Question

1. An economist estimated that the cost function of a single-product firm is: Cost(Q) = 200 + 10Q + 20Q2 + 5Q3 ; based on this equation calculate:

a. The fixed cost of producing 8 units of output

b. The variable cost of producing 8 units of output

c. The total cost of producing 8 units of output

d. The average fixed cost of producing 8 units of output

e. The average variable cost of producing 8 units of output

f. The average total cost of producing 8 units of output

g. The marginal cost when producing 8 units of output

Answer 1

a. The fixed cost of producing 8 units of output

Cost(Q) = 200 + 10Q + 20Q^2 + 5Q^3

FC=the cost is same at all level and it is equal to the total cost at Q=0 and it is a constant term in the cost function

FC=200 at all level of output

b. The variable cost of producing 8 units of output

VC=TC-FC=the cost function except constant term =10Q + 20Q^2 + 5Q^3=10*8 + 20*8^2 + 5*8^3=3920

c. The total cost of producing 8 units of output

TC=FC+VC=200+3920=4120

d. The average fixed cost of producing 8 units of output

AFC=FC/Q

AFC=200/8=25

e. The average variable cost of producing 8 units of output

AVC=VC/Q=3920/8=490

f. The average total cost of producing 8 units of output

ATC=AFC+AVC=25+490=515

g. The marginal cost when producing 8 units of output

MC=dC/dQ=10+40Q+15Q^2

Q=8

MC=10+40*8+15*8^2=1290