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On the General Structure of Ricardian Models with a Continuum of Goods: Applications to Growth, Tariff Theory, and Technical Change

Econometrica 1980 48(7), 1675
A continuum of goods is introduced into the general Ricardian model of international trade. By looking at the derived demand for labor, it is demonstrated that the analysis of the model can be reduced to the analysis of an equivalent model of pure exchange in which each country essentially trades its own labor for the labor of other countries. Furthermore, unlike the case where the number of goods is finite, the derived demand for labor becomes a differentiable function of the relative wages of the different countries. How this facilitates the analysis of comparative statics exercises is illustrated by establishing a number of propositions in the theory of growth, technical change, and tariffs. THE RICARDIAN MODEL IS perhaps the simplest formulation in which the technology can be explicitly incorporated into an analysis of international trade. In a general form, it consists of an arbitrary number of countries each of whom use only one factor of production, called labor, to produce an arbitrary number of goods. Each country has a constant returns to scale technology but they differ in the relative amounts of labor required to produce different goods. This generates an incentive for each country to specialize in the production of only certain goods which in turn generates the gains from trade. Although the model is frequently employed to illustrate many of the basic principles of international trade, it is not commonly used to examine those issues which require a detailed analysis of comparative statics. Questions such as how a shift in demand affects the pattern of trade and the relative prices of goods, or the corresponding impact of a tariff, technical change, or growth in the labor force are generally analyzed either with simpler models which do not explicitly incorporate the technology at all or else more sophisticated models which include a technology with several factors of production. The problem with the Ricardian model is that the qualitative properties of the results typically depend upon the pattern of specialization. In order to determine the general equilibrium effect of a small change in the tariff rates, for instance, we must know precisely which countries are completely specialized in the production of which goods and which goods are jointly produced by more than one country. A general analysis of any of these issues, therefore, will require a separate analysis for each possible pattern of specialization. Even with two countries and two goods, there are generally several cases to examine. An even more serious defect is the fact that the first order effect in any one of these cases tells only part of the story of what happens in a world with many goods and discrete parameter changes. In general, a change in some

Equilibrium and Adverse Selection

American Economic Review 1979
A common characteristic of a large class of markets is that one side of the market is more informed than the other about the properties of one of the goods being traded. In some instances, this presents no serious problem. If the informed agents deal on a regular basis with the less-informed agents (for example, local grocers, barbers), there may be little incentive for the informed agents to take advantage of their superior information. In other cases, the problem may be avoided if it is profitable for specialists (or some government agency) to provide the information at a relatively low cost (for example, credit agencies, Consumer Reports). Frequently, however, these kinds of market responses provide at best a partial reduction in the informational asymmetry. There may still be substantial benefits to the less-informed agents from acquiring more information. How the market will respond under these circumstances has been the focus of much recent research. Most of the attention, however, has been directed at examining the possibility that a signalling convention will emerge. The essential idea is that sellers of high quality products may choose contracts or invest in observable characteristics which distinguish their products from those of lower quality. Although I believe that signalling is an important and pervasive phenomenon, the conditions necessary for effective signalling to emerge may not always be satisfied. It is important, therefore, that we understand how the allocation of goods is affected in the absence of signalling, when the only variable that agents may use to distinguish quality is the price. This paper provides an overview of some of my recent research on this question. My investigation begins with a welfare analysis of the Walrasian equilibrium. Specifically, the question is whether or not it is necessarily desirable for trade to take place at a price which clears the market. My analysis indicates that it is not. Under some conditions, it may be possible to make every agent in the market better off simply by raising the price. Besides generating some obvious policy implications, this result also suggests that the Walrasian equilibrium may not always be the appropriate equilibrium concept for this model. In a market with homogeneous goods, it is generally argued that independently of how the prices are set, as long as there is a large number of buyers and sellers, competitive pressures will force the price toward a stable Walrasian equilibrium. When an adverse selection problem appears, however, the possibility that some buyers may prefer a price higher than the one which clears the market casts some doubt as to whether such pressures will still be present. It is no longer obvious that the market will clear or even that all trade will take place at a single price. These points can be conveniently illustrated using George Akerlof's model of the used car market. There is a set of cars of varying quality q distributed over an interval [ql, q2] with densityf (q). Each agent in the economy has an identical utility function u(c, q; t) = c + tq where c is consumption of other goods, q is the quality of car he consumes, and t is a parameter equal to his marginal rate of substitution of car quality for consumption. (If an agent does not consume a car, q may be set equal to zero.) The set of agents can be divided into two subsets, those that initially own exactly one car and those that own none. Each owner has the same utility parameter, t = 1; for the nonowners, however, t is distributed continuously over some interval [tl, t2] with density h(t). As long as each owner can directly identify the quality of his own car, the supply curve will have the usual positive slope. A utility maximizing owner with a car of quality q will sell at price p if and only if q _ p. As the price rises, therefore, more cars will be supplied. If *Department of economics, University of Wisconsin. This research was supported by the National Science Foundation under Grant SOC-77-08568.

On the Optimal Pricing Policy of a Monopolist

Journal of Political Economy 1988 96(1), 164-176
[The paper presents a simple explanation of price dispersion by a monopolist assuming only that consumers arrive in a random order and are served on a first-come-first-served basis. A firm can sometimes increase its profits by charging two different prices for the same good and rationing sales at the lower price. However, it is never necessary to charge more than two prices, and a single price is sufficient as long as either the marginal revenue curve is everywhere downward sloping or the marginal cost of production is constant.]

On the Optimal Pricing Policy of a Monopolist

Journal of Political Economy 1988 96(1), 164-176
The paper presents a simple explanation of price dispersion by a monopolist assuming only that consumers arrive in a random order and are served on a first-come-first-served basis. A firm can sometimes increase its profits by charging two different prices for the same good and rationing sales at the lower price. However, it is never necessary to charge more than two prices, and a single price is sufficient as long as either the marginal revenue curve is everywhere downward sloping or the marginal cost of production is constant.

Anticipated Shocks and Exchange Rate Dynamics

Journal of Political Economy 1979 87(3), 639-647
The paper extends Dornbusch's analysis of exchange rate dynamics to include the case where changes in government policy are anticipated before they occur. It is demonstrated that simply the announcement of an expansionary policy will cause the exchange rate to jump, which induces an expansionary impact on the economy even before the policy is implemented.

Anticipated Shocks and Exchange Rate Dynamics

Journal of Political Economy 1979 87(3), 639-647
The paper extends Dornbusch's analysis of exchange rate dynamics to include the case where changes in government policy are anticipated before they occur. It is demonstrated that simply the announcement of an expansionary policy will cause the exchange rate to jump, which induces an expansionary impact on the economy even before the policy is implemented.

A Stochastic Model of Sequential Bargaining with Complete Information

Econometrica 1995 63(2), 371
The authors consider a k-player sequential bargaining model in which the size of the cake and the order in which players move follow a general Markov process. For games in which one agent makes an offer in each period and agreement must be unanimous, the authors provide characterizations of the sets of subgame perfect and stationary subgame perfect payoffs. With these characterizations, they investigate the uniqueness and efficiency of the equilibrium outcomes, the conditions under which agreement is delayed, and the advantage to proposing. Copyright 1995 by The Econometric Society.

Auctions for Oil and Gas Leases with an Informed Bidder and a Random Reservation Price

Econometrica 1994 62(6), 1415
The paper analyzes a first price, sealed bid auction with a random reservation price where the object has an unknown common value, but one buyer has better information than the others. We permit the reservation price to be correlated with the information of the informed buyer, which reflects both his assessment of the value of the object and probability of rejection at any bid. Assuming all random variables are affiliated, we establish the following results. (1) The rate of increase in the distribution of the uninformed bidder is never greater than the rate of increase in the distribution of the informed bid. (2) The distributions are identical at bids above the support of the reservation price. (3) The informed buyer is more likely to submit low bids. We demonstrate that these restrictions are satisfied by bid data from the federal sales of offshore drainage leases.