Suppose that a monopolist sells to two groups that have...

Suppose that a monopolist sells to two groups that have constant elasticity demand curves, with elasticity $\epsilon_{1}$ and $\epsilon_{2} .$ The marginal cost of production is constant at $c .$ What price is charged to each group?

Key Concepts

Monopolist Price Discrimination

Monopolist price discrimination involves charging different prices to different consumer groups based on their willingness to pay or elasticity of demand. In this context, the monopolist exploits differences in demand elasticities between the groups to maximize overall profits by setting group-specific markups above marginal cost.

Constant Elasticity Demand

A constant elasticity demand curve means that the percentage change in quantity demanded resulting from a percentage change in price is constant, regardless of the price level. This property simplifies the analysis of consumer behavior and the derivation of optimal pricing rules, as the elasticity remains the same along the entire demand curve.

Marginal Cost

Marginal cost is the additional cost incurred by producing one more unit of a good. In this problem, the marginal cost is constant at c, which allows the monopolist to directly compute markup over cost using the elasticity-based pricing formula without dealing with increasing or decreasing marginal production costs.

Markup Rule (Lerner Index)

The markup rule, often expressed through the Lerner Index, relates a monopolist's pricing power to the elasticity of demand. Specifically, for a group with constant elasticity of demand, the optimal price is given by p = c(?/(? - 1)), implying that the percentage markup (p - c)/p equals 1/?. This rule shows that consumers facing less elastic (more inelastic) demand are charged a higher markup, while those with more elastic demand are charged a lower markup.

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