4)A monopolist practices price discrimination in the sale of its product. It can properly segment its

market into two, 1 & 2. Suppose the demand curves and total cost function are as follows

Q1 = 50 - 0.5(P1) Q2 = 76 - (P2) TC = 3(Q1) + 2(Q1)^2 (Q2) +2(Q2)^2 + 55

(a)Form the profit function for this firm.

(b)Find, for each market, the equilibrium price and quantity transacted.

(c)Find the price elasticity of demand in each market and provide a brief explanation of the relationship

between the calculated values and the relative prices charged in each market.

(d)Evaluate the second order condition for profit to be maximized.