Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Summary. Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion. Received: June 25, 1999; revised version: March 2001     

Optimal patent length and breadth in an economy with creative destruction and non-diversifiable risk

In this paper, I examine the optimal patent shape in an economy in which R&D firms innovate and imitate, households face non-diversifiable risk and there is externality in production and R&D. With non-diversifiable risk, a household’s consumption and investment decisions are interlinked. This economy contains industries of two kinds: monopoly industries with an innovator only, and duopoly industries with an innovator and an imitator. I define patent length as the expected time in which an innovation is imitated, and patent breadth as the innovator’s profit share in an industry after a successful imitation. The government can control patent length by the requirements for accepting a substitute for a patented good, and patent breadth by imposing compulsory licensing and royalties for the patentee after a successful imitation. I show that the stronger the externality in production relative to R&D is, the slower the optimal growth rate, the larger the optimal proportion of duopoly industries, and the longer and narrower the optimal patent.     

Does a strong patent regime discourage innovation?

Does a strengthening of the patent regime impact R&;D expenditure? For the US semiconductor industry, a strengthening of the patent regime in the 1980s was followed by a sharp increase in patenting but had almost no impact on R&;D expenditure. This paper attempts to understand this patent paradox by taking some of the industry features into account. We present a model of invention and product development in complex industries where product development involves putting together a large number of inventions and where licensing of patentable inventions is common. While a stronger patent regime leads to higher patenting in both in presence and absence of licensing, the positive relationship between patenting and R&;D is weakened in presence of licensing since licensing provides an alternative way of accessing inventions. A stronger patent regime, therefore, may only create weak incentives to increase R&;D, while strongly increasing patenting activities in such an industry.     

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.     

Severance Payment: Incentive or Lethargy Effect?

The aim of the paper is to determine the impact of severance payment on the motivation of the worker to make an effort, when there is a risk for him to be dismissed once his effort was made. We highlight through a two‐stage model the various factors which influence the dismissal decision by the firm and the worker's effort, such as the initial wage, the litigation costs and the relative bargaining powers of the parties when the relationship ends or goes on. In this context, we show that the impact of the severance payment paid ex post in case of dismissal on the level of effort chosen by the worker ex ante may depend on such characteristics.     

Equity-settled share-based payments and their (strategic) use under asymmetric information

Share-based payments are of widespread use in today's economy. Consulting firms are increasingly accepting equity compensation for their services (particularly from startups) and many governments provide fiscal incentives to support this choice. Likewise, profit-sharing licensing is an on-trend business practice by innovative firms and patent holders when transferring their technology to interested adopters. This paper unveils strategic considerations according to which an agent/seller designs its optimal policy in regard to the equity share to request in exchange for its service, technology, or trademark. The model assumes a fringe of interested users/customers differentiated by both the support they need from the seller and the value of the underlying relationship; and also holding an informational disadvantage on their own type. Given the seller's cost configuration, equilibrium outcomes entail entering a profit-sharing relationship either with the high-type customers only or with all customers. Yet, in this case, equity-based payment claims are —for rent extraction purposes— common (i.e., not differentiated) across types.     

Drastic innovations and multiplicity of optimal licensing policies

Considering the licensing of a drastic cost-reducing innovation by an outside innovator in an n-firm Cournot oligopoly, we show that when the innovator uses combinations of fees and royalties, there are either n − 1 or n optimal licensing policies.     

MEASURING VARIATIONS IN LIFETIME WELFARE EX ANTE AND EX POST: SOME EXPLORATORY CALCULATIONS

Whereas longevity‐adjusted consumption measures have become increasingly used as indicators of lifetime standards of living, it remained unnoticed that those measures, by relying on period – rather than cohort – life tables, constitute indicators of expected – rather than actual – lifetime standards of living. In order to estimate the actual gap between ex ante and ex post measures of lifetime welfare, this paper computes, for 19th‐century European economies, longevity‐adjusted consumption measures based on period and cohort life tables. It is shown that the gap between ex ante and ex post measures is statistically significant, and that attempts to reduce it are likely to be unsuccessful, because standards of living tend to exhibit, over temporal horizons as long as a human life, structural breaks, which make the ex ante measurement of lifetime welfare highly speculative.     

Uncertainty,Learning and Heterogeneity in International Environmental Agreements

This paper concerns the formation of International Environmental Agreements under uncertainty about environmental damage with different models of learning (complete learning, partial learning or no learning). The results of the existing literature are generally pessimistic: the possibility of either complete or partial learning generally reduces the level of global welfare that can be achieved from forming an IEA relative to no learning. That literature regards uncertainty as a parameter common to all countries, so that countries are identical ex ante as well as ex post. In this paper we extend the literature to the case where there is no correlation between damage costs across countries; each country is uncertain about a particular parameter (in our case the benefit-cost ratio) drawn from a common distribution but, ex post, each country’s realized parameter value is independently drawn. Consequently, while countries remain identical ex ante, they may be heterogeneous ex post. We show that this change reinforces the negative conclusions about the effects of partial learning on international environmental agreements, but, under certain conditions, moderates the negative conclusions about the effects of complete learning.     

Hybrid Contests

This paper examines hybrid contests where participants commit two types of resources to improve their probability of winning the prize. The first type is forfeited ex ante, before the prize is allocated, by winners and losers alike, while the second is committed ex ante by all contenders but expended ex post, after the prize is allocated, and only by the contestant that wins the prize. The model yields a number of interesting results. Among them is the finding that, as the number of contestants increases, the ex ante expenditures of individual contestants decrease while the ex post expenditure increases. Even more interesting, the total of the ex ante and ex post expenditures by the contenders in a hybrid contest may decrease with the number of competitors. The study also finds that there is no rent overdissipation, and compares the total expenditures in the contest and “all‐pay” allocation mechanisms.