When is Price Discrimination Possible and Profitable? | Monopoly | Economics

Price discrimination arises when a firm sells its (homogeneous) product at different prices at the same time. The monopolist is able to sell his product in some situations in two or more markets at different prices and thereby increases his profit.

Discrimination is possible if, and only if:

1. The market is segment-able, that is, customers should be distinguishable on some basis so that they remain almost ignorant of discrimination. In certain cases doctors charge two types of fees for their services, high for the rich and low for the poor. Books are priced at different rates — low price for home buyers and high price for foreigners.

2. There is no resale. Otherwise some customer-speculators would buy at the cheaper rate and resell it in the high priced area and thus would render price discrimination ineffective. Of course, services like haircuts or consultancy cannot be resold.

Price discrimination is profitable if, and only if, the price elasticity of demand is different in different markets.

Equilibrium of a Discriminating Monopolist:

Total profit of a price discriminating monopolist is the difference between his total revenue from both the markets and his total cost of production:

That is, price will be lower in the market with greater price elasticity of demand. Fig. 22.15 illustrates pricing under price discrimination when both the market segments have some degree of imperfect competition. At point E the firm is in equilibrium where CMR = MC in Fig 22.15 (c).

Here MC = MR, in Fig. 22.15(a) gives output in market 1 equal to 0Q₁ and MC = MR₂ in Fig. 22.15(b) gives output in market II equal to 0Q₂. Corresponding to these output levels (0Q₁ and 0Q₂) prices are OP₁ and 0P₂ in markets I and II, respectively. Although MR₁ = MR₂, P₁ ≠ P₂. Therefore, the monopolist is discriminating.

Note OP₁ > 0P₂ since demand curve for market I is relatively steeper than that for market II (i.e., E₁ < E₂). So the more inelastic the demand, the higher the price.

Other Types of Price Discrimination:

Monopolists can practice price discrimination in two other ways. Second degree price discrimination is said to occur when a monopolist sells blocks of output to different customers at different prices.

For example in Fig. 22.16 a monopolist supplier of electricity like the Calcutta Electric Supply Corporation (CESC) may charge a high price, P_a, for the first few units demanded, and a lower price P_c for additional units sold up to Q_c. The shaded area in Fig. 22.16 shows the addition to total revenue (and profit) from such discrimination compared with that which could be earned by selling the whole output, Q_c, at a uniform price, P_c.

Finally, the monopolist may practice first degree price discrimination. This is considerably more difficult to implement than either of the two foregoing types. It is because the monopolist will have to take away from each customer the maximum amount that he or she is ready to pay. This is known as charging as much as the traffic will bear.

Fig. 22.17 shows first degree price discrimination. Suppose the pizza seller identifies his profit-maximising output as Q_m and sells it at P_m. It may seem that there are many who are ready to pay less than P_m. Suppose the pizza seller first sells quantity Q_m at P_m, and then sells to each of the remaining customers at the maximum possible price, up to the point at which the last customer pays only P_min.

We know that the difference between the maximum each of the remaining consumers is ready to pay for a quantity of pizza and what each is required to pay for that quantity is consumers’ surplus. In this case consumers’ surplus for the market is shown by the area EFG.

By taking away this amount of consumers’ surplus the monopolist pizza seller is practising first degree price discrimination. He could sell to those customers who would have remained unsatisfied in the absence of discrimination exactly those quantities they are prepared to buy, at the maximum price they can be made to pay.

While the marginal customer pays a price P_min exactly equal to marginal costs, all the pre-marginal buyers pay a higher price. The profits of the monopolist are, no doubt, larger than they would have been if he had charged the same price for all the units (he succeeded in selling).

Output under Price Discrimination:

So long as the price-discriminating monopolist manages to reap part of the consumers’ surplus his total revenue and his total profits will be higher, if he sells the same quantity which corresponds to the intersection of his marginal curve with his (original) marginal revenue curve.

However, the quantity that the discriminating monopolist supplies will be higher than OQ in Fig. 22.18 if he can charge more than two prices in various sub-markets and his total revenue will be higher still. The increase in output is due to the gradual shift of the MR curve upwards and the consequent change of the point of its intersection with the same MC curve.

The shift of the MR curve (due to rise in total sales revenue), under unchanged demand conditions, is due to the fact that the MR (at all levels of output) is higher when price discrimination is practiced.

This is because the lower price at which the new marginal unit is sold is not the same as for all previously sold units, which have been sold at higher prices through individual negotiation with the buyers. In Fig. 22.18, if price were uniform, the monopolist would sell 0Q₀ units of output.

If price discrimination is practiced, only the additional units are sold at lower and lower prices. So the MR curve shifts to MR’. Now equilibrium is at point F, at which 0Q₁ > 0Q₀. In the extreme situation of perfect price discrimination the MR coincides with the demand (AR) curve, since each unit is sold at a different price, i.e., the maximum price that the buyers are willing to pay on a ‘take-it-or- leave-it’ basis.

The equilibrium will be at point G, at which output will be 0Q₂ and the following condition will hold: 

MC = MR = AR = P

and the monopolist will have achieved the maximum increase in his revenue, capturing the entire consumers’ surplus.

Example 1:

Suppose that the total demand is

Q = 50 – 5.0P (or P = 100 – 2Q)

Suppose further that the demand functions of segmented markets are

Q₁ = 32- 0.4P₁ or P₁ = 80 – 2.5Q₁

Q₂ = 18 – 0.1P₂ or P₂ = 180 – 10Q₂

(Clearly Q₁ + Q₂ = Q)

Finally, assume that the cost function is

C = 50 + 400 = 50 + 40(Q₁ + Q₂)

Find out the equilibrium output as also the profit of the discriminating monopolist.

Solution:

The firm aims at the maximisation of its profit

Thus e₁ > e₂ and P₁ < P₂.

Comparing the above results with those for the example of the simple monopolist we observe that Q is the same in both cases but the profit (∏) of the discriminating monopolist is larger.

Example 2:

In two separate (isolated) markets supplied by a monopolist, the two corresponding demand functions are: 

P₁ = 12 – Q₁ and P₂= 20 – 3Q₂.

and the cost function is

C = 3 + 2(Q₁ + Q₂).

(a) What will prices, sales and marginal revenues be in the two markets under price discrimination and the profit of the monopolist?

(b) What will be the corresponding values if the monopolist cannot discriminate?

Solution:

(a) The total profit in the two markets together will be;

∏ = P₁Q₁ + P₂Q₂ – C = 12Q₁ – Q₁² 4- 20Q₂ – 3Q₂² – 2(Q₁ + Q₂) – 3

= 10Q₁ – Q₁² + 18Q₂ – 3Q₂² – 3.

It is interesting to note that in the discrimination case marginal revenues were equal in both markets while, where prices were equal in both markets, marginal revenue in one of the markets was actually negative. Moreover, one price rose and the other fell under discrimination but that the monopolist’s profits were higher in the discriminatory case.

Price Discrimination at the International Level: Economic Effects of Dumping:

An international monopolist often adopts a discriminatory practice called dumping. This is no doubt a form of price discrimination.

Many multinational corporations adopt a restrictive pricing practice, i.e., price discrimi­nation at the international level. This is known as dumping. And this is the trading practice of many Japanese companies which charge high prices from domestic consumers and low prices from foreign buyers. This is why it sounds like a paradox that a Japanese camera costs less in New York than it Tokyo.

Let us consider a domestic monopolist which is protected from foreign competition by tariffs and other import restrictions. In the absence of any export restriction in the home country and import control in the world market, it can sell as much at it likes at a competitive world price.

The situation faced by such a firm is shown in Fig. 22.19. In part (a) we show that the firm is a monopolist in the domestic market where it faces a downward sloping demand curve for its product (D_d). The corresponding marginal revenue curve is MR_d. In the world market the firm is able to sell any quantity it likes at the competitive price P_c. Since the monopolist is a price taker in the world market its demand curve (which is also its MR curve) is horizontal at the world price P_c.

In order to maximise total profit from its overall operations, the international monopolist will have to follow the same marginalist rule of profit maximisation which is adopted by a discriminating monopolist which operates domestically. It will have to allocate its output between the two markets in such a fashion that MR is the same in both. In part (c) we show the horizontal sum of MR_d and D_c.

The downward sloping portion AB in part (c) corresponds to that part of MR_d which lies above the world price. Thus if output is 0Q₀ or less, the monopolist will sell his entire output in the domestic market. Nothing will be exported at a lower price that prevails in the competitive world market. For any output larger than OQ₀ the relevant MR is the foreign price P_c. This is shown by the horizontal segment of the line MR_d + P_c in part (c). For any output greater than 0Q₀, the MR in the domestic market is less than the world price P_c. Thus the monopolist is never required to charge less than the competitive world price for selling a positive quantity.

We find that the profit-maximising monopolist’s total output is 0Q_T which corresponds to point F where its MC curve in part (c) intersects the horizontal sum of the two MR curves. The output 0Q_T is greater than output 0Q₀ because the monopolist sells a positive quantity (Q₀Q_T) in the world market.

Since from part (a) of Fig. 22.19 we see that the monopolist cannot sell more than 0Q₀ units in the domestic market, any output is excess of 0Q₀ (in this case Q₀Q_T) will be exported at a competitive price. The domestic sales occur at price P_d in part (a) and the foreign sales are made at the competitive world price P_c.

In this case the domestic price is higher than the world price because the firm is a price- discriminating monopolist. If demand is not much elastic in the domestic market, the monopolist gains by selling less in the domestic market and charging as much as the domestic consumers will bear.

It cannot raise price in the world market where demand is completely elastic. This practice is known as dumping. The government of a country may encourage 2 firm to export at a low competitive price by giving a subsidy per unit of s in which case the price receded by the monopolist is P_c + s.

The effect of such a subsidy is to increase total output of the firm above 0Q₀ and to increase exports both in absolute and in relative terms. Such subsidy restricts domestic supply by making domestic sales less profitable than foreign sales.