Under third-degree price discrimination, a profit-maximizing monopolist allocating output … — JAMB UTME

Under third-degree price discrimination, a profit-maximizing monopolist allocating output between two separated sub-markets with identical marginal costs will set a higher price in the sub-market exhibiting a higher price elasticity of demand.

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The statement is False. A profit-maximizing monopolist charges a lower price in the sub-market with higher price elasticity of demand and a higher price in the sub-market with lower price elasticity of demand.

The statement is false because the optimal pricing strategy under third-degree price discrimination requires charging a lower price in the sub-market where demand is more price-elastic and a higher price where demand is less price-elastic.

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Express Marginal Revenue (

MR

) in terms of Price (

P

) and Price Elasticity of Demand (

|E_d|

MR = P \left(1 - \frac{1}{|E_d|}\right)

This formula relates marginal revenue to product price and market elasticity.

Apply the multi-market equilibrium condition for a third-degree price discriminator.

MR_1 = MR_2 = MC

To maximize overall profit, marginal revenue earned from the last unit sold in each sub-market must be equal and matched to common marginal cost.

Equate the marginal revenue expressions for sub-market 1 and sub-market 2.

P_1 \left(1 - \frac{1}{|E_1|}\right) = P_2 \left(1 - \frac{1}{|E_2|}\right)

This sets up the comparative pricing equation between the two markets.

Analyze the pricing relationship when

|E_1| > |E_2|

Since

|E_1| > |E_2|

\left(1 - \frac{1}{|E_1|}\right) > \left(1 - \frac{1}{|E_2|}\right)

, which requires

P_1 < P_2

for equality to hold.

A higher elasticity term yields a larger bracketed multiplier, meaning price must be lower in market 1.

Anahtar Kavram

Inverse elasticity rule in third-degree price discrimination

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