Assortative Matching with Explicit Search Costs

In this paper, I analyze a decentralized search and matching economy with transferable utility composed of heterogeneous agents. I explore whether Becker's assortative matching result generalizes to an economy where agents engage in costly search. In an economy with explicit additive search costs, complementarities in joint production (supermodularity of the joint production function) lead to assortative matching. This is in contrast to previous literature, which had shown that in a search economy with discounting, assortative matching may fail even when the joint production function is supermodular.     

Sorting and Decentralized Price Competition

We investigate the role of search frictions in markets with price competition and how it leads to sorting of heterogeneous agents. There are two aspects of value creation: the match value when two agents actually trade and the probability of trading governed by the search technology. We show that positive assortative matching obtains when complementarities in the former outweigh complementarities in the latter. This happens if and only if the match‐value function is root‐supermodular, that is, its nth root is supermodular, where n reflects the elasticity of substitution of the search technology. This condition is weaker than the condition required for positive assortative matching in markets with random search.     

An Elementary Theory of Comparative Advantage

Comparative advantage, whether driven by technology or factor endowment, is at the core of neoclassical trade theory. Using tools from the mathematics of complementarity, this paper offers a simple yet unifying perspective on the fundamental forces that shape comparative advantage. The main results characterize sufficient conditions on factor productivity and factor supply to predict patterns of international specialization in a multifactor generalization of the Ricardian model which we refer to as an “elementary neoclassical economy.” These conditions, which hold for an arbitrarily large number of countries, goods, and factors, generalize and extend many results from the previous trade literature. They also offer new insights about the joint effects of technology and factor endowments on international specialization.     

Supermodularity and the Comparative Statics of Risk

In this article, it is shown that a wide range of comparative statics results from expected utility theory can be extended to generalized expected utility models using the tools of supermodularity theory. In particular, a range of concepts of decreasing absolute risk aversion may be formulated in terms of the supermodularity properties of certainty equivalent representations of preferences.     

Comparative Statics,Informativeness, and the Interval Dominance Order

We identify a new way to order functions, called the interval dominance order, that generalizes both the single crossing property and a standard condition used in statistical decision theory. This allows us to provide a unified treatment of the major theorems on monotone comparative statics with and without uncertainty, the comparison of signal informativeness, and a non‐Bayesian theorem on the completeness of increasing decision rules. We illustrate the concept and results with various applications, including an application to optimal stopping time problems where the single crossing property is typically violated.     

The Economics of Labor Coercion

The majority of labor transactions throughout much of history and a significant fraction of such transactions in many developing countries today are “coercive,” in the sense that force or the threat of force plays a central role in convincing workers to accept employment or its terms. We propose a tractable principal–agent model of coercion, based on the idea that coercive activities by employers, or “guns,” affect the participation constraint of workers. We show that coercion and effort are complements, so that coercion increases effort, but coercion always reduces utilitarian social welfare. Better outside options for workers reduce coercion because of the complementarity between coercion and effort: workers with a better outside option exert lower effort in equilibrium and thus are coerced less. Greater demand for labor increases coercion because it increases equilibrium effort. We investigate the interaction between outside options, market prices, and other economic variables by embedding the (coercive) principal–agent relationship in a general equilibrium setup, and studying when and how labor scarcity encourages coercion. General (market) equilibrium interactions working through the price of output lead to a positive relationship between labor scarcity and coercion along the lines of ideas suggested by Domar, while interactions those working through the outside option lead to a negative relationship similar to ideas advanced in neo‐Malthusian historical analyses of the decline of feudalism. In net, a decline in available labor increases coercion in general equilibrium if and only if its direct (partial equilibrium) effect is to increase the price of output by more than it increases outside options. Our model also suggests that markets in slaves make slaves worse off, conditional on enslavement, and that coercion is more viable in industries that do not require relationship‐specific investment by workers.     

The Comparative Statics of Constrained Optimization Problems

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^l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R^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.