Question Part

Question 1.

A price discriminating monopoly sells in two markets. Assume that consumers cannot resell the product so no arbitrage is possible. The demand curve in market 1 is given by p1 = 50(q1)/2. The demand curve in market 2 is given by p2 = 50 - q2. The monopoly's aggregate production is Q = q1 + q2. The monopoly's cost function depends on total production and is given by C (Q) = Q^2.

(a) Monopoly: what is the profit function as a function of q1 and q2?

(b) Determine the monopoly's profit-maximizing price and the quantity sold in market 1 and market 2.

(c) Let's pretend now that the CEO's son inherits the company and chooses to try something new. He decomposes the monopoly plant into two plants, where plant 1 sells in market 1 only and plant 2 sells in market 2 only. Each plant has the same cost function: C(qi)=(qi)2C(qi)=(qi)2. Calculate the profit-maximizing output sold by each plant.

(d) Find out how much money was made between the two plants. Does the factory decomposition increase or decrease profits?