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John K H Quah - One of the best experts on this subject based on the ideXlab platform.

  • the Comparative Statics of constrained optimization problems
    Econometrica, 2007
    Co-Authors: John K H Quah
    Abstract:

    This paper develops and applies some new results in the theory of monotone Comparative Statics. Let f be a real-valued function defined on R-super-l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R-super-l. We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle. Copyright The Econometric Society 2007.

  • Comparative Statics informativeness and the interval dominance order
    Economics Papers, 2007
    Co-Authors: John K H Quah, Bruno Strulovici
    Abstract:

    We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone Comparative Statics based on this order. This way of ordering functions is weaker then the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the Comparative Statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics – specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann’s (1988) concept of informativeness – generalize to payoff functions obeying the interval dominance order.

  • Comparative Statics with Concave and Supermodular Functions
    2004
    Co-Authors: John K H Quah
    Abstract:

    Certain problems in Comparative Statics, including (but not exclusively) certain problems in consumer theory, cannot be easily addressed by the methods of lattice programming. One reason for this is that there is no order on the choice space which orders choices in a way which conforms with the comparison desired, and which also orders constraint sets in the strong set order it induces. The objective of this paper is to show how lattice programming theory can be extended to deal with situations like these. We show that the interaction of concavity and supermodularity in objective or constraint functions yield a structure that is very useful for Comparative Statics.

  • market demand and Comparative Statics when goods are normal
    Journal of Mathematical Economics, 2003
    Co-Authors: John K H Quah
    Abstract:

    Abstract This paper examines the impact of the normality assumption on the structure of market demand and on general equilibrium Comparative Statics. We define a new notion of Comparative Statics which is fundamentally related to normality and examine its incidence in exchange, production and financial economies.

  • Comparative Statics and Welfare Theorems When Goods are Normal
    2001
    Co-Authors: John K H Quah
    Abstract:

    We examine the impact of the normality assumption, together with the weak axiom, in three related areas of general equilibrium theory. Most obviously, these properties have important implications for equilibrium Comparative Statics, in the context of exchange, production or (incomplete) financial economies. They also shed light on the relationship between Comparative Statics and the structure of the excess demand function, which could be thought of as an aspect of the correspondence principle (Samuelson (1947)). Lastly, these properties permit the construction of welfare-like theorems which do not rely on the classical assumptions of individual rationality.

Michael R. Caputo - One of the best experts on this subject based on the ideXlab platform.

  • Comparative Statics OF A MONOPOLISTIC FIRM FACING RATE‐OF‐RETURN AND COMMAND‐AND‐CONTROL POLLUTION CONSTRAINTS
    Bulletin of Economic Research, 2014
    Co-Authors: Michael R. Caputo, Dmitriy Popov
    Abstract:

    The intrinsic Comparative Statics properties of a general rate-of-return regulated, profitmaximizing model of a monopolist facing a command-and-control pollution constraint are derived. Recent advances in the theory of Comparative Statics are used to derive the basic Comparative Statics of the model, which are contained in an observable negative semidefinite matrix and possess the form of Slutsky-like expressions. We consider several command-and-control pollution constraints that are commonly implemented in practice, and conclude that the intrinsic Comparative Statics properties of the model are qualitatively invariant to the type of command-andcontrol pollution constraint imposed. We compare our results with those extant, and find that several basic results from the standard A-J model no longer hold in our model.

  • Comparative Statics of a monopolistic firm facing rate of return and command and control pollution constraints
    Bulletin of Economic Research, 2014
    Co-Authors: Michael R. Caputo, Dmitriy Popov
    Abstract:

    The intrinsic Comparative Statics properties of a general rate-of-return regulated, profitmaximizing model of a monopolist facing a command-and-control pollution constraint are derived. Recent advances in the theory of Comparative Statics are used to derive the basic Comparative Statics of the model, which are contained in an observable negative semidefinite matrix and possess the form of Slutsky-like expressions. We consider several command-and-control pollution constraints that are commonly implemented in practice, and conclude that the intrinsic Comparative Statics properties of the model are qualitatively invariant to the type of command-andcontrol pollution constraint imposed. We compare our results with those extant, and find that several basic results from the standard A-J model no longer hold in our model.

  • Comparative Statics of a monopolistic firm facing price-cap and command-and-control environmental regulations
    Energy Economics, 2014
    Co-Authors: Michael R. Caputo
    Abstract:

    An exhaustive Comparative Statics analysis of a model of a monopolistic firm facing price-cap regulation and a variety of commonly implemented command-and-control environmental regulations is carried out. The Comparative Statics are intrinsic to each of the models and thus form their basic, empirically testable properties. Several unanticipated results emerge from the analysis. In particular, it is shown that a subset of the intrinsic Comparative Statics are qualitatively invariant to all of the commonly employed command-and-control environmental regulations that a price-cap regulated profit-maximizing monopoly might face, while others are specific to the type of command-and-control environmental regulation in place.

  • A Complete Method of Comparative Statics for Optimization Problems (Unabbreviated Version)
    arXiv: Optimization and Control, 2013
    Co-Authors: M. Hossein Partovi, Michael R. Caputo
    Abstract:

    A new method of deriving Comparative Statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally, it applies to any differentiable system governed by an extremum principle, be it a physical system subject to the minimum action principle, the equilibrium point of a game theoretical problem expressible as an extremum, or a problem of decision theory with incomplete information treated by the maximum entropy principle. The method of generalized compensated derivatives is natural and powerful, and its underlying structure has a simple and intuitively appealing geometric interpretation. Several extensions of the main theorem such as envelope relations, symmetry properties and invariance conditions, transformations of decision variables and parameters, degrees of arbitrariness in the choice of Comparative Statics results, and rank relations and inequalities are developed. The relationship of the new method to existing formulations is established, thereby providing a unification of the main differential Comparative Statics methods currently in use. A second theorem is also established which yields exhaustive, constraint-free Comparative Statics results for a general, constrained optimization problem. This theorem subsumes all other Comparative Statics formulations. The method is illustrated with a variety of models, some well known, such as profit and utility maximization, where several novel extensions and results are derived, and some new, such as the principal-agent problem, the efficient portfolio problem, a model of a consumer with market power, and a cost-constrained profit maximization model.

  • a complete theory of Comparative Statics for differentiable optimization problems
    Metroeconomica, 2006
    Co-Authors: Hossein M Partovi, Michael R. Caputo
    Abstract:

    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.

Susan Athey - One of the best experts on this subject based on the ideXlab platform.

  • monotone Comparative Statics under uncertainty
    Quarterly Journal of Economics, 2002
    Co-Authors: Susan Athey
    Abstract:

    This paper analyzes monotone Comparative Statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for Comparative Statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single-crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.

Christian Gollier - One of the best experts on this subject based on the ideXlab platform.

  • Relatively weak increases in risk and their Comparative Statics
    Economics Letters, 2002
    Co-Authors: Georges Dionne, Louis Eeckhoudt, Christian Gollier
    Abstract:

    Abstract We propose in this paper a new condition on increases in risk to obtain the desirable Comparative Statics properties for non-linear payoffs. Our new concept of relatively weak increases in risk extends the definition of relatively strong increases in risk (Black and Bulkley, International Economic Review , 1989, 30, 119–130).

  • Comparative Statics Under Multiple Sources of Risk with Applications to Insurance Demand
    Geneva Risk and Insurance Review, 1992
    Co-Authors: Georges Dionne, Christian Gollier
    Abstract:

    In this paper we propose an answer to the following problem of Comparative Statics in models with multiple sources of risk: How a risk averse agent will change his coinsurance demand when the distribution of the insurable loss is shifted? To answer the question, we first comment on Jack Meyer's results and then we show how an alternate approach leads to more definitive Comparative Statics. The Geneva Papers on Risk and Insurance Theory (1992) 17, 21–33. doi:10.1007/BF00941955

  • Comparative Statics Under Multiple Sources of Risk with Appllications to Insurance Demand
    1991
    Co-Authors: Georges Dionne, Christian Gollier
    Abstract:

    In this paper we propose an answer to the following problem of Comparative Statics in models with multiple sources of risk: How a risk averse agent will change his coinsurance demand when the distribution of the insurable loss is shifted? To answer the question, we first comment on Jack Meyer's results and then we show how an alternate approach leads to more definitive Comparative Statics. The Geneva Papers on Risk and Insurance Theory (1992) 17, 21–33. doi:10.1007/BF00941955(This abstract was borrowed from another version of this item.)

Chris Shannon - One of the best experts on this subject based on the ideXlab platform.

  • strict monotonicity in Comparative Statics
    Journal of Economic Theory, 1998
    Co-Authors: Aaron S. Edlin, Chris Shannon
    Abstract:

    This note provides sufficient conditions to draw strict monotone Comparative Statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first- order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems.

  • Strict Monotonicity in Comparative Statics - eScholarship
    1995
    Co-Authors: Aaron S. Edlin, Chris Shannon
    Abstract:

    U N I V E R S I T Y O F CALIFORNIA A T B E R K E L E Y Department of Economics Berkeley, California 94720-3880 Working Paper No. 95-238 Strict Monotonicity in Comparative Statics Aaron S. Edlin Department of Economics University of California, Berkeley and National Bureau of Economic Research Chris Shannon Department of Economics University of California, Berkeley July 1995 Key words: strict monotonicity, Comparative Statics, single crossing property JEL Classification: C60, C61, D i l , H21 Abstract This note provides sufficient conditions to draw strict monotone Comparative Statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first-order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems. Thanks to Eric Emch, Steve Goldman, and Paul Milgrom for their comments. This work has been supported in part by the National Science Foundation under grant SBR-9321022.