# Price Discrimination

Price discrimination is when a seller sells a specific commodity or service to different buyers at different prices for reasons not concerning differences in costs. In this article, we will look at the conditions, objectives, and equilibrium under price discrimination.

Before we start, let’s look at some examples:

• A local physician charges more to rich patients as compared to poor patients for the same service.
• Electricity companies sell electricity at a cheaper rate in rural areas as compared to urban areas.

These are examples of price discrimination. In a monopoly, the seller adopts this method of pricing to earn abnormal profits. It is important to remember that price discrimination cannot persist under perfect competition since the seller has no control over the market price of the product/service. It requires an element of monopoly to allow him to influence the price.

Table of content

## Conditions for Price Discrimination

Price discrimination is possible under the following conditions:

1. The seller must have some control over the supply of his product. Such monopoly power is necessary to discriminate the price.
2. The seller should be able to divide the market into at least two sub-markets (or more).
3. The price-elasticity of the product must be different in different markets. Therefore, the monopolist can set a high price for those buyers whose price-elasticity of demand for the product is less than 1. In simple words, even if the seller increases the price, such buyers do not reduce the purchase volume.
4. Buyers from the low-priced market should not be able to sell the product to buyers from the high-priced market.

Hence, we can conclude that a monopolist who employs price discrimination, charges a higher price from the market with inelastic demand. On the other hand, the market which is more responsive is charged less. Here is an example to understand price discrimination more clearly.

#### Example

The single monopoly price of a product is Rs. 30. The elasticities of demand for the product in markets A and B are 2 and 5 respectively. Therefore, the marginal revenue in market A (MRA) is

$$\text{MRA} = \text{ARA} \frac{e-1}{e} = 30 \frac{2 – 1}{2} = 15$$

Similarly, the marginal revenue in market B (MRB) is

$$\text{MRB} = \text{ARB} \frac{e-1}{e} = 30 \frac{5 – 1}{2} = 24$$

Hence, we can see that the marginal revenues of the markets A and B are different when the elasticities of demand at a single price are different. Further, we also find that the MR of the market with higher elasticity is higher than the MR of the market with a low elasticity of demand.

A monopolist, in such a case, transfers some amount of product from market A to market B. This is because, in market B, the high elasticity of demand implies larger marginal revenue. It is important to note here that when units are transferred from A to B, price in A will rise and fall in B.

However, there is a limit to which the monopolist can transfer between markets A and B. Once he reaches that limit and reaches a point where the MRs in both the markets become equal due to the transfer of output, transferring more will no longer be profitable. At this stage, the monopolist starts charging different prices in the two markets. So, he charges a higher price in the market with a lower elasticity of demand and a lower price in the market with a higher elasticity of demand.

## Equilibrium under Price Discrimination

Under price discrimination, a monopolist charges different prices in different sub-markets. To begin with, he divides the market into sub-markets based on their elasticity of demand. We will take the case when a market is divided into two sub-markets, for simplicity.

Next, the monopolist is faced with making two decisions:

1. How much output should he produce?
2. How should he divide the output between the two sub-markets and how should he price them?

The monopolist compares the marginal revenues with the marginal cost of the output. However, before that, he must calculate the aggregate marginal revenue of both sub-markets taken together and compare this value with the marginal cost of the total output.

In Fig. 1 above, MRa is the marginal revenue curve in the sub-market A having a demand curve Da. Similarly, MRb is the marginal revenue curve in the sub-market B having a demand curve Db. The aggregate marginal revenue curve (AMR), shown in III above, is an addition of MRa and MRb. The AMR curve shows the total amount of output sold in both the sub-markets. Further, the marginal cost curve (MC) is also depicted in III above.

#### Step 1

The monopolist maximizes his profits by producing the level of output at which MC intersects AMR. From III above, we can see that the intersecting point is E which corresponds to OM level of output. Once the monopolist determines the total output to be produced, he starts planning about distributing the output between the two sub-markets. He distributes it in a manner that the marginal revenues in both the sub-markets are equal. This ensures maximum profits.

#### Step 2

If he does not ensure that the marginal revenues in the two sub-markets are equal, then he will transfer from one to another since it offers him profits. Once the MRs are equal, the transfer becomes unprofitable. However, for price discrimination, he must also ensure that the MRs are equal to the marginal cost of the total output. This ensures that the amount sold in both the sub-markets is equal to the whole output OM which is fixed after equalizing AMR with the marginal cost. From figure III above, we can see that at equilibrium output (OM), the marginal cost is ME.

From figure I above, we can see that OM1 must be sold in sub-market A because the marginal revenue at M1E1 at amount OM1 = marginal cost ME. Similarly, OM2 must be sold in sub-market B because the marginal revenue at M2E2 at amount OM2 = marginal cost ME. It is important to note that OM = OM1 + OM2.

#### Step 3

Finally, to determine the price for markets A and B, the monopolist looks at the demand curve and does the following:

• Sets the price in sub-market A = OP1.
• Sets the price in sub-market B = OP2.

Since, the price in A > the price in B (because demand in A is less elastic than in B), OP1 > OP2.

## Solved Question on Price Discrimination

Q: Price discrimination is profitable only if the elasticity of demand in different sub-markets is:

1. uniform
2. different
3. less
4. zero

Answer: Price discrimination is possible only when the buyers from different sub-markets are willing to purchase the same product at different prices. If the elasticity of demand is the same, then the effect of the price change on the buyer will be identical too. Therefore, the correct answer is option b.

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