Week 8 - Price Discrimination (Second Degree) - Non-Linear pricing

What is second-degree price discrimination?

Prices are based on observable characteristics of the purchase that correlate with customers' preferences.

What does a monopolist offer in second-degree price discrimination?

A menu of price-quantity bundles designed for self-selection by consumers.

What is the utility function used in the nonlinear pricing framework?

U = θV(q) − T(q), where q is the amount consumed and T(q) is the amount paid.

What does θ represent in the utility function?

θ indexes consumer type, indicating the strength of preference for the good.

What are the two types of consumers in the second-degree price discrimination model?

High types (θh) and low types (θl), where θh > θl > 0.

What is the significance of the population share λ?

λ represents the proportion of low types in the consumer population.

What is the condition for the monopolist to sell to both types of consumers?

The population share λ must be large enough.

What is the perfect (first-degree) price discrimination benchmark?

The monopolist can distinguish between consumers and offers personalized prices to maximize surplus.

What happens if a high type pretends to be a low type in second-degree price discrimination?

The high type can choose the low type's bundle, gaining utility without revealing their true type.

What is the monopolist's strategy to prevent high types from pretending to be low types?

Offer different quantities and prices to make the high type's bundle more attractive.

What are the two constraints faced by the monopolist in profit maximization?

Individual Rationality (IR) and Incentive Compatibility (IC).

What is the Individual Rationality (IR) constraint?

Both types must receive non-negative utility from their respective bundles.

What is the Incentive Compatibility (IC) constraint?

High types must prefer their own bundle over the low type's bundle.

How does the monopolist ensure both constraints hold?

By making both constraints hold with equality to avoid leaving money on the table.

What is the mathematical expression for the monopolist's profit?

πm = λ(Tl − cql) + (1 − λ)(Th − cqh).

What does the First Order Condition (FOC) indicate for low types?

θlV′(ql) = c, meaning the marginal utility equals marginal cost.

What does the FOC indicate for high types?

θhV′(qh) = c, ensuring efficient pricing for high-demand consumers.

What is the implication of having qh > ql?

High types receive a higher quantity than low types, reflecting their greater willingness to pay.

How does the monopolist distort quantities under second-degree price discrimination?

By reducing the low type's quantity to make it less attractive to high types.

What is a real-life example of second-degree price discrimination?

Airlines offering different classes of seating, where economy class is less comfortable.

What is the role of quality in second-degree price discrimination?

Higher quality goods can be priced higher, attracting high types willing to pay more.

What is the outcome of nonlinear pricing for high-demand consumers?

They often pay a lower per-unit price due to the structure of the pricing model.

What happens when the monopolist maximizes profit under the given constraints?

They choose transfers T as large as possible while ensuring consumer acceptance.

What is the effect of the IR and IC constraints on pricing?

They ensure that the monopolist does not lose potential profits by underpricing.

What is the significance of the area under the demand curve?

It represents total surplus, which is maximized in perfect price discrimination scenarios.

How does the monopolist adjust quantities to maximize profit?

By balancing marginal profit losses and gains across consumer types.

What is the relationship between surplus and price in second-degree price discrimination?

Surplus is maximized when the monopolist can effectively segment consumers by willingness to pay.