A monopolistic producer of two goods, G₁ and G₂, has a joint total cost function

TC = 10Q₁ + 4Q₁ Q₂ + 5Q₂

Where Q₁ and Q₂ denote the quantities of G₁ and G₂ respectively. If P₁ and P₂ , denote the

corresponding prices then the demand equations are

P₁ = 50 1.5Q₁ + Q₂

P₂ = 52.5 + Q₁ 1.5Q₂

a) Find the total revenue function for the monopolist.

b) Find the profit function for the firm.

c) Determine the firm's pricing policy that maximizes profit using the first and

second order conditions.

d) Calculate the value of the maximum profit.

e) Now, supposed the firm is contracted to produce a total of 12 goods of either

type, find the level of Q₁ and Q₂ that maximises profit.

f) Estimate the new optimal profit if the production quota increases to 14 units