## Equilibrium of the discriminating monopolist

Figure 1 Equilibrium of the discriminating monopolist
The profit gain from price discrimination is (x + y) - z

In figure 1 there are two distinct markets, Market A and Market B. A third market, Market C, which is the combined market, is obtained by the horizontal summation of the individual AR and MR curves from A and B. Market A has an inelastic demand curve, whilst Market B has a more elastic demand curve. The gradient of the combined market demand curve will lie between that of A and B.

In the combined market, MC is equated with MR to give a single profit maximising price of OPc with an output of OQc, and a total profit equal to the shaded area z is earned. With a single price, this is the maximum profit that could be earned as the charging of a higher price would reduce demand and the area of profit, z.

However, total profits can be increased through price discrimination, with the total output OQc being sold at different prices in markets A and B. Price will always be higher in the market with a more inelastic demand as consumers will be less responsive to price changes.

As price discrimination only occurs where the differences in price are not associated with any cost differences, the combined market MC curve will also apply to markets A and B, and the output of each sub-market is therefore determined by equating MR in each market with the marginal cost of producing OQc units of output. Thus in figure 1, it can be seen that the marginal cost of production, OM, is projected back from the combined market as a horizontal line to enable the monopolist to find the equilibrium points Ea and Eb where MC = MR in each of the individual markets, A and B. Similarly the average cost of production, OC, is projected back from the combined market to determine the area of profit in markets A and B. As the level of profit is denoted by the amount by which AR exceeds AC, the areas x and y will represent the total profit for A and B respectively.

From the producer's standpoint, price discrimination will be a success if total profits increase as a result. In the diagram, it can be seen that Area x + Area y is greater than Area z, so the producer has succeeded.