Question

. [Multi-product Firm’s Profit Maximization]

Find (i) the profit maximizing output levels x and y and (ii) the maximum profit for a firm producing two goods x and y with the profit function π(x, y) = 122x−2x 2 −2xy−4y 2 +180y−200.

Answer 1

(i)

Profit is given by :

Maximize :

First order contion :

Solving them we get 8y - y = 180 - 61 => y = 17

=> x = (61 - 17)/2 = 22

Hence, Profit maximizing level of x = 22 and Profit maximizing level of y = 17

(ii)

So, Profit earned is given by :

Hence, Maximum profit for this firm = 2672