EXISTENCE OF AN EQUILIBRIUM WITH DISCONTINUOUS PRICES, ASYMMETRIC INFORMATION, AND NONTRIVIAL INITIAL σ-FIELDS

In this paper, we solve the problems of optimization and equilibrium on a continuous-time financial market with discontinuous prices, in which agents have different random endowments and different information on the structure and future behavior of the prices. Our purpose is to go over and to extend the work of Pikovsky and Karatzas (1996) by using the theory developed by Amendinger (2000) about martingale representation theorems for initially enlarged filtrations, and to generalize the results in the case of discontinuous prices.     

On the transformation of theorems

Professor W. Ethier (1979) has argued that replacing land by capital in the familiar 2×2 trade model leaves the four basic theorems unaffected, with time-phasing and a positive interest rate. In fact, Ethier's HOS and FPE theorems are different in kind from the traditional ones. The traditional theorems predict certain results in terms of trade-independent data: Ethier's theorems describe equilibrium in terms of factor endowments and intensities defined by equilibrium prices. Hence his theorems do not support his central message that nothing is lost in trade theory by treating capital as if it were homogeneous land.     

The theorems of international trade in time-phased economies

Numerous recent studies conclude that the basic results of the Heckscher-Ohlin theory are vitiated by ‘capital’: a collection of heterogeneous produced means of production. where production takes time and the interest rate is positive. This paper examines the sensitivity of the four basic theorems to the presence of capital and concludes that all four are impervious. The pessimistic conclusions permeating the literature are consequently due not to the nature of capital but rather to other departures from the two-by-two neoclassical model, departures that can be handled fully in a timeless context and, for the most part, have been.     

The theorems of international trade with joint production

This paper analyzes the implications of joint production for the four basic results of the factor-endowments theory of international trade. The nature of the relationship between commodity prices and factor rewards is first elucidated in detail. It is then shown that, in sharp contrast to prevalent opinion, there is in fact a strong presumption that the basic theorems will continue to hold in essence. The paper then considers applications and extensions of the analysis to higher dimensions.     

Intertemporal gains from trade

The gains-from-trade theorems of atemporal trade theory have direct analogues in intertemporal models. The apparent paradoxes which arise in the comparison of steady states disappear when the complete time paths of perfectly competitive trade and autarky equilibria in a general intertemporal linear production model are considered. The analysis can be extended to cover international investment.     

Adjustment costs and theory of investment under uncertainty

It is shown that the stochastic investment rule for the price-setting monopolist facing random demand differs from the deterministic rule, due to the presence of the covariance of the marginal utility of profits and the MRTS between capital and labor. For the risk-neutral quantity-setting monopolist, the optimal current investment under random demand is shown to be greater than that under deterministic conditions, given that production technology is of the Cobb-Douglas type with constant returns to scale. When random wages and prices follow first-order autoregressive schemes, the risk-neutral competitive firm's current investment level is shown to be at least equal to that under certainty.     

The effect of variation in foreign production on domestic factor prices

In this article, the effects of random versus nonrandom foreign production on the average commodity price ratio and on average domestic factor prices are examined within the context of the Heckscher-Ohlin framework. It is shown that the average price ratio is changed when production is random. Thus, the condition derived by Murray C. Kemp and Chulsoon Khang for expected factor prices to be changed when the commodity price ratio is random, must be altered in accordance with the Stolper-Samuelson theorem.     

RICARDO'S THEOREMS ON RELATIVE PRICES A NOTE ON PROF. MORISHIMA

It is argued that Prof. Morishima's treatment of Ricardo's theorems concerning relative price movements following changes in income distribution cannot count as a reasonable interpretation of Ricardo. Firstly, Ricardo linked up these price movements not only to diverging capital intensities, but also to diverging depreciation rates. Secondly, Prof. Morishima's proof seems to depend on a technology specification which is also characteristic of Sraffa's nonbasic commodity. A more reasonable interpretation seems to be that Ricardo tried to investigate a number of modifications on the ‘principle’ that relative prices are regulated by labour values. It is shown that Ricardo's theorems were, as first approximations, not at all bad.     

Variable returns to scale in general equilibrium theory once again

This paper relaxes some assumptions made by Jones (1968) and reconsiders the implications of variable returns to scale (VRS) for the Stolper-Samuelson and Rybczynski theorems. It also analyses for the first time the relationship between factor-returns and factor-supplies at constant commodity-prices. It is shown that the validity of the Rybczynski and/or Stolper-Samuelson theorem is neither necessary nor sufficient for the production possibilities frontier to be locally strictly concave to the origin. Several other new results are derived and an attempt is made to give an intuitive explanation of the most important findings.     

Fixed Point Theorems for Discontinuous Maps on a Non‐convex Domain

This paper introduces economists to some fixed point theorems for discontinuous mappings with non‐convex images on a non‐convex domain. These theorems have recently been developed based on a new approach by mathematical economists and mathematicians. The new method of proof is first transformed into a sort of metatheorem, which is then used to obtain a set of necessary and sufficient conditions for a map to have a fixed point. Some fixed point theorems for discontinuous maps are then explained in more concrete cases. The formulations are intended for easier applications towards economic models involving discontinuity as well as non‐convexity.     

Production uncertainty and trade policy commitment

Agricultural markets are characterized by production and marketing lags. Uncertainty is also an inherent feature of agricultural markets. This paper investigates if two policy active importers will choose to commit to their import levels or keep the flexibility to revise their ex-ante import levels once production decisions are made and the uncertainty is resolved. This is the constant dilemma faced by prospective WTO members. We assume production in both importing countries is subject to an asymmetric random shock. We show that a government will not want to commit to its import level when there is a high degree of uncertainty in production. However, an importing country is likely to commit to a trade policy in equilibrium although the equilibrium may be Pareto dominated. Under certain conditions, an equilibrium in which one country commits to its ex-ante import level while the other chooses the flexibility option can emerge. In this setting, international trade agreements play an important role.     

Fundamental Theorems of Asset Pricing for Good Deal Bounds

We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.     

SZPILRAJN,ARROW AND SUZUMURA: CONCISE PROOFS OF EXTENSION THEOREMS AND AN EXTENSION

This paper extends the classical extension theorem established by Edward Szpilrajn (Fundamenta Mathematicae, 16, pp. 386–389, 1930). Szpilrajn's theorem states that every quasi‐ordering has an ordering extension. Because of its usefulness in various themes of economics, it has been applied by many researchers. Important generalizations have been presented by two authors, Kenneth Arrow and Kotaro Suzumura, among others. First, we provide concise proofs of four extension theorems by Szpilrajn, Arrow and Suzumura. We then show an extension of their extension theorems.     

Bell System scale economies estimated from a random coefficients model

This paper uses a variant of the Cobb-Douglas production function whose log-linear form looks like translog frontier. The parameters of the production function are estimated by a new method called the two stage ridge (TSR) estimator. It is applicable whenever multicollinearity is present both in the estimation of the means and variances of the random coefficients. The results seen to support the presence of scale economics in the Bell System. For our data it appears the TSR estimation is valid and provides additional insights. Thus it should be a valuable tool in similar models elsewhere.     

THE TWO FUNDAMENTAL THEOREMS OF ASSET PRICING FOR A CLASS OF CONTINUOUS‐TIME FINANCIAL MARKETS

The paper is concerned with the first and the second fundamental theorems of asset pricing in the case of nonexploding financial markets, in which the excess‐returns from risky securities represent continuous semimartingales with absolutely continuous predictable characteristics. For such markets, the notions of “arbitrage” and “completeness” are characterized as properties of the distribution law of the excess‐returns. It is shown that any form of arbitrage is tantamount to guaranteed arbitrage, which leads to a somewhat stronger version of the first fundamental theorem. New proofs of the first and the second fundamental theorems, which rely exclusively on methods from stochastic analysis, are established.     

Industry equilibrium under price distribution and cost shifts

Using a reference utility entry and exit criterion, we consider an equilibrium model of production where market price is random but endogenous with respect to industry output. General conditions are identified for industry output to increase under shifts in costs and in the distribution of demand. Comparative statics of firm level production and firm numbers are also studied. Results confirm the intuition that improvements in cost and demand conditions increase industry production. However, firm level responses are not as intuitive, and depend upon the relationship between the source of disturbance and the compensation through the altered distribution of output price.     

Reswitching,primary inputs and the Heckscher-Ohlin-Samuelson theory of trade

The 2× 2 × 2 Heckscher-Ohlin-Samuelson model of trade is examined under all the usual assumptions, except that a positive rate of interest is assumed. The factor-price-equalization and Stolper-Samuelson theorems are shown to be unaffected by the positive interest rate. The H-O-S theorem on the pattern of trade still holds in its ‘quantity’ form but is shown to be invalid in its ‘price’ form. Consequently trade need not ‘harm’ a country's scarce factor. It is to be expected that, in general, international equilibrium will not be unique.     

随机弹性及利润预测应用研究

利润预测是企业进行科学管理的重要环节。利用随机弹性理论研究产销量为随机变量时,利润对产销量的随机弹性,给出了利润弹性的分布函数和概率密度函数,销售量的变化对利润弹性产生影响。进一步论证了利润弹性的经济意义。通过实例研究了当产销量服从某种分布时,利润弹性的变化范围及在该变化范围的可信度。     

A note on ‘trade pattern reversals’

Samuelson's 1975 paper investigating the possibilities of immiserizing trade reversals stemming from autonomous variations of the rate of profit strongly criticizes Emmanuel's Unequal Exchange treatment of that issue. The author of the present note believes that the Samuelson theorems are both inconsistent in themselves and irrelevant to his treatment. This note, however, is confined to the second contention: showing the main points of misrepresentation of the Emmanuel analysis.     

The Harris-Todaro hypothesis and the Heckscher-Ohlin-Samuelson trade model : A synthesis

We report a model of the Harris-Todaro variety in which capital is mobile and the urban wage is endogenous. Our model subsumes several other models presented in the literature. We extend the central theorems of trade to our model and also present formulae for the shadow wage and shadow rental. Our principal findings include (a) nonexistence of equilibrium in an important specialization of the model; (b) a factor-price and unemployment rate equalization theorem: and (c) an identical subsidy to labor but a differential subsidy to capital for obtaining a second-best optimum.