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

Question

An economist estimated that the cost function of a single-product firm is: C(J = 70 + 300+20 Q2 + 1003 Based a. The fixed cost of producing 10 units of output. on this information, determine the following: 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

1)

a) FC = 70 (Cost when Q = 0)

b) VC = TC - FC = 12300

c) TC = 12370 (place Q = 10 in the cost equation)

d) AFC = FC/10 = 7

e) AVC = VC/10 = 1230

f) ATC = TC/10 = 1237

g) MC = dC/dQ = 30 + 40Q + 30Q2

MC = 30 + 400 + 3000 = 3430

2)

a) Output produced = min (2x2, 4x3) = 4 units

b) 4 units of output would require : 2K = 4L = 4

K = 2 and L = 1

c) Answer would not change as K =2 and L = 1 are the minimum inputs required to produce 4 units of output

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