The Envelope Theorem and Comparative Statics of Nash Equilibria

The Envelope Theorem for Nash equilibria shows that the strategic reaction of the other players in the game is important for determining how parameter perturbations affect a given player's indirect objective function. The fundamental comparative statics matrix of Nash equilibria for theithplayer in anN-player static game includes the equilibrium response of the otherN−1players in the game to the parameter perturbation and is symmetric positive semidefinite subject to constraint. This result is fundamental in that it holds for all sufficiently smooth Nash equilibria and is independent of any curvature or stability assumptions imposed on the game.Journal of Economic LiteratureClassification Numbers: C72, C61.     

A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS

A new comparative statics formalism using generalized compensated derivatives is presented that, in contrast to existing methodologies, directly yields constraint‐free semidefiniteness results for any differentiable, constrained optimization problem. The formalism provides a natural and powerful method of constructing comparative statics results, free of constraints and unrestricted in scope. New results on envelope relations, invariance conditions, rank inequalities and non‐uniqueness are derived that greatly extend their utility and reach. The methodology is illustrated by deriving the comparative statics of multiple linear constraint utility maximization models and the principal‐agent problem with hidden actions, both highly nontrivial and hitherto unsolved problems.     

Enhancing environmental information transparency through corporate social responsibility reporting regulation

This research aims to contribute to the scientific debate about the lack of interlinkages between mandatory non-financial reporting and sustainable business models. For our purposes, a counter-accounting analysis was conducted on the non-financial reports of a sample of 145 Italian firms interested by the Directive 2014/95/EU effects. Specifically, the study adopts an empirical approach to evaluate environmental information transparency, which represents one of the main critical issues concerning the non-financial declarations prepared by European Italian Public Interest Entities (PIEs) to comply with Directive 2014/95/EU. The results highlight that corporate governance and report characteristics affect environmental transparency. Furthermore, the results confirm the overall attitude to avoid the disclosure of unfavourable or unavailable environmental information through impression management strategies. Finally, the analysis underlines the opportunities for policymakers to rethink mandatory non-financial reporting to sustain the ecological transition of European PIEs.     

Potential Tax Revenue from a Regulated Marijuana Market A Meaningful Revenue Source

A bstract . Dissatisfaction with current drug policy measures has led to a push for the regulation of drugs , especially marijuana . On the premise that such regulation is a real possibility, estimates of potential tax revenue from a regulation scheme and critical comments on other estimates of the size of the marijuana market are presented. For 1991, potential tax revenue is estimated to range from 2.55 to 9.09 billion dollars. The uncertainty surrounding the price elasticity of demand for marijuana, home cultivation of marijuana by individual users, and the extent to which purchases may still be made from the black market are discussed, as are their implications for potential tax revenue.     

Common labor market,attachment and spillovers in a large metropolis

In this paper, we extend the home-attachment model to a setting with multiple (more than two) jurisdictions and consider non-cooperative policy making for provision of different types of metropolitan public goods in the presence of a common labor market. Migration and working place choices are independent. We show that the optimal redistributive policy implemented by a central authority always yields equalization of private consumption levels across jurisdictions. This result holds whether or not policy makers are able to anticipate migration responses to their policy choices. In the decentralized leadership games, jurisdictions make choices that fully internalize externalities.     

Comparative Statics of Money-goods Specifications of the Utility Function

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem. Received March 9, 2001; revised version received September 3, 2001     

How to do comparative dynamics on the back of an envelope in optimal control theory

The dynamic primal-dual methodology of Caputo (1988) is extended and applied to a general nonautonomous optimal control problem with a fixed and finite time horizon, a fixed vector of initial states, a free vector of terminal states, a time-independent vector of parameters, and a vector of nondifferential constraints on the state and control variables. A symmetric negative semidefinite matrix subject to constraint is shown to characterize the qualitative properties of the model as implied by the dynamic maximization assertion.