Q.A monopolist sells in two separate markets with demand functions $P_1 = 20 - Q_1$ in Market I and $P_2 = 15 - 0.5Q_2$ in Market II, and a constant marginal cost of ₹5. Find the price charged in each market under third-degree price discrimination.

Price discrimination occurs when a seller (typically a monopolist) charges different prices to different buyers for the same product, and the price gap is not justified by any difference in cost. The aim is to capture more consumer surplus as profit.

How it works

The firm splits buyers into groups and charges each group what it is willing to pay. In third-degree discrimination it allocates output so that marginal revenue is equal across markets ($MR_A = MR_B$). Using $MR = P\left(1 - \tfrac{1}{|e|}\right)$, equal MR forces the less elastic market to carry the higher price.

Quick example

A monopolist serves two separable markets. At the profit-maximising output it sets a common marginal revenue of MR = ₹30. Market A has elasticity $e_A = 2$; Market B has $e_B = 4$. Find each price.

1. Rearrange the formula: $P = \dfrac{MR}{\,1 - \tfrac{1}{e}\,}$.
2. Market A: $P_A = \dfrac{30}{1 - \tfrac{1}{2}} = \dfrac{30}{0.5} = ₹60$.
3. Market B: $P_B = \dfrac{30}{1 - \tfrac{1}{4}} = \dfrac{30}{0.75} = ₹40$.