Question

1)For a monopolistic firm demand and total cost (TC) functions are as follows:
q = 230 – (1/2) P and TC = 20 + (1/2) q2
What is the equilibrium level of P (P*) that maximizes the profit of firm?

2)) If the total cost function (TC) of a competitive firm is TC = 20 + 0.2 Q2 and the price is (P) = 400 what is the equilibrium level of quantity (Q*) that maximizes profit?

Answer 1

1)$TC=20+(1/2)*(230-(1/2)P)^2=20+(1/2)*(52,900-230P+P^2/4)=20+26,450-115P+P^2/8=26,470-115P+P^2/8$

$Profit=P*Q-TC$

$P(230-(1/2)P)-26,470+115P-P^2/8=0$

$345P-(5/8)P^2-26,470=0$

$P^*(maxProfit)=-\frac{345}{-2*(5/8)}=276$

2) $q=30$

$TC=20+(1/2)*30=35$

$Q^*=\frac{35-20}{0.2}=75$