Question

Let the demand function of natural monopolist be Q = 50 - 5P and the cost function be TC = 10 + 2Q. Here TC represents total cost, P represents price and Q is quantity. What is the average cost and total profit of the natural monopolist in the selected energy market?

Answer 1

The firm produces at MR=MC to maximize profit

Converting the demand function to inverse demand function

Q=50-5P

5P=50-Q

P=10-0.2Q

MR=10-0.4Q --------- MR curve is double sloped than an inverse linear demand curve

MC=change in the total cost and it is found by first differentiation of the TC function =dTC/dQ=2

equating MR=MC

10-0.4Q=2

0.4Q=8

Q=20

P=10-0.2*20=6

TC=10+2Q=10+2*20=50

ATC=TC/Q=50/20=2.5

TR=P*Q=6*20=120

Profit=TR-TC

=120-50=$70

The ATC is $2.5 and Profit is $70