Question:

A monopolist is producing 2 goods. A demand for the first good: A demand for the second good: The total cost expression:

P1= 21-2(Q1-Q2) P2= 30-3(Q2-Q1)

TC = Q1(1+ Q2)

(I) Maximize the profit of the monopolist. Find optimal outputs, prices and profit. (Using the second order conditions prove that you have found the maximum profit.)

(II) Now monopolist is restricted to produce a total of 10 units of either good. Find the maximum profit of the monopolist in this case using the substitution method. Maximize the profit of the monopolist using the method of Lagrange multipliers. What is the interpretation in this case of the value of the Lagrange multiplier?