A monopolist manufacturer (M) sells its product to a downstream retailer (R) which then makes the final sale to the consumers at price p. Demand for the product is given by D(p) = 20-2p and the cost of production for M is given by C(q)= 2 + 2q.
1. Suppose M sells the product at a per-unit price of w to R. What are the equilibrium values of w, p, and q?
2. Concerned with the double marginalization problem, M offers a revenue sharing plan to R. According to the plan, M will sell R the good at marginal cost, and then it will collect 50% of R’s revenues. Find the equilibrium values of p and q.
3. Compute the profits of M and R under the above cases (a and b). Who benefits and who loses from the revenue sharing plan? Does the plan solve the double marginalization problem? Explain.
4. Now suppose that another retailer enters the downstream market and the two retailers compete in prices ( ala Bertrand Price competition as described in class). M sells its product at w, and then the retailers choose prices. Find the equilibrium values of w, q (total output) and p. Comment on the dilemma faced by the manufacturer. Propose a solution to solve the problem.
