Comparative statics for state-contingent technologies

The implications of supermodularity conditions in comparative-static analysis are analyzed for a generalized version of the separable-effort representation of a firm facing stochastic prices and a stochastic technology. Previous analysis is generalized in two ways. General risk-averse, as opposed to expected-utility, preferences are considered. The stochastic technology is represented by an Arrow–Debreu state-space representation. It is shown that results familiar from the theory of the price-taking firm in the absence of risk generalize to the uncertain case.      

Assessing complementarity in organizational innovations for technological innovation: the role of knowledge management practices

We empirically investigate the pattern of complementarity among four organizational practices. Firm-level data were drawn from the Community Innovation Survey, carried out in Luxembourg. Supermodularity tests confirm the crucial role of organizational innovation in raising firms’ technological innovation. The pattern of complementarity across organizational practices differs according to the type of innovation (i.e. product or process), as well as according to whether the firm is in the first stage of its innovation process (i.e. being innovative or not) or in a later stage (i.e. sales of new products).     

Output Price Subsidies in a Stochastic World

This article studies the comparative statics of output subsidies for firms, with monotonic preferences over costs and returns, that face price and production uncertainty. The modeling of deficiency payments, support-price schemes, and stochastic supply shifts in a state-space framework is discussed. It is shown how these notions can be used, via a simple application of Shephard's lemma, to analyze input-demand shifts once comparative-static results for supply are available. A range of comparative-static results for supply are then developed and discussed.     

Spatial and Temporal Marketing Considerations under Marketing Loan Programs

Marketing assistance loan (MAL) and loan deficiency payment (LDP) programs differ in their treatment of transportation costs. Marketing decisions are analyzed under these programs when producers are differentiated by location with respect to the terminal market. Under certain conditions, a complete characterization of equilibrium is developed. The proposed model broadly fits several "stylized" facts about producer enrollment in these programs. If LDPs are uniform at all locations, LDP programs do not interfere with marketing decisions. MAL programs distort the optimal marketing pattern by providing incentives to store for producers who should be among the first ones to supply the market.     

The Neglect of Monotone Comparative Statics Methods

Monotone methods enable comparative static analysis without the restrictive assumptions of the implicit-function theorem. Ease of use and flexibility in solving comparative static and game-theory problems have made monotone methods popular in the economics literature and in graduate courses, but they are still absent from undergraduate mathematical economics courses and textbooks. In this article, the authors illustrate the generality of monotone comparative statics relative to the implicit function approach. For example, to sign the effect of a discrete policy shift on a choice variable, the marginal returns will increase with the policy parameter. They also apply monotone methods in game theory settings. As mathematical economics courses and majors gain popularity, incorporating monotone methods into curriculum and textbooks would provide a modern treatment of comparative static analysis.     

The value of information in oligopoly with demand uncertainty

This paper discusses the value of information in supermodular and submodular games, using a simple duopoly model where the level of demand is uncertain. It is shown that the value of information issuperadditive (resp.,subadditive) between players if the game issupermodular (resp.,submodular). For example, in a Bertrand (resp., Cournot) market with (possibly imperfect) substitute products, one firm's information acquisition increases (resp., decreases) the other firm's incentive to acquire the same information. Furthermore, when the game is either supermodular or submodular, the value of information is higher when the player isexpected to be informed according to the opponent's belief than when the player is expected to be uninformed; this result is reversed when the game has asymmetric modularity (i.e., one player's action is substitutional to the other's, and the latter's action is complemental to the former's). These qualitative observations have a potential to be applied to a larger class of games with uncertainty where payoffs are smooth (e.g., twice continuously differentiable) in actions and states.