Price Regulation and Network Spillovers

Abstract

We study price regulation for a monopolist operating in networked markets with demand spillovers. Achieving efficiency requires price reductions proportional to consumers' Katz-Bonacich centralities, which generally cannot be implemented by commonly used price regulations. Moreover, these regulations become asymptotically welfare neutral as spillovers grow. Nevertheless, some price regulations may still benefit consumers. In particular, average-price regulation robustly increases consumer surplus. By contrast, banning price discrimination increases consumer surplus only when more central consumers have higher intrinsic willingness to pay.

Figures (14)

• Figure 1: Three types of price regulations
• Figure 2: Firm's indifference curves and optimal pricing
• Figure 3: The black curve is the profit indifference curve and the red one is the surplus indifference curve. Pareto efficiency requires that the feasible set contains $\bm{\mathbbm{p}}$ and lies entirely within the shaded region. An illustrative feasible set is shown in blue.
• Figure 4: As $\delta$ increases, the firm’s indifference curve flattens in directions orthogonal to $\mathbf{w}_1$, and the gradient of profit for a given price $\mathbf{p}$ becomes increasingly aligned with $\mathbf{w}_1$. In the limit, the gradient is parallel to $\mathbf{w}_1$, implying that all prices with the same $\mathbf{w}_1$–weighted average yield the same profit.
• Figure 5: The dashed hyperplane consists of all price vectors whose average level equals that of $\mathbf{p}^{ur}$. Hence, whenever the feasible set intersects this hyperplane, the limiting optimal price lies on this intersection, and the regulation becomes neutral in the limit.

Theorems & Definitions (25)

• Lemma 1
• Example 1
• Lemma 2
• Lemma 3
• Theorem 1
• Lemma 4
• Theorem 2
• Lemma 5
• Proposition 1
• Proposition 2