Analyzing the Double Marginalization Problem and Revenue Sharing in a Monopoly and Oligopoly Setting

Introduction

In this essay, we will explore a scenario where a monopolist manufacturer (M) sells its product to a downstream retailer (R), and subsequently, consumers purchase the product at price p. We will examine two scenarios: one where M operates without a revenue-sharing plan and another where a revenue-sharing plan is implemented. Additionally, we will consider a situation where a new retailer enters the market, leading to price competition between retailers.

Monopoly Scenario without Revenue Sharing

In this scenario, M operates as a monopoly and sells its product to R at a per-unit price of w. The demand for the product is given by D(p) = 20 – 2p, and M’s cost of production is C(q) = 2 + 2q.

1.1 Equilibrium Values: To find equilibrium values, we need to determine w, p, and q. The monopolist maximizes profit by equating marginal cost (MC) to marginal revenue (MR). In this case, MR = D(p) * (p – w). Solving for w, we get: MR = MC (20 – 2p)(p – w) = 2 + 2q Solving for w yields the equilibrium per-unit price w*.

Next, we can find p* and q* based on the demand function and the monopolist’s profit maximization. These values constitute the equilibrium in the absence of a revenue-sharing plan.

1.2 Profits: M’s profit can be calculated as the difference between total revenue and total cost. Similarly, R’s profit can be computed as the difference between total revenue and the amount paid to M. Analyzing these profits will reveal who benefits and who loses in this scenario.

Monopoly Scenario with Revenue Sharing

Now, let’s consider a revenue-sharing plan where M sells the product to R at marginal cost and collects 50% of R’s revenues. We need to find equilibrium values for p and q in this setup.

2.1 Equilibrium Values: Under the revenue-sharing plan, M no longer has an incentive to set a monopolistic price, and it sells the product at cost. R sets the price p. Equilibrium values for p and q can be determined by analyzing R’s profit maximization and considering M’s revenue-sharing arrangement.

2.2 Profits: We will calculate the profits of M and R under the revenue-sharing plan and compare them with the profits in the previous scenario. This will allow us to assess the impact of revenue sharing on both parties.

Oligopoly Scenario with Price Competition: Now, let’s introduce a new retailer into the market, creating an oligopoly. M sells the product to both retailers at price w, and they compete in setting prices.

3.1 Equilibrium Values: In an oligopoly with Bertrand price competition, retailers will undercut each other until price equals marginal cost. We will determine equilibrium values for w, q (total output), and p under this competitive setting.

3.2 Dilemma Faced by the Manufacturer and Proposed Solution: The manufacturer faces a dilemma in this scenario because price competition may lead to lower prices and reduced profits. To solve this problem, M could consider offering exclusive deals or contracts to retailers to discourage aggressive price competition.

Conclusion

In summary, we have analyzed three scenarios: monopoly without revenue sharing, monopoly with revenue sharing, and oligopoly with price competition. We examined equilibrium values, profits for M and R, and the implications of each scenario. Revenue sharing helps address the double marginalization problem but may not always benefit both parties. In an oligopoly, the manufacturer must devise strategies to maintain profitability in the face of price competition.