Question

Given the following demand and cost function, find the prices and output in each Market and the total profit, Assume that there are only two firms in the market.

P1 = 32 – 2Q1

P1 = 22 – Q2

TC = 10 + 2Q1 + Q2

Answer 1

$TR1=Q1*P1=(32 – 2Q1)Q1$

$TR2=Q2*P2= (22 – Q2)Q2$

$MR1=32-4Q1$

$MR2= 22 – 2Q2$

$MC=TC=3$

$32-4Q1=3$

$Q1=7.25$

$22 – 2Q2=3$

$Q2=9.5$

$P1=32 – 2Q1=32-2*7.25=17.5$

$P2= 22 – Q2=22-9.5=12.5$

$TC = 10 + 2Q1 + Q2=10+2*7.25+9.5=34$

$TR=7.25*17.5+9.5*12.5-34=211.625$