Question

A firm’s demand curve in period 1 is Q=25 - P. Fixed costs are 20 and marginal costs per unit are 5. (5 marks) a. Derive equations for total revenue and marginal revenue. b. At what output will marginal revenue be zero? c. At what price will total revenue be maximized? d. At what price and output will profit be maximized? e. Calculate the maximum profits the firm makes.

Answer 1

(a) Total revenue $=Price\times Quantity,$

Rearranging the demand equation, we get

$P=25-Q$

So,

Total Revenue $e=PQ=(25-Q)\times Q=25Q-Q^{2}$

Marginal Revenue would be differentiation of Total revenue. So,

Marginal revenue$=25-2Q$

(b). Equating MR to zero, we get

$25-2Q=0$

$2Q=25$

$Q=12.5$

(c)Revenue would be maximized where Marginal Revenue would be zero. As this happens at $Q=12.5$ , the price is

$P=25-12.5=12.5$

(d) Profit would be maximized where MR=MC. MC is given at 5. So,

$25-2Q=5.$

$Q=10$

$P=25-10=15$

The maximum profit would be

$Total \space revenue-Total\space cost.$

At Q=10 and P=15, the total revenue is

$5\times 10=150$

The total cost would be Fixed Cost+Marginal Cost.

$=20+5Q$

$At Q=10$

Total cost$=20+5\times10=70.$

Maximum profit$=150-70=80.$