Question

suppose the inverse demand curve of a firm is given by p=1800 - 7.5 Q compute the total revenue and marginal revenue and determine the quantity that maximizes revenue

Answer 1

Answer

(i)

Total Revenue(TR) = price*quantity = p*Q

Here p = 1800 - 7.5 Q

=> Total Revenue = (1800 - 7.5 Q)*Q

=> Total Revenue(TR) = 1800Q - 7.5Q²

(ii)

Marginal Revenue(MR) = d(TR)/dQ = 1800 - 2*7.5Q

=> Marginal Revenue = 1800 - 15Q

(iii)

Max : Total Revenue(TR) = 1800Q - 7.5Q²

First order condition

d(TR)/dQ = 0 => 1800 - 15Q = 0

=> Q = 120

Thus, quantity that maximizes Revenue = 120 units