Question

Describe the effects of a monopolist choosing to discriminate between two markets (assume a starting condition of equal prices in both markets). Is it always possible to profit from this kind of discrimination? Does elasticity matter? How should quantities be adjusted?

Answer 1

If the monopolist chooses to discriminate between two markets, then this is known as Third Degree Price Discrimination. We assume that prices in both markets are equal to each other.

Let the Marginal Revenue in firm 1 = MR1

Marginal Revenue in firm 2 = MR2

Marginal Cost = MC

Chances of getting more profit is always there as higher prices can be charged based on elasticity of demand for two different markets.

Below derivation shows why elasticity matters in the third degree price discrimination:

TR = P*Q

MR = derivate of TR wrt Q

= P + Q*(dP/dQ)

= P*{1 + (Q/P)*(dP/dQ)}

= P*[1 + (1/e)]

Since, Elasticity = (dQ/dP)*((P/Q)

Now at equilibrium, MR1 = MR2 = MC

Elasticiy in market 1 = e1

Elasticity in market 2 = e2

So, MR1 = MR2

P1*[1 + (1/e1)] = P2*[1 + (1/e2)]

So, higher price is charged in the market where elasticity of demand is lower (inelastic demand) and lower price is charged in the market who has elastic demand.

So, Elasticities matters. Quantities to be sold in these market are also to be adjusted based on respective elasticity. Once, we know P1 and P2 we can derive the individual markets q1 and q2.