Question

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

C(Q) = 50 + 30Q + 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.

$  

Answer 1

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

$50

Reason- fixed cost the cost when Q=0. C(0) = 50 + 30*0 + 15(0)² + 10(0)³.

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

$ 11800

Reason- Variable cost is the cost which varies with the Quantity. C(10) = 30(10)+ 15(10)² + 10(10)³

300+ 1500+10000= $11800

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

$ 11850

Reason- Total cost= Fixed cost+ variable cost = 50+11800= $11850

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

$5

Reason- AFC= TFC/Q= =50/10= $5

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

$1180

Reason- AVC= TVC/Q= =11800/10= $1180

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

$ 1185

Reason- ATC= TC/Q= =11850/10= $1185

g. The marginal cost when Q = 10.

$3330

Reason- MC= dTC/dQ=30 + 30Q + 30Q²

When Q=10

MC= 30+30*10+30(10)^2= 30+300+3000= 3330