Analytic solutions for Hamilton-Jacobi-Bellman equations

Closed form solutions are found for a particular class of Hamilton- Jacobi-Bellman equations emerging from a differential game among fims competing over quantities in a simultaneous oligopoly framework. After the derivation of the solutions, a microeconomic example in a non-standard market is presented where feedback equilibrium is calculated with the help of one of the previous formulas

A multi-factor inequality approach to a transfer scheme: the case of Common Agricultural Policy

The purpose of this paper is to propose theoretical foundations on the impact of transfer scheme, e.g. Community Agricultural Policy, on income inequality within European Countries. First, we show that ex-post inequality (in the after-transfer distribution) may increase if either initial aggregate income or the amount of fiscal contributions are sufficiently high. Second according to welfare ordering, we characterize a multi-factor decomposition of the Atkinson index to gauge the impact of each income source on the inequality profile. Third, we introduce a methodology to construct a cooperative game played by different income factors (as net incomes and/or incoming transfers) explicitly measuring the cost of inequality across the population in terms of welfare loss. We finally rely on Banzhaf and Shapley values to determine the marginal contributions of each factor to overall inequality

Government Spending Under Non-Separability: a Theoretical Analysis

In this paper we derive analytic implicit form conditions for the qualitative analysis of government spending multipliers and the optimal level of government spending in presence of non-separability between private and public components of aggregate demand. Using the simplest neo-classical flexible price model with no capital accumulation, we show that Edgeworth dependence is not a suitable condition to utomatically assess the signs of the consumption and income multipliers, for which a more complex analysis must be carried out. We propose a detailed investigation of the form and the characteristics of the involved utility functions, which are crucial to such evaluation. We also show that if Edgeworth complementarity is strong enough, a public spending stimulus can raise at the same time private consumption and real activity. In order to reconcile our general framework with existing literature, we discuss recent examples of non-separable functional forms from the standpoint of our results, and argue that their consistency relies on specific assumptions about steady- state points

On Lie point symmetries in differential games

A technique to determine closed-loop Nash equilibria of n-player differential games is developed when their dynamic state-control system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems

The Incentive to Invest in Environmental-Friendly Technologies: Dynamics Makes a Difference

The established view on oligopolistic competition with environmental externalities has it that, since firms neglect the external effect, their incentive to invest in R&D for pollution abatement is nil unless they are subject to some form of environmental taxation. We take a dynamic approach to this issue, using a simple differential game to show that the conclusion reached by the static literature is not robust, as the introduction of dynamics shows that firms do invest in R&D for environmental-friendly technologies throughout the game, as long as R&D is accompanied by an output restriction exhibiting a distinctively collusive flavour. We also examine the social planning case and the effects of Pigouvian taxation, to show that there exists a feasible tax rate inducing profit-seeking firms to choose a combination of output and R&D such that the resulting social welfare level is the same as in the first bestpollution, environmental externality, R&D, differential games, social planning

Regulating Environmental Externalities Through Public Firms: A Differential Game

We investigate the possibility of using public firms to regulate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the Cournot-Nash game among profit-seeking firms; (ii) the Markov Perfect Nash equilibrium under social planning, where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) the Markov Perfect Nash equilibrium in a mixed setup where at least one firm is public, while the others remain profit-seeking agents. Our analysis identifies the conditions whereby having a mixed market as a regulatory instrument suffices to drive the industry to the same output, externality and social welfare as under planning, both along the optimal path and in steady state

Quality, Distance and Trade: a Strategic Approach

This paper contributes to the literature on distance and quality by identifying a firm-based force contributing to explain the observed increase of the quality of shipped goods with the distance of their destination market. This force originates from the influence of distance on firms' strategic behavior when the quality level of goods is a choice variable for them, and complements the ones already proposed in the literature. Our approach differs from the extant literature because it does not rely on technology or preference/income differentials to identify the determinants and drivers of trade flows. Moreover, it allows to clearly disentangle between the price setting and quality choice of firms. We find that distance has an unambiguously positive effect on the average quality of traded goods. Our results suit the empirical evidence on distance and quality and contribute to the analysis of the determinants of firms' trade performance

On the feedback solution of a differential oligopoly game with capacity adjustment

We propose a simple method for characterising analytically the feedback solution of oligopoly games with capital accumulation à la Solow-Swan. As a result, it becomes possible to contrast the feedback equilibrium against the corresponding one generated by open-loop information. Our method accommodates extensions of the stripped down oligopoly model in several directions. As an example, we expand the setup to include environmental effects and Pigouvian taxation

Emission taxation, green innovations and inverted-U aggregate R&D efforts in a linear state oligopoly game

We revisit the well known differential Cournot game with polluting emissions dating back to Benchekroun and Long (1998), proposing a version of the model in which environmental taxation is levied on emissions rather than the environmental damage. This allows to attain strong time consistency under open-loop information, and yields two main results which can be summarized as follows: (i) to attain a fully green technology in steady state, the regulator may equivalently adopt an appropriate tax rate (for any given number of firms) or regulate market access (for any given tax rate); (ii) if the environmental damage depends on emissions only (i.e., not on industry output) then the aggregate green R&D effort takes an inverted-U shape, in accordance with Aghion et al. (2005), and the industry structure maximising aggregate green innovation also minimises individual and aggregate emissions

Open Innovation in a Dynamic Cournot Duopoly

We analyze an Open Innovation process in a Cournot duopoly using a differential game approach where knowledge spillovers are endogenously determined via the R&D process. The game produces multiple steady states, allowing for an asymmetric solution where a firm may trade off the R&D investment against information absorption from the rival