Answer to Question #279052 in Microeconomics for Gshs

Question

given the data solve the following asked to maximize profit in a monopoly market

(1) Q = 100 - p; (demand curve for firm output)

(2) TC(Q) = 100 + 20Q +Q2; (cost curve)

a. Compute the MR and MC curves

b. Compute the profit maximizing output

c. Compute the price of that output that maximizes profit

d. Compute the profit to be realized for that output

Answer 1

a. MR and MC curves:

$Q=100-p$

$p=100-Q$

$TR(Q) = pQ =(100-Q)Q$

$TR(Q)=100Q-Q^2$

$MR(Q)=\frac{dTR(Q)}{dQ}=100-2Q$

$TC(Q)=100+20Q+Q^2$

$MC(Q)=\frac{dC(Q)}{dQ}=20+2Q$

b. Profit maximizing output:

At profit maximizing;

$MC=MR$

$20+2Q=100-2Q$

$4Q=80$

$Q=\frac{80}{4}=20$

c. Profit maximizing price:

$p=100-20=80$

d. Profit:

$Profit=TR-TC$

$Profit=(p\times Q)-(100+20Q+Q^2)$

$Profit=(80\times 20)-(100+20\times 20+20^2)$

$Profit=1600-900=700$