Bilateral Duopoly Efficiency

Most of the products sold on the final market are the result of several production stages. For instance, the food products are firstly packed and branded, then distributed to the stores and retailers and finally sold to the final consumers.

The purpose of this essay is to compare the performance of two different market structures in an industry characterized by two production stages: an upstream and a downstream one.

For the sake of clarity, we will assume that the production of one unit of output at the downstream stage requires the use of one unit of output from the upstream stage. As a consequence, the downstream output Y will equal the upstream one.

The two market structures taken under examination are a bilateral duopoly and a vertically integrated monopoly.

A bilateral duopoly is a market structure where there are two firms at each stage of production, whereas in a vertically integrated monopoly there is just one firm carrying out both processes.

Throughout the essay it will be assumed that consumer demand in the final market is a linear function of the final output Y and is described by the linear equation:

p=a-bY (a), where a is the consumer reservation price.

The performance, or efficiency, of the two models will be measured by the total ‘welfare’ they entail. From society’s point of view, the total gain is the sum of the consumer surplus and producer surplus, which is known as total surplus.

Consumer surplus is defined as “the difference between what a consumer is willing to pay and what she has to pay” (Katz and Rosen, 1998, p. 110) and is calculated simply as the area under the demand curve and above the market price.

FIGURE 1

The shaded area in FIGURE 1 indicates the consumer surplus CS and is given by the formula: CS=(a-p)Y/2 (b).

Instead, the producer surplus PS is simply the producer’s profit. For the purpose of this essay it will be also assumed that firms act in order to maximize their profits.

Bilateral Duopoly

In a bilateral duopoly market, there are two firms, U1 and U2, at the upstream stage and two firms, D1 and D2, at the downstream stage, as FIGURE 2 below shows.

FIGURE 2

The analysis of this market holds on the following assumptions. First of all, the two firms at each stage must be identical, i.e. incur in the same costs of production, and must produce homogeneous good, i.e. goods that are perfect substitutes.

This implies that, in equilibrium,