Answer to Question #290828 in Microeconomics for mame

Question

1)     Suppose the average revenue of a short run perfectly competitive firm is 2 and its Marginal cost and fixed cost is given as: MC=3Q² -8Q+6 and TFC=10 then,

A.   Derive the function of TC, AVC and TR

B.    Calculate equilibrium price and quantity

C.    Find the profit at the equilibrium point and identify whether the firm makes positive profit, normal profits or incurs loss.

D.   What price is needed for the firm to stay in the market? 

Answer 1

$MC=3Q^{2}-8Q+6$

$TFC=10$

$TC=\int(MC)dQ$

a)$TC=\int(3Q^{2}-8Q+6)dQ$

$\int\frac{3Q^{3}}{3}-\frac{8Q^{2}}{2}+6Q+C$

$TC=Q^{3} -4Q ^{2}+6Q+C$

$FC=10 when Q=0,TC=FC$

Therefore, $C=10$

$TC=Q^{3}-4Q^{2}+6Q+10$

$VC= TC-FC$

$VC=Q^{3}-4Q^{2}+6Q+10-10$

$VC=Q^{3}-4Q^{2}+6Q$

Therefore, $AVC=VC/Q$

=$\frac{Q^{3}-4Q^{2}+6Q}{Q}$

$AVC=Q^{2}-4Q+6$

$TR=P×Q=10Q, P=10$

$MR=\frac{dTR}{dQ}=10$

b)$MC=MR$

$3Q^{2}-8Q+6=10$

$3Q^{2}-8Q=4$

$3Q^{2}-8Q-4=0$

$3Q^{2}-6Q-2Q-4=0$

$3Q(Q-2)+2(Q-2)=0$

$Q-2=0, Q=2$ positive value

c) $profit=TR-TC$

$10Q-Q^{3}-4Q^{2}+6Q+10$

$at Q=2$

$10(2)-(2)^3-4(2)^2+6(2)+10$

$20-8-16+12+10=18$

The firm makes positive profits

d)At a price that exceeds the average variable cost.