Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Authoritarian Responses to Foreign Pressure: Spending, Repression, and Sanctions

This paper explores how international sanctions affect authoritarian rulers’ decisions concerning repression and public spending composition, and how different authoritarian rulers respond to foreign pressure. If sanctions are assumed to increase the price of loyalty to the regime, then rulers whose budgets are not severely constrained by sanctions will tend to increase spending in those categories that most benefit their core support groups. In contrast, when constraints are severe due to reduced aid and trade, dictators are expected to greatly increase their levels of repression. Using data on regime types, public expenditures and spending composition (1970–2000) as well as on repression levels (1976–2001), we show that the empirical patterns conform well to our theoretical expectations. Single-party regimes, when targeted by sanctions, increase spending on subsidies and transfers which largely benefit more substantial sectors of the population and especially the urban classes. Likewise, military regimes increase their expenditures on goods and services, which include military equipment and soldiers’ and officers’ wages. Conversely, personalist regimes reduce spending in all categories, especially capital expenditures, while increasing repression much more than other regime types when targeted by sanctions.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Two weight inequalities for discrete positive operators

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Product differentiation, competitive pressure and the effects of innovation on the success and survivability of firms in oligopoly markets

In a recent paper Tishler and Milstein (2009) fi…nd that increased competition may increase aggregate R&D spending while market output decreases. Therefore, they obtain the surprising result that R&D spending is excessive when competition becomes intense. Their result is based on the standard linear demand function for differentiated products introduced by Bowley (1924) where decreased product differentiation is interpreted as more competitive pressure. In this paper I show that at an aggregate level this interpretation is problematic because equilibrium effects are dominated by a demand reduction effect. A slight modifi…cation of the standard demand function eliminates this effect. For the Tishler and Milstein (2009) setting it is shown that then increased competition increases both R&D spending and aggregate market output. Therefore, at least for consumers, more intense competition increases welfare. Journal of Economic Literature Classi…fication Numbers: D43, L1, O3. Keywords: Oligopoly markets, Product differentiation, Competitive pressure.

Innovation or Imitation? The effect of spillovers and competitive pressure on firms' R&D strategy choice

This article provides a theoretical and empirical analysis of a firm's optimal R&D strategy choice. In this paper a firm's R&D strategy is assumed to be endogenous and allowed to depend on both internal firms. characteristics and external factors. Firms choose between two strategies, either they engage in R&D or abstain from own R&D and imitate the outcomes of innovators. In the theoretical model this yields three types of equilibria in which either all firms innovate, some firms innovate and others imitate, or no firm innovates. Firms'equilibrium strategies crucially depend on external factors. We find that the efficiency of intellectual property rights protection positively affects firms'incentives to engage in R&D, while competitive pressure has a negative effect. In addition, smaller firms are found to be more likely to become imitators when the product is homogeneous and the level of spillovers is high. These results are supported by empirical evidence for German .rms from manufacturing and services sectors. Regarding social welfare our results indicate that strengthening intellectual property protection can have an ambiguous effect. In markets characterized by a high rate of innovation a reduction of intellectual property rights protection can discourage innovative performance substantially. However, a reduction of patent protection can also increase social welfare because it may induce imitation. This indicates that policy issues such as the optimal length and breadth of patent protection cannot be resolved without taking into account specific market and firm characteristics. Journal of Economic Literature Classification Numbers: C35, D43, L13, L22, O31. Keywords: Innovation; imitation; spillovers; product differentiation; market competition; intellectual property rights protection.