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Price-output determination under price discrimination

Let us suppose there are two markets – Market A and Market B to which a price discriminating monopolist has to sell his products. Both markets have different price elasticities i.e., Market A – inelastic demand and Market B – elastic demand.
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The diagram shows Da and Db as the Average Revenue curves. MRa and MRb are the Marginal revenue curves of the respective markets. Since all output is under one organization in Monopoly, there is only one Marginal Cost curve. TMR is the total Marginal revenue curve. It is a lateral summation of the two curves MRa and MRb. The twin conditions for equilibrium (i) MC = TMR (ii) MC = MRa = MRb
The discriminating monopolist not only has to decide how much to produce but also has to decide the output in two sub-markets. In such a way and such a price that he maximizes his profits. In the diagram MC and TMR intersect at E. OM is the total output of the monopolist. EM is line of equal of MR. It indicates OM1 is sold in market A at P1 price. OM2 is sold in market B at P2 Price. Under this arrangement the MC of the total output EM is equal to MR in cash separate market.
Thus the discriminating monopolist charges a higher price from the market which has in-elastic demand and charges a lower price from the market which has elastic demand. To conclude, the monopolist benefits from both the markets.
A monopolist charges a higher price from the market which has a relatively inelastic demand.
Suppose the price of a product is ₹ 45 and the elasticity of demand in markets A and B are 3 and 5 respectively. Then,
MR of market A = AR x (e-1)/e
= 45 x (3-1)/3
= 30
MR of market B = AR x (e-1)/e
= 45 x (5-1)/5 = 36
Thus, we see that the marginal revenues in the two markets are different when the elasticity of demand at a single price is different. Also, the MR in the market in which elasticity is high i.e. market B, is greater than the MR of the market where the elasticity is low i.e. market A. Now, it is profitable for the monopolist to transfer some quantity of the product from A to B. When he does so, the loss in revenue (₹ 30) will be compensated by the gain in revenue (₹ 36). On the whole, the gain in revenue will be ₹ 6 (36-30). We see that the monopolist is now discriminating between markets A and B. The monopolist continues to transfer units from A to B upto a point when the MR in the two markets become equal. After this, the monopolist will charge different prices in the markets, that is, higher price in market A which has lower elasticity of demand.

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