Answer to Question #185337 in Macroeconomics for HASAN ALI KHAN

Question

Find the optimum level of output and profit from the cost function

TC = 50 + 6Q²

 and price

P = 100 – 4Q

Also derive marginal cost and marginal revenue. 

Answer 1

$P=100-4Q , total revenue =price \times quantity$

$total\space revenue(TR)=(100-4Q)Q=100Q-4Q^2$

$dTR/dQ=100-8Q=MR$

$MC=dTC/dQ=12Q$

Profit is maximized at the level of output where MR=MC

$MR=MC$

$100-8Q=12Q$

$20Q=100$

$Q=5 \space (optimal \space output)$

$TR=100Q-4Q^2=100(5)-4(5^2)=400$

$TC=50+6Q^2=50+6(5)^2=200$

$profit=TR-TC=400-200=200 \space (profit\space at\space the \space optimal\space level\space of\space output)$