Answer to Question #150830 in Microeconomics for Ben

Question

The demand curve function of a monopolist is given by P= 100 - 2Q. If the marginal cost is constant and is equal to 20, what is the amount of profit made?

Answer 1

Solution:

$P=100-2Q$

Derive MR:

$R=(100)\times (Q)- (2Q)(Q) = 100Q-2Q^{2}$

$MR=\frac{dR}{dQ} = 100-4Q$

$MC =20$

$MR=MC$

$100-4Q=20$

$4Q=100-20$

$4Q=80$

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

$Q=20$

Substitute to get the price:

$P=100-(2)\times (20) =100-40=60$

$P=60$

Derive Total Revenue (TR) and Total Cost (TC):

$TR=(60\; per\; unit)\times (20 \;units\; per\; unit) = 1,200$

$TC=(10\; per\; unit)\times (20 \;units\; per\; unit) = 200$

$Profit=TR-TC=1,200-200 = 1,000$

$Profit \;made = 1,000$

Profit made = 1,000