Problem 4.6 (Tirole, Industrial Organization)

Problem 4.6 (Tirole, Industrial Organization)

Problem: The Horizontal Externality

Consider a setting where a single manufacturer seeks to distribute its product through N identical retailers. Suppose that the demand function is given by , where and is the level of services offered by retailer i, and and is the price set by any retailer. Assume that a retailer setting the lowest price captures the whole demand; in case of a tie the demand is split equally among those retailers who set the lowest price.Let be the cost of providing the service at a single retail outlet that is independent on the quantity sold to the final consumers, where For the sake of exposition, you can think that and

(A) Find the pair that maximizes the industry-wide monopoly profit (note that it is profitable to avoid multiplication of efforts). is the outcome that would be most preferred by a single entity comprising of the manufacturer and the downstream firms selling the product to the final consumers.

(B) Suppose now that the upstream market is decentralized, i.e., the manufacturer has to sell its product to each of N retailers on a non-discriminatory basis. The retailers then resell the product to the final consumers. Formally, the game unfolds as follows:

Stage 1. The manufacturer offers to each retailer a contract C (specified below).

Stage 2. Each retailer decides whether to accept the contract. In the latter case, it chooses the level of services and the price to set to the final consumers.

Stage 3. Consumers observe the level of services (i.e., ) and the prices set in each retail outlet. The demand (at each retail outlet) is realized and all the payments are made.

Assuming that the contract C specifies just the wholesale price w (i.e., the total payment made to the manufacturer is ), determine the optimal contract.

(C) Which of the following contracts would be most preferred by the manufacturer?

(i)C specifies a wholesale price and RPM

(ii)C specifies a whole price, RPM and a minimum quantity

(iii)C specifies a two-part tariff and RPM

(iv)C specifies a two-part tariff and exclusive territories

(B) What can be said about the welfare effects of the vertical restraints (assuming that the social planner seek to maximize just the consumer surplus)? In this respect, which contract would the social planer favor the most or the worst?