Price and Output under Second and Third Degree Discrimination

Price and Output under Second Degree Discrimination

In discrimination of the second degree, the monopolist is able to get a part of consumer’s surplus but not the entire consumer’s surplus. In other words, the monopolist charges different prices for different consumers and different prices for different units of the same product, but not the maximum possible price that the consumers could pay for it. He will be able to charge a lesser price than the maximum imaginary price of the consumers, leaving a certain amount of consumer’s surplus with the consumers. The monopolist will sell the consumer several units at one price and other several units at a lower price, etc. Mrs. Joan Robinson meant it ‘imperfect discriminating monopoly.’ This has been illustrated in the following figure.

In the figure, DD is the demand curve of the consumers for the monopolist’s product. It indicates that the monopolist charges a high price for a low level of output and for additional levels of output he charges lower prices. For instances, the OX1 output is sold at price OP1, X1X2 (additional units) output is sold at an OP2 price and further X2X3 output is sold at the OP3 price. The demand curve shows that the consumers will consume these various output levels at the said prices. Now the total revenue of the monopolist will be equal to the total area under the demand curve up to point C and nor will be equal to the rectangle OP3CX3 if the monopolist sells an OX3 quantity of output. But in this situation, the total revenue will be equal to the rectangles. The monopolist in this way snatches a part of the consumer’s surplus. The part which the monopolist leaves with the consumers is equal to the sum of the areas of three little triangles are DDP1A + DARB + DBSC.

This type of second-degree price discrimination is normally practiced in such markets where there are a number of buyers of the product. Since tastes and incomes of the consumers differ, the monopolist is able to seize some part of their consumer’s surplus depending upon their ( different groups of consumers ) desire to buy the commodity.

Price and Output Determination under Third Degree Discrimination

The monopolist divides his consumers into two or more classes or groups or markets and charges different prices from different markets in discrimination of the third degree. It is very common in practice. The simple form of this kind of price discrimination is that when the monopolist sells his output, already produced, in two separate markets. Since he has some given amount to sell, his costs of production can be ignored. When he sells his output only in the two markets, he can adjust the amount in each market in such a way that the marginal revenue derived from the first market becomes equal to the marginal revenue derived from the second market.

In order to arrive at the profit-maximizing output, the discriminating monopolist has to take two decisions: 1) how much of total output should be produced, and 2) how much of this total output should be sold in the two sub-markets and what prices should be charged in the two sub-markets?

In order to maximize profits, the monopolists will compare the aggregate or combined marginal revenue with the marginal cost of the output. The aggregate marginal revenue can be derived by combining the marginal revenues of the two sub-markets. AR1 and AR2 are the average revenue curve in the sub-market A and sub-market B respectively as shown in the figure C. MR1 and MR2 are the marginal revenue curves in sub-market A and sub-market B respectively. We have derived Aggregate Marginal Revenue (MR) curve by adding up MR1 and MR2 horizontally, i.e. by adding up the output corresponding to each level of marginal revenue in the two sub-markets. Therefore, aggregate marginal revenue shows the total amount of output that can be sold in the two sub-markets taken together corresponding to this marginal revenue. The marginal cost of the monopolist is shown by the curve MC in figure C.

Given this basic framework, we can spell out the basic equilibrium conditions in the context of a discriminating monopoly. The basic equilibrium conditions are:

1. MC = ∑MR. It means that the discriminating monopolist will maximize his profits by producing the level of output at which MC equals the aggregate marginal revenue. This is the basic profit maximizing rule in the context of price discrimination.
2. It will be most profitable for a discriminating monopolist dividing the total amount of output produced in the two sub-markets in such a way that the two marginal revenues are equal. If the two sub-markets are not equal, then the monopolist can always increase his profits by switching sub-units of output from the sub-market in which marginal revenue is less to the sub-market in which the marginal revenue is more. Therefore, in the context of price discrimination, profit maximization requires that MR1 = MR2 = MC. This means that MC has to be equal to MR in each of the two markets.

According to the figure, profit maximizing output is determined by the intersection of MC curve and ∑MR in panel (iii). This gives E as the equilibrium point, OQ as the equilibrium quantity, and EQ as the combined marginal revenue. This output has to be distributed in the two sub-markets in such a way that marginal revenues in the two markets equal this combined marginal revenue and marginal cost. (i.e., EQ). To get the same amount of marginal revenues in the two markets, a perpendicular is drawn from E in panel (iii) to the Y-axis of a panel (i) and (ii). This gives us aQ1 and bQ2 marginal revenues in two markets equal to combined marginal revenue of EQ. Accordingly, we get equilibrium a and b in the two sub-markets which correspond to OQ1 and OQ2 output respectively where aQ1 = bQ2 = EQ. This implies that OQ1 and OQ2 output would be sold in the two markets so as to equalize the marginal revenues in the two markets. The prices at which these quantities will be sold is given by the corresponding AR curves. It is clear from a panel (i) and (ii) that less quantity OQ1 would be sold in market A at high price OP1 and more quantity OQ2 would be sold at low price OP2. Thus, higher price OP1 would be charged in the less elastic market A and lower price OP2 would be charged in the more elastic market. It should be noted that OQ will be equal to OQ1 + OQ2. The monopolist’s profit is shown by the region PES in panel (iii).

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan