cost when Q = 10. $

Explanation / Answer

C(Q) = 100 + 20Q + 15Q2 + 10Q3

(a) Fixed cost (FC) = $100 (which is fixed irrespective of output level)

(b) Variable cost (VC) = 20Q + 15Q2 + 10Q3

When Q = 10, VC = (20 x 10) + (15 x 10 x 10) + (10 x 103) = 200 + 1,500 + 10,000 = $11,700

(c) Total cost (TC) = FC + VC = $(100 + 11,700) = $11,800

(d) Average fixed cost (AFC) = FC/Q = $100 / 10 = $10

(e) Average variable cost (AVC) = VC/Q = $11,700 / 10 = $1,170

(f) Average total cost (ATC) = TC/Q = $11,800 / 10 = $1,180

(g) Marginal cost (MC) = dC(Q)/dQ = 20 + 30Q + 30Q2

When Q = 10, MC = 20 + (30 x 10) + (30 x 10 x 10) = 20 + 300 + 3,000 = $3,320

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