The discrete time version of the Romer model

Summary. This paper presents a discrete time version of the Romer 1986 model of endogenous growth. The purpose of this work is to propose detailed and simple proofs of existence of optimal solutions and of a competitive equilibrium. The framework implemented here reduces the complexity of the proofs given by Romer (1983) in his Ph.D dissertation in a continuous time framework. Received: March 7, 2000; revised version: April 25, 2001     

Real and financial effects of insider trading with correlated signals

Summary. In this paper we study the real and financial effects of insider trading in a Static, Kyle-type model. In our model the insider is also the manager of the firm. Hence the insider chooses both the amount of the real output to be produced and the amount of the stock of the firm to trade. The aim of the paper is to study the relationship between financial decisions and real decisions. In particular, we examine how insider trading on the stock market affects the real output and price and how the real decision making affects the financial variables, such as the extent of insider trading, stock prices, and the stock pricing rule of the market maker. In the model, the market maker observes two correlated signals: the total order flow and the market price of the real good. We study the informativeness of the stock price and the effects on insider's profits. We also construct a compensation scheme that aligns the interests of the insider and the firm. Finally, we generalize the pricing rule set up by a competitive market maker and analyze the comparative statics of the model. Received: October 3, 1999: revised version: December 1, 1999     

Sustainable finance: The role of savings and credit cooperatives in Ecuador

The current world situation leads us to consider that sustainable development needs to be a global priority to ensure the future of the planet and improve the quality of life. There is a need for sustainable finance to support this. Savings and credit cooperatives could help to achieve this impact as they serve the microfinance and microlending market. They facilitate the financial inclusion of the most vulnerable people, most of whom live in rural areas and are members of organizations, such as agricultural cooperatives and associations. Previous studies have focused exclusively on overall profitability, so this paper contributes to extending the literature by analyzing the whole population of savings and credit cooperatives in Ecuador (510 institutions), focusing on their profitability in two ways: the overall profitability necessary for the viability of the business and, in addition, the microcredit portfolio profitability, as a specific measure of its contribution to sustainability and social value creation. Another novelty is that the analysis has been carried out using several machine learning techniques for the wider generalization of the results. These show that size is the most relevant variable for predicting the ROE and that the microcredit portfolio profitability is conditioned by the credit variables.     

Optimal fiscal policy in the Uzawa-Lucas model with externalities

Summary. This paper devises a fiscal policy by means of which the first-best optimum equilibrium is attained as a market equilibrium in the Uzawa-Lucas model when average human capital has an external effect on productivity. The optimal policy requires the use of a subsidy to investment in human capital which can be financed by a tax on labor income. Lump-sum taxation is not required to balance the government budget either in the steady state or in the transitional phase. Physical capital income should not be taxed. Alternatively, the optimal growth path can be attained by means of a subsidy to human capital. Received: March 21, 2002; revised version: September 4, 2002 RID="*" ID="*" Financial support from the Spanish Ministry of Science and Technology through PNICDYIT grant SEC2002-03663 is gratefully acknowledged.     

Incomplete risk sharing arrangements and the value of information

Summary. The paper constructs a theoretical framework in which the value of information in general equilibrium is determined by the interaction of two opposing mechanisms: first, more information about future random events leads to better individual decisions and, therefore, higher welfare. This is the ‘Blackwell effect’ where information has positive value. Second, more information in advance of trading limits the risk sharing opportunities in the economy and, therefore, reduces welfare. This is the ‘Hirshleifer effect’ where information has negative value. We demonstrate that in an economy with production information has positive value if the information refers to non-tradable risks; hence, such information does not destroy the Blackwell theorem. Information which refers to tradable risks may invalidate the Blackwell theorem if the consumers are highly risk averse. The critical level of relative risk aversion beyond which the value of information becomes negative is less than 0.5. Received: May 14, 2001; revised version: March 5, 2002     

Equilibrium valuation of illiquid assets

Summary. We develop an equilibrium model of illiquid asset valuation based on search and matching. We propose several measures of illiquidity and show how these measures behave. We also show that the equilibrium amount of search may be less than, equal to or greater than the amount of search that is socially optimal. Finally, we show that excess returns on illiquid assets are fair games if returns are defined to include the appropriate shadow prices. Received: June 25, 2000; revised version: October 24, 2000     

On the optimal size of a joint savings association

We develop a formula for the optimal size of a joint savings association between individuals who share the same financial goal and who can save towards that goal at the same rate. Our motivating example and the core of our analysis is a Rotating Savings and Credit Association (ROSCA). We measure the efficiency of a ROSCA by the expected waiting time that it takes a participant to attain his goal when no participant reneges on his commitment to contribute to the common fund, and when each of the participants receives (once) the funds needed to meet his goal. Given this criterion, we define the optimal size of a ROSCA as the number of participants that results in the minimal expected waiting time. We show that an optimal size of a ROSCA exists, that it is limited, and that it is a multiple of the number of time periods that it takes an individual to save on his own. Somewhat surprisingly, we find that when treated as a function of the size of a ROSCA, the expected waiting time is not monotonic when the size builds up from an individual saving on his own to the optimal size. A similar result obtains when we study cases where a ROSCA is enlarged beyond the optimal size. Our findings help explain the limited size as well as other features of ROSCAs observed in developing countries all over the world.     

Contests where there is variation in the marginal productivity of effort

Summary. We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function, that output is increasing in ability, and that marginal effort is increasing in ability, while effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win, with independently distributed abilities. We analyze the contest designer's decisions in choosing contest rules optimal from her perspective. We show that the output produced, probability of winning, and contest designer's expected revenue are generally increasing in contestants' ability. We examine the relationship between the marginal cost of producing output and marginal utility per dollar of the net award for winning. Received: July 30, 1998; revised version: August 7, 2000     

Is gold an efficient store of value?

Summary. Gold and tobacco have both been used as commodity money. One difference between the two is that gold yields utility, on account of its beauty, without diminishing its quantity. Tobacco yields utility when it is consumed. If this were the only difference, Received: January 2, 2001; revised version: February 22, 2002 Correspondence to: J. Geanakoplos     

The evolution of debt and equity markets in economic development

Summary. As noted by Gurley and Shaw, there is a typical pattern of economic development in which the evolution of the financial system is an essential aspect of the growth process. We focus on one component of this evolution: the increasing importance of equity markets as an economy grows. We develop a growth model where capital accumulation is financed externally through a combination of debt and equity. We illustrate why equity market activity might grow – often very rapidly – as an economy develops. We also illustrate why access to equity markets may not be needed in the early stages of economic development. Received: December 30, 1997; revised version: May 26, 1998     

A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition

Summary. Ekeland and Scheinkman (1986) prove the necessity of a standard transversality condition under certain technical conditions. Their result is one of the most powerful on the necessity of a transversality condition currently available in the literature, and their proof involves numerous estimations and relies on Ekeland's variational principle and Fatou's lemma. This note relaxes some of their assumptions and provides a simple proof that uses neither Ekeland's principle nor a convergence result like Fatou's lemma. Received: April 24, 1998; revised version: September 8, 1998     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Parametric characterizations of risk aversion and prudence

Summary. Our first main result says that whether one decision maker is more risk averse than another can be determined from their attitudes toward a given two-parameter family of risks. When all risks belong to this family, risk aversion can be compared even when initial wealth is random. Our second main result solves a long-standing problem in mean-variance analysis: what is the interpretation of the concavity of utility as a function of mean and variance? We show that in the case of normal distributions, this utility function is concave if and only if the agent has decreasing prudence. Received: July 29, 1996; revised: October 2, 1998     

The likelihood of dubious election outcomes

Summary. A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the “correct” one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes. Received: April 11, 1997; revised version: November 12, 1997     

More on parametric characterizations of risk aversion and prudence

Summary. This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [4], cannot be generalized. Received: November 27, 2000; revised version: November 26, 2001 Correspondence to: T. Eichner     

A new proof of the maximum principle

Summary. We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Received: April 11, 2002; revised version: June 26, 2002 Correspondence to: K. Shimomura     

The option of joint purchase in vertically differentiated markets

Summary. Within the framework proposed by Mussa and Rosen (1978) for modelling quality differentiation, consumers are assumed to make mutually exclusive purchases. A unique pure strategy equilibrium exists in this case. In this note, we allow consumers to buy simultaneously different variants of the differentiated good. We call this the “joint purchase option”. The paper proposes a detailed analysis of price competition when this option is opened: first, we show that either uniqueness, or multiplicity, or absence of price equilibrium arise, depending on the utility derived from joint purchase relative to exclusive purchase. Second, we characterize these equilibria, whenever they exist. Received: July 25, 2001; revised version: October 21, 2002 RID="*" ID="*" The second author gratefully acknowledges the financial support from Interuniversity Attraction Pole Program- Belgian State- Federal Office for Scientific, Technical and Cultural Affairs under contract PAI 5/26. Correspondence to: X.Y. Wauthy     

Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

Summary. Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima. Received: February 16, 2000; revised version: July 7, 2001     

The relative interior of the base polyhedron and the core

Summary. This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core. Received: June 25, 1999; revised version: May 8, 2000     

The convergence of least squares learning in stochastic temporary equilibrium models

Summary. This paper provides conditions for the almost sure convergence of the least squares learning rule in a stochastic temporary equilibrium model, where regressions are performed on the past values of the endogenous state variable. In contrast to earlier studies, (Evans and Honkapohja, 1998; Marcent and Sargent, 1989), which were local analyses, the dynamics are studied from a global viewpoint, which allows one to obtain an almost sure convergence result without employing projection facilities. Received: April 7, 2001; revised version: September 5, 2001