Answer to Question #200045 in Economics of Enterprise for Henok Gezahegn

Question

a firm’s demand curve in period 1 is q=25 - p. fixed costs are 20 and marginal costs per unit are 5

At what output will marginal revenue be zero?

At what price will total revenue be maximized? 

At what price and output will profit be maximized?

Calculate the maximum profits the firm makes

Answer 1

P=25-Q

Total revenue =PQ

$= (25-Q)Q \\ = 25Q+Q^2$

Marginal revenue would be differentiation of Total revenue.

Marginal revenue = 25-2Q

If MR=0

25-2Q=0

Q=12.5

Revenue would be maximized where marginal revenue would be zero. As this happens at Q=12.5, the price is

P=25-12.5 = 12.5

Profit would be maximized when MR=MC.

MC=5

25-2Q=5

Q=10

P=25-10-15

The maximum profit would be

Total revenue-Total cost

At Q=10

P=15

The total revenue $= 15 \times 10 = 150$

The total cost would be Fixed Cost +Marginal Cost

= 20+5Q

At Q=10

Total cost $=20+5 \times 10 = 70$

Maximum profit = 150-70=80