Question

Given the following functions; 

TC=
 50Q+20Q²(Cost Function) 

P= 400-20Q (Demand function) 

Determine the profit maximizing level of price and output. 

Answer 1

$TC=50Q+20Q^2$

$MC=50+40Q$

$P=400-20Q$

For any linear demand curve of the form $P=a-bQ$ , the marginal revenue function has the form $MR=a-2bQ$

$\implies MR=400-2(20)Q$

$MR=400-40Q$

At maximum profit, $MC=MR$

$50+40Q=400-40Q$

$Q=4.375$

$P=400-20Q$

$P=400-20(4.375)$

$P=400-87.5$

$P=312.5$

The profit maximizing level of price is 312.5 and output is 4.375