Question

Assume that firm M (the manufacturer) sells an input (a lawn mower) to firm R (the retailer). Now R sells the lawn mower to the public. R does not incur any cost associated with providing its retail service (that is, its retail cost is zero). Let X represent the number of lawn mowers. Assume that M is monopolists, R is competitive industry, and P is the lawn mower price charged to the public with the (inverse) demand P=100 – X. Let P^W denote the wholesale price R pays to M per lawn mower.

1. 1. Find the derived demand for lawn mowers facing M (i.e., the demand function for M as a function of P^W). Hint: Make use of the fact perfect competition equilibrium is defined by demand equals supply, where supply is simply a horizontal line P = MC for the retail sector which is simply P^W because we assume that there is no additional retail cost. Solving for X gives the derived demand.
2. 2. Find the equilibrium prices and quantity, P^W, P, X and the profits of the two firms.
   3. Assume that M vertically integrates forward into the competitive industry R, thereby extending its monopoly to cover both manufacturing and retailing. Find the equilibrium values of P and X and the profit of the combined firm M-R.
   4. Compare the unintegrated case in part b with the integrated case in part c. Is it profitable to monopolize forward? What is the intuitive explanation for your result?

Answer 1

Let us assume that the production is costless

Hence,the manufacturer faces the following problem:

where denotes the profit of the manufacturer

Note that the quantity that the producer will produce should be equal to the quantity demanded.

The Retailer faces the following problem:

where denotes the profit of the Retailer

Since the Retailer is in a perfectly competitive market, the equilibrium condition is given by

Total cost of Retailer:

Marginal Cost of Retailer:

At equilibrium:

The derived demand function faced by the Manufacturer

The manufacturer faces the problem:

Since

Profits:

The Retailer makes no profits since she is operating in the Perfectly Competitive Market