Suppose there is a single manufacturer, M and two retailers R1 and R2. First, the manufacturer posts a price h for its good; Second, the two retailers observe h and simultaneously place orders q1 and q2 for the manufacturer's good (the two retailers participate in a simultaneous Cournot market, where their marginal cost is h). The market price of the good is p(q1, q2) = 12 (q1 + q2). The manufacturer's total costs of production are C(q1 + q2) = 8 (q1 + q2)..

a). Solve for a subgame perfect Nash equilibrium of the game. What are the firms' profits? What is the market price and market quantity? Think carefully about how to handle the simultaneous-move subgame between the two retailers.

(b). Suppose the two retailers merge into a single firm, or horizontally integrate, so that there is a single manufacturer and a single retailer. Is this profitable for the retailers (in the sense that the joint profits are higher after the merger)?

(c). Suppose the manufacturer decided to vertically integrate by buying one of the retailers and refusing to sell its good to the other retailer. Is this profitable for the manufacturer and integrated retailer, in the sense that the vertically integrated monopolist generates more profits than the manufacturer and a single retailer make in the presence of the other firm?

(d). Public policy generally discourages horizontal and vertical integration as anti-competitive. Explain whether your results support this conclusion.