# Useful Notes on Price Determination Under Monopoly

The objective of price discrimination is to secure maximum profits by adjusting the price and the output in each distinct sub-market according to the demand conditions. Assuming constant cost conditions in each market, the monopolist has to determine (i) how much total output is to produced and its distribution in each market, and (ii) what prices should be charged in different markets.

For the sake of analytical simplicity we assume that the monopolist is able to divide the market for his product into two sub-markets, viz., I and II, whose demand curves are AR, and AR2 respectively with different price elasticities of demand (Fig. 14.10).

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The marginal revenue curves corresponding to these given demand or average revenue curves are given by MR1, and MR2 respectively. To determine the overall output, we need to know aggregate marginal revenue (AMR). To find AMR, we merely add the separate quantities in each market corresponding to each particular marginal revenue. In Fig. 14.19, AMR curve is obtained from the horizontal summation of the marginal revenue curves MR and MR as shown Fig 14.10 (a) and Fig 14.10 (b) respectively.

Given the marginal cost curve MC for the whole output of the monopolist, the discriminating monopolist would attain equilibrium at point ‘E’ where the curve intersects the AMR curve from below. At equilibrium, the monopolist produces and sells total output OQ (in the two sub-markets together) with aggregate marginal revenue or marginal cost of EQ.

The monopolist under consideration will distribute this output in the two markets in such a way that marginal revenue in each market is equal to this marginal cost of the entire output. In order to locate the equilibrium price and output levels in the two sub-markets I and II, a horizontal line is drawn from the market equilibrium point ‘E’ in Fig. 14.10 (c) so that it intersects the marginal revenue curves MR, and MR2 at points E, and E2 as shown in Fig. 14.10 (a) and Fig. 14.10(b) respectively.

At these equilibrium points, E1Q1 (orMR1,) = E2 Q2 (or MR2) = EQ (or AMR)= MC. With this, equilibrium condition of the marginal principle (equality of MR and MC) is satisfied in each sub-market (MR, = MC and MR2 = MC) besides in the market as a whole. Thus, the total profits of the discriminating monopolist are maximum and he attains equilibrium in both the markets, when the following condition is satisfied

MR1= MR2=AMR = MC

A discriminating monopolist produces and sells such quantities in each market at which, the marginal revenue in each of the markets is equal to the combined or common marginal cost of production, which is also equal to aggregate marginal revenue.

Thus, it follows that the monopolist will allocate sales between the separated markets until the marginal revenue of the last unit sold in each market is the same. If the marginal revenue in one market exceeds that in the other, it becomes profitable for the monopolist to divert sales from the other market towards the market, wherein the sale of an additional unit of output yields more revenue at the margin.

In other words, if the marginal revenues were unequal in the two sub-markets, the discriminating monopolist could increase total revenue without affecting total cost by shifting sales from lower marginal revenue market to the higher one. It will always pay a monopolist to reallocate a given total output between the sub-markets, till marginal revenue becomes equal in each market.

The combined marginal cost of the monopolist at equilibrium (EQ) is equal to marginal revenue in the first sub-market (E1Q1), when he sells OQ, output in this market. Likewise, this combined marginal cost of the monopolist is equal to marginal revenue in the second sub-market (E2Q2), when he sells OQ2 output in this market.

Thus, given demand and cost conditions, the discriminating monopolist will produce and supply total output of OQ, out of which OQ, amount will be sold in sub-market I and OQ2 amount will be sold in sub-market II. Hence, total output OQ = OQ, + OQ2. Here, an important thing to note is that the total output under price discrimination may be higher or lower than the one under uniform profit maximising price. However, for perfect price discrimination, total output is invariably higher.

The prices in the two sub-markets I and II are given by the heights of points R, and R2 on the demand curves AR, and AR2 corresponding to their quantities OQ1, and OQ2 in Fig. 14.10 (a) and Fig. 14.10 (b) respectively. Thus, output OQ1, of the product can be sold at a price of Q1R1 or OP, in sub-market I.

Similarly, output OQ2 of the product can be sold at a price of Q2R2 or OP2 in sub- market I. The price OP1 charged in sub-market I is higher than the price OP2 charged in sub-market II, since, elasticity of demand is comparatively lower in sub-market I.

The discriminating monopolist finds only an inappreciable fall in demand by charging a higher price in sub-market I. In fact, this price will be at a higher level as compared to the single monopoly price. Further, the monopolist should keep the price low in sub-market II to enable him to sell more quantity of output on account of higher price elasticity of demand in this market.

Here, the price determined under price discrimination will be lower than the single monopoly price. The total profits earned by the discriminating monopolist are given by the shaded area BCDE lying between AMR and MC curve (Fig. 14.10(c)).

Now, it can be inferred that a profit maximising discriminating monopolist attains equilibrium by charging a higher price in the sub-market, wherein the price elasticity of demand is low and a lower price in the sub-market, wherein the price elasticity of demand is relatively higher. As a result, lower and higher output will be sold in the two markets respectively than otherwise.

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