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) = 110 + 20Q + 30Q2 + 10Q3. Based on this information, determine the following:

a. The fixed cost of producing 10 units of output. $ 110

b. The variable cost of producing 10 units of output. $ 13200

c. The total cost of producing 10 units of output. $ 13310

d. The average fixed cost of producing 10 units of output. $ 11

e. The average variable cost of producing 10 units of output. $ 1320

f. The average total cost of producing 10 units of output. $ 1330

g. The marginal cost when Q = 10. $ 3620

Explanation / Answer

C(Q) = 110 + 20Q + 30Q^2 + 10Q^3

a.       Fixed cost= Constant term in above equation=$110

b.      Variable cost =20Q + 30Q^2 + 10Q^3

Variable cost for 10 units=20*10+30*(10^2)+10*(10^3)= 13200

c.       The total cost for 10 units = Fixed cost + Variable cost=13200+110=13310

d.      The average fixed cost for 10 units= fixed cost/Quantity =110/10=11

e.      The average variable cost of producing 10 units = Variable cost/Unit=13200/10=1320

f.        The average total cost of producing 10 units=Total cost=Total cost/unit=13310/10=1331

g.       The marginal cost=d(C(Q)/dQ=20+60Q+30*Q^2 =20+60*10+30*(10^2)=3620

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