Durable-Goods Monopolists, Network Effects and Penetration Pricing

We study the pricing problem of a durable-goods monopolist. With network effects, consumption externalities among heterogeneous groups of consumers generate a discontinuous demand function. Consequently, the lessor has to offer a low price in order to reach the mass market, whereas the seller has the option to build a customer base by setting a lower initial price and raise the price later in the mass market, which explains the practice of introductory pricing. Contrary to the existing literature, we show that profits from selling network goods may be higher than from leasing. Further, the seller in fact over-invests in R&D and makes the product more durable than necessary.Penetration pricing, network externality

The Optimal Decoupled Liabilities: A General Analysis

The “decoupled” liability system awards the plaintiff an amount that differs from what the defendant pays. The previous approach to the optimal decoupling design is based on the assumption of complete information, which results in an optimal liability for the defendant “as much as he can afford.” This extreme conclusion may hinder the acceptability of the decoupling system. This paper proposes an alternative design based on the assumption that agents in the post-accident subgame have asymmetric information. Our model indicates that the optimal penalty faced by the defendant is generally greater than the optimal award to the plaintiff. When the potential harm is sufficiently large, the optimal penalty can be approximated by a multiple of the harm, but the plaintiff receives only a finite amount of the damages regardless of the loss suffered. Such a decoupling scheme deters frivolous lawsuits without reducing the defendants’ incentives to exercise care. Additionally, this paper derives comparative static results concerning how the trial costs of the plaintiff and defendant affect the optimal design of decoupling.

The Thresholding Greedy Algorithm versus Approximations with Sizes Bounded by Certain Functions ff

Let $X$ be a Banach space and $(e_n)_{n=1}^\infty$ be a basis. For a fixed function $f$ in a certain collection $\mathcal{F}$ (closed under composition), we define and characterize ($f$, greedy) and ($f$, almost greedy) bases. These bases nontrivially extend the classical notion of greedy and almost greedy bases. We study relations among ($f$, (almost) greedy) bases as $f$ varies and show that while a basis is not almost greedy, it can still be ($f$, greedy) for some $f\in \mathcal{F}$. Furthermore, we prove that for all non-identity function $f\in \mathcal{F}$, we have the surprising equivalence \mbox{($f$, greedy)}\ \Longleftrightarrow \ \mbox{($f$, almost greedy)}.Comment: 20 page