Question

4) A firm faces the demand curve, P-80-3Q, and has the cost equation, What is the equation for the firm's total revenue? 200+20Q. a) b) What is the equation for the firm's marginal revenue? c) What is the quantity that maximizes total revenue? d) Find the optimal quantity and price for the firm if they are trying to maximize profit e) What is the firm's profit at the price and quantity in (d)? f) Now suppose that the demand for the firm's product changes to P 110-30 Does this represent an increase or decrease in demand? g) Find the new optimal quantity and price for a firm maximizing profit with the new demand curve (and original cost equation).

Answer 1

Answer 4

a)

P = 80 - 3Q

Total Revenue(TR) = PQ = (80 - 3Q)Q = 80Q - 3Q²

Hence TR = 80Q - 3Q²

b)

Marginal Revenue(MR) = d(TR)/dQ = 80 - 6Q

Hence MR = 80 - 6Q

c)

Max: TR = 80Q - 3Q²

First order condition :

d(TR)/dQ = 0 => 80 - 6Q = 0

=> Q = 13.33 units.

Hence. Q = 13.33 units will maximize Total Revenue

d)

According to profit maximizing condition, a firm produces that quantity at which MR = MC(Marginal Cost)

MC = dC/dQ = 20

MR = MC => 80 - 6Q = 20

=> Q = 10.

Hence, P = 80 - 3*10 = 50

Hence Profit maximizing quantity = 10 units and profit maximizing price = 50