LeChatelier-Samuelson Principle Research Articles

Lechatelier-Samuelson Principle in Games and Pass-Through of Shocks

The LeChatelier-Samuelson principle ("the principle") states that as a reaction to a shock, an agent's short-run adjustment of an action is smaller than the long-run adjustment of that action when the other related actions can also be adjusted. We extend the principle to strategic environments and to shocks that affect more than one action directly. We define long run as an adjustment that also includes the affected player adjusting its other actions and other players adjusting their strategies. We show that the principle holds for 1) supermodular games (strategic complements), 2) submodular games (strategic substitutes) for shocks that affect only one player's action directly and when the players' payoffs depend only on their own strategies and the sum of the rivals' strategies (for example, homogeneous Cournot oligopoly). We also provide other sufficient conditions for the principle to hold in games of strategic substitutes. Our results imply that when the principle holds a multiproduct oligopoly might have lower cost pass-through in the short run than in the long run. Hence, we argue that the principle might explain the empirical findings of overshifting of cost and unit tax by multiproduct firms.

LeChatelier-Samuelson Principle in Games and Pass-Through of Shocks

We show that the LeChatelier-Samuelson principle holds in many strategic environments: the adjustment to changes in parameters (shocks) in the short run (only by one player) is smaller in magnitude than the adjustment in the long run (allowing other players to adjust as well). We show that the principle holds for supermodular games (strategic complements) regardless of whether the shock directly affects only one player's action (idiosyncratic shock). The principle holds for submodular games (strategic substitutes) if the shock is idiosyncratic and there are only two players. We provide a simple sufficient condition for the principle to hold in submodular games with more than two players. The principle might fail to hold in submodular games if the shock is not idiosyncratic. We show that our findings explain the breakdown of the principle in non-strategic environments as well, apply our results to multiproduct monopoly and oligopoly cost pass-through, and argue that the principle might explain the empirical findings of overshifting of cost and tax changes.

Aggregation with Cournot Competition: the Le Chatelier Samuelson Principle

This paper studies the aggregate substitution and expansion effects triggered by changes in input prices in a context where firms supply a homogeneous commodity and compete in quantities a la Cournot. We derive a sufficient condition for the existence of a Cournot equilibrium and show that this condition also ensures that the Le Chatelier-Samuelson principle is satisfied in the aggregate at the Cournot equilibrium, although it may not be satisfied at the firm level.

The Aggregate Le Chatelier Samuelson Principle with Cournot Competition

This paper studies the aggregate substitution and expansion effects triggered by changes in input prices, in a context where firms supply a homogenous commodity and compete in quantities a la Cournot. We derive a sufficient condition for the existence of a Cournot equilibrium and show that this condition also ensures that the Le Chatelier-Samuelson principle is likely to be satisfied in the aggregate at the Cournot equilibrium, although it may not be satisfied at the firm level. These results are confirmed by the empirical findings obtained for two-digit US manufacturing industries, which also highlight the importance of imperfect competition for understanding aggregate growth, investment and employment.

A Global Analysis of Constrained Behavior: The LeChatelier Principle "In the Large"

New global results are obtained on the LeChatelier-Samuelson principle reflecting the properties of constrained behavior. Relying on the saddle point characterization of the Lagrangean, simple yet powerful LeChatelier results are derived and investigated under general conditions. The results do not require differentiability assumptions or unique solution, and they hold for discrete changes. The usefulness of the approach is illustrated in several applications, showing how the analysis generates insights into global economic adjustments.

An environmental input-output model with multiple criteria

It is often claimed that there is a trade-off between economic goals and the quality of the environment. For this reason, an environmental input-output optimization model with multiple objectives is formulated. The criteria are the minimization of factor costs to produce the Gross National Product and the minimization of net pollution for a given level of final demand. Using the LeChatelier-Samuelson principle, we analyze the changes in the production of the sectors and in the prices of the goods (described by the dual model) due to the change in the preferences of the decision makers. It can be shown that higher weights for the environmental objectives imply — in tendency —non-decreasing production of the sectors andnon-decreasing abatement activities. The changes of prices are ambiguous. The condition for increasing prices is given. To some degree, the opposite results can be achieved, if maximization of the value of final demand (or of private consumption) and minimization of net pollution under the constraints for primary input are taken as objective functions. In this case, increasing weights for environmental goals will leadin tendency tonon-increasing final demand and tonon-increasing net pollution. Under given conditions, higher environmental quality will be achieved bynon-increasing gross production and abatement activities.

The LeChatelier-Samuelson principle revisited

Within the context of a linear Leontief model, the LeChatelier-Samuelson principle examines the effects of an increase in some final demand on the output levels under the constraint that the production of certain goods is held at its original value. The principle states that the increase in any output is larger when fewer output levels are kept constant. The present paper discusses bounds for such incremental changes, second-order effects, the consequences on the markets for the products with restricted output levels, and generalizations of the original assumptions.

Taxation and Welfare in an Oligopoly with Strategic Commitment

This paper establishes comparative statics results for an oligopoly model with strategic commitment. Firms compete in two stages. In the first stage, firms decide on strategic cost-reducing R&D investment, whereas they choose output in the second stage. Taking an excise tax/subsidy as a shift parameter in the second stage game, the short-run as well as long-run effects on output, cost-reducing R&D investment, and second-best welfare will be examined. The crucial role played by the strategic substitutability of outputs as well as cost-reducing R&D investments is clarified, and a variant of the Le Chatelier-Samuelson principle in the authors' game-theoretic model is obtained. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A simple proof of the LeChatelier-Samuelson principle and the theory of cost and production

We provide a simple proof of a version of the so-called strong LeChatelier-Samuelson principle particularly suitable for the application to the theory of cost and production. We will illustrate its usefulness and fundamental nature in the case of the classical theory of cost and production.

Structure of the Correspondence Principle at an Extremum Point

One of the most powerful principles of microeconomics is that comparative static properties of a given behavioural equation can often be derived from the postulate that it is a solution function of some extremum problem. Applying this principle, economists have individually analyzed a wide variety of specific economic models-usually through complicated derivations involving bordered Hessians. The main purpose of the present article is to derive general formulae of comparative statics for the extremum problem with many constraint functions, where the same shift parameters appear in both target and constraint functions and all of the constraint and target functions are non-linear. This problem contains most of the models whose comparative statics have been studied so far. Our method of comparative statics is related to those proposed by Houthakker (1951-52), Samuelson (1960, 1965), Diamond and McFadden (1974), Silberberg (1974) and Gorman (1976). Threefeatures distinguish the present approach from those ofthis literature. First, our method yields satisfactory comparative static conditions when constraints contain parameters. In particular, they contain the theorems of recent applied economic models whose shift parameters appear in both target and constraint functions.' Second, only unconstrained extremum conditions are used in our derivation of comparative statics for constrained extremum problems; the Lagrangean multiplier method is dispensed with as an analytical tool. Third, the present framework yields heuristic proofs of both the Lagrangean method and the Kuhn-Tucker conditions. The method may be outlined as follows. We transform the original constrained extremum problem into an unconstrained extremum problem of the associated gain function. This function contains as the variables vectors of both decision variables and parameters of the original problem. The unconstrained extremum conditions of the gain function with respect to the decision variables establish the Lagrangean method, while those with respect to the parameter vector yield the comnparative static formulae. Our method of derivation may be called the gain function method. In the present paper we will nowhere assume convexity, nor will we employ theories on convex sets and functions. The next section illustrates the gain function approach in the simplest possible situation by proving the Lagrangean method. Comparative static results are derived in Section 2. The Le Chatelier-Samuelson Principle is generalized in Section 3. The gain function method is applied to maximization problems with inequality constraints in Section 4. The final section presents economic applications of the results.

Global Characterization of the Weak Le Chatelier-Samuelson Principles and Its Applications to Economic Behavior, Preferences, and Utility-- "Embedding" Theorems

Formal analogies between (dynamic) systems and economics have been pointed out by Paul A. Samuelson. The Le Chatelier-Samuelson principle, as a common property of extremum equilibrium (optimal) systems in respect to exogenous conditions, is such an analogy with theory of rational behavior and preference. The weak principle classifies a generalized weak principle. We shall argue that this generalized principle is economic integrability condition itself in a broader sense and, going beyond that, asserts the existence of a maximal system so as for any affiliated systems, such as the equilibrium system, to be imbeddable therein. In consumer theory, this principle, with its identity with a maximal ordinal utility representation (without any regularity conditions), is implied by, or becomes equivalent for a non-satiable individual to, the (modified) strong axiom of revealed preference. The present characterization of the weak principles, making use of the mathematical results of R. Tyrrell Rockafellar [36, 37], completes Samuelson's general principle of economic method [40, pp. 22].

Extensions of the Le Chatelier-Samuelson Principle and Their Application to Analytical Economics--Constraints and Economic Analysis

Extensions of the Le Chatelier-Samuelson Principle and Their Application to Analytical Economics--Constraints and Economic Analysis

A global non-linear extension of the Le Chatelier-Samuelson Principle for linear Leontief models

The extension is concerned with non-linear mappings A(·) which map the space of n-vectors of total gross outputs into the space of n-vectors of final demands. Roughly speaking, it is shown that, if throughout the non-negative orthant the Jacobian matrix of A(·) is of the Leontief type and satisfies the Hawkins-Simon condition, and if A(·) satisfies a certain other condition, then propositions of a global nature entirely analogous to the Le Chatelier-Samuelson Principle in both the weak and strong forms for linear Leontief systems are valid for A(·).

A Nonlinear Input-Output Model of a Multisectored Economy

This paper reports on some mathematical and analytical properties of a static nonlinear model of a national economy or, more generally, of a multisectored economy. The model is a nonlinear version of the well-known linear input-output model of Leontief. Conditions are given for the nonlinear model to be workable in the sense that (i) there is a unique nonnegative vector of output production levels for each nonnegative final-demand vector, and (ii) the vector of output levels depends in a certain reasonable manner on the finaldemand vector. Attention is also focused on several other properties of the model of economic interest. For example, it is shown that propositions completely analogous to the LeChatelier-Samuelson principle in both the weak and strong forms for workable Leontief systems are valid within the context of the nonlinear model.