Production externalities and convexity

This paper explores in some detail the relation between production externalities (detrimental or positive) and convexity of the production-possibilities set. A set of sufficient conditions to rule out local non-convexity is derived in terms of the original production functions. The problem is illustrated for the case of one productive input. Regardless of whether externalities lead to non-convexity they may still give rise to a multiplicity of local private maxima even when the social maximum is a global one. The possibility of unique private maximum coupled with multiple local social maxima had been mentioned before by Baumol among others. The fact that externalities may lead to the converse case, as shown in the paper, seems not to have been noticed before.     

Option values,stipends and the returns to educational investment

In this paper we use a dynamic model of the returns to educational investment to analyze the flow of students moving through the various stages of an educational system. Dropout and graduation rate are linked to the profitability of an educational stage and thus may be influenced by an appropriate choice of stipend level. To determine the effects of changes in stipends on the output of the educational system we hypothesize a probability distribution of abilities in the population. The parameters of this distribution permit the estimation of the effects of stipends on the graduation rate of each educational stage.     

Evaluating capital investment projects

The risk-adjusted discount rate method for evaluating capital investment projects applies the risk-adjusted rate to equilibrium as well as disequilibrium expected returns, leading to biased NPV calculations. This paper uses the CAPM framework, and suggests a procedure for applying the risk-adjusted rate without causing a bias. The procedure is shown to result in NPVs identical to those obtained by the certainty equivalent approach. A comparison with a previously suggested procedure is also provided.     

Auctions with a random number of identical bidders

We examine and compare the (normally, mixed) symmetric equilibrium bidding strategies in first-price and all-pay common value multiple item auctions with a random number of bidders, who only seek one of the identical items and have the same budget.     

The independent and joint effects of the skill and physical bases of relatedness in diversification

By examining the independent and joint effects of the skill and physical bases of relatedness, this study develops a multidimensional view of relatedness in diversification. The paper compares the ways the two bases identify relatedness, and examines empirically the relationship between relatedness and performance for a sample of 158 large diversified manufacturing firms. Each base of relatedness alone had no significant effect on financial performance. However, when the two approaches were combined, there was a strong positive effect on most indicators of performance. The findings demonstrate how different bases of relatedness complement and extend one another, and they clarify findings of previous studies that used a single base of relatedness. © 1998 John Wiley & Sons, Ltd.     

Some properties of the minimum and the maximum of random variables with joint logconcave distributions

It is shown that if (X ₁, X ₂, . . . , X _n ) is a random vector with a logconcave (logconvex) joint reliability function, then X _P = min _i∈P X _i has increasing (decreasing) hazard rate. Analogously, it is shown that if (X ₁, X ₂, . . . , X _n ) has a logconcave (logconvex) joint distribution function, then X ^P  = max _i∈P X _i has decreasing (increasing) reversed hazard rate. If the random vector is absolutely continuous with a logconcave density function, then it has a logconcave reliability and distribution functions and hence we obtain a result given by Hu and Li (Metrika 65:325–330, 2007). It is also shown that if (X ₁, X ₂, . . . , X _n ) has an exchangeable logconcave density function then both X _P and X ^P have increasing likelihood ratio.     

Stochastic orderings of convolution residuals

In this paper we study convolution residuals, that is, if $X_1,X_2,\ldots ,X_n$ are independent random variables, we study the distributions, and the properties, of the sums $\sum _{i=1}^lX_i-t$ given that $\sum _{i=1}^kX_i>t$ , where $t\in \mathbb R $ , and $1\le k\le l\le n$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described.     

Congestion games with load-dependent failures: Identical resources

We define a new class of games, congestion games with load-dependent failures (CGLFs). In a CGLF each player can choose a subset of a set of available resources in order to try and perform his task. We assume that the resources are identical but that players' benefits from successful completion of their tasks may differ. Each resource is associated with a cost of use and a failure probability which are load-dependent. Although CGLFs in general do not have a pure strategy Nash equilibrium, we prove the existence of a pure strategy Nash equilibrium in every CGLF with nondecreasing cost functions. Moreover, we present a polynomial time algorithm for computing such an equilibrium.