Question

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

C(Q) = 80 + 20Q + 25Q² + 5Q³.

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.

FC = $\$ 80$

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

$VC(10) = 20\times 10 + 25\times 10\\^2 + 5\times 10\\^3 =\$ 7700$

Variable cost = $\$ 7700$

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

Total Cost $= FC + VC$

TC = $\$80 +\$ 7700 = \$7780$

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

$AFC(10) = \frac{80}{10} = \$ 8$

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

$AVC(10) = \frac{7700}{10} = \$770$

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

$ATC = 770 + 8 = \$ 778$

g. The marginal cost when Q = 10.

$MC(10) = 20 + (2\times 25)(10) + (3\times5)(10)\\^2= \$2,020$