Question

Suppose that the firm operates in a perfectly competitive market. the market price of its product is $2.the firm estimates its cost of production with the following cost production with the following cost function: C=100-6Q+2Q²

Based on this information, answer the following question.

A.what is the total fixed cost for 4 unit of output?

B.what is MC when the firm produces 4 unit of output?

C. What is the value of AFC at 4 units of output?

D.what is total variable cost for 4 unit of output?

E.What level of output should the firm produce to maximize its output?

Answer 1

P=$2

$C=100-6Q+2Q^2$

TR=P×Q=2Q

A) $C=100-6Q-2Q^2$

$FC=TC-VC$

$FC=\$100$

B) $MC=\frac{dC}{dQ}=-6+4Q$

At Q=4

$MC=-6+4(4)=10$

C) $AFC=\frac{FC}{Q}$

At Q=4,

$AFC=\frac{100}{4}=25$

D) $TVC=TC-FC$

$TVC=100-6Q+2Q^2-100$

$TVC=-6Q+2Q^2$

At Q=4

$TVC=-6(4)+2(4)^2$

$TVC=8$

E) To maximize output, MR=MC

TR=2Q

MR=2

2=-6+4Q

$Q^*=2$