ALBERT

Notes: Summary We show that for every discount factorρε(0,1) one can find infinitely many strictly concave discrete-time optimal growth models in reduced form which have optimal policy functions exhibiting ergodic chaos. These reduced form models are interpreted in a two-sector optimal growth setting with utility functions depending on consumption as well as on capital.

Notes: Summary We consider a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous households. Under the standard assumptions of strictly concave and time-additive utility functionals and a strictly concave production function we show that perfect foresight equilibria can be non-unique, even locally non-unique (indeterminate), and periodic of arbitrary long periodp. Moreover, we prove that there can exist non-trivial rational expectations (sunspot) equilibria when the agent's expectations about future factor prices depend on extrinsic uncertainty.

Notes: Summary The perfect folk theorem (Fudenberg and Maskin [1986]) need not rely on excessively complex strategies. We recover the perfect folk theorem for two person repeated games with discounting through neural networks (Hopfield [1982]) that have finitely many associative units. For any individually rational payoff vector, we need neural networks with at most 7 associative units, each of which can handle only elementary calculations such as maximum, minimum or threshold operation. The uniform upper bound of the complexity of equilibrium strategies differentiates this paer from Ben-Porath and Peleg [1987] in which we need to admit ever more complex strategies in order to expand the set of equilibrium outcomes.

Notes: Summary An experimental examination of the assignment problem, matching individuals to positions or slots, is conducted in which various assignment mechanisms are analyzed. Generalized versions of both the Vickrey and English auctions are designed to solve the assignment problem along with oridinal ranking mechanisms (serial dictator and “funny” money system). The generalized auctions result in efficient allocations. In contrast, the ordinal ranking mechanisms, which require no monetary transfers, are significantly less efficient in their assignments. However, the efficient allocations obtained from the competitive bidding processes are at the expense of consumers' surplus since demanders retain significantly larger profits with the ordinal ranking mechanisms.

Notes: Summary Posted offer and double auction pricing institutions are examples of fixed and flexible pricing institutions, respectively. In laboratory settings, double auction markets dominate posted offer institutions in terms of the amount of potential surplus which traders are able to extract. These results are invariant with respect to the experience of traders or the perishability of the good traded. Performance differences across institutions may be due to information differences. The introduction of a second price-posting in the posted offer institution results in a pricing institution which is closer to the double auction's flexible pricing environment. Laboratory results suggest that under otherwise comparable conditions, this innovation is sufficient to remove the performance differences which have been demonstrated to exist between the posted offer and double auction institutions.

Notes: Summary This paper applies an experimental testbed methodology to the evaluation of a proposed mechanism for allocating the right to land at the New York airports. The mechanism is called a “zero-out auction” because it is supposed to allocate the rights efficiently like an auction while leaving all of the consumer's surplus with the buyers (as opposed to allocating some to the seller as would be the case with an ordinary auction). A new behavioral hypothesis is introduced to account for limited rationality of individuals and unusual behaviors of the process. The axiom, called theunbiased expectations hypothesis, does a good job of modeling individual behavior in the context of a game model.

Notes: Summary We design and analyze experimental versions of monetary overlapping generations economies under alternative policy regimes. Economies with a constant level of real deficit financed through seignorage, economies in which the level of deficit is adapted in order to follow a monetary policy with a target rate of inflation, and economies with preannounced changes in deficit levels are reported here. We also examine the behavior of an economy with no stationary competitive equilibrium. Our time series are compared to rational expectations equilibrium paths and to adaptive learning dynamics.

Notes: Summary A new axiom for preference orderings over lotteries, called the projective independence axiom, is formulated. Given suitable continuity and monotonicity assumptions, the axiom implies that utility is either in the weighted utility class or is quadratic in probabilities. The betweenness axiom is used to distinguish between these two classes of functions.

Notes: Summary The purpose of this paper is to derive the structure of optimal multilateral contracts in a costly state verification model with multiple agents who may be risk averse and need not be identical. We consider two different verification technology specifications. When the verification technology is deterministic, we show that the optimal contract is a multilateral debt contract in the sense that the monitoring set is a lower interval. When the verification technology is stochastic, we show that transfers and monitoring probabilities are decreasing functions of wealth. The key economic problem in this environment is that optimal contracts areinterdependent. We are able to resolve this interdependency problem by using abstract measure theoretic tools.

Notes: Summary This paper investigates the existence of competitive equilibria in dynamic exchange models with countably many periods and countably many agents. At each period the commodity space can be finite or infinite dimensional. The preferences of agents are not assumed to be transitive or complete. A first equilibrium existence theorem is established under the classical assumption that there exists a finite set of non-negligible agents. In the particular case of an overlapping generations model, a second existence theorem allows simultaneously for finite-lived assets and infinite-lived assets and limits the previous assumption to infinite-lived assets. This theorem covers obviously the standard case of an overlapping generations model where the agents have no endowment outside their lifetime.

Notes: Summary We examine the continuity of maps between linearly ordered spaces and apply the results to utility functions representing preference relations. In particular, we show that the continuous function constructed by Debreu is, in essence, unique.

Notes: Summary In this paper we study a repeated principal-agent situation with moral hazard. We focus on a class of incentive schemes, calledbankruptcy contracts. The agent is “scored” in each period, and is paid a fixed wage per period until the current score falls to zero, at which time the agent is terminated and the principal hires a new agent. The agent's current score at any time equals an initial score, plus the total output up to that time, minus an amount that is proportional to the total time. With standard assumptions about the utility functions of the principal and agent, we characterize the second-best bankruptcy contracts and show that in such a contract, the principal pays the agent an efficiency wage. We also demonstrate that such contracts lead to approximately first-best (Pareto efficient) outcomes if the principal and agent are sufficiently patient (have small discount rates). Most importantly, if the two players have a common discount rateδ, then the loss of efficiency under the second-best bankruptcy contract goes to zero at least as fast asO(gd 1/2lnδ). In order to obtain increased precision, the analysis is carried out in a continuous-time framework.

Notes: Summary An overlapping generations model with parental altruism is examined. The existence of the optimal value function in a model with an endogenous discount rate is proven. Two development regimes are produced: a high fertility, low income and no growth steady state, and a perpetual growth equilibrium with low fertility and rising income.

Notes: Summary The aim of this paper is to demonstrate that uncertainty about the quality of a particular commodity does not necessarily exclude it from emerging as commodity money. This is shown in the context of the model of a simple economy with specialized agents and decentralized trade described in Kiyotaki and Wright (1989). In order to derive this result, considerations about marketability of the different goods are taken into account.

Notes: Summary Aumann's notion of correlated equilibrium is extended to games with payoff uncertainty. A type correlated equilibrium is a correlated equilibrium for Harsanyi's game in player-types. An equivalent definition is a probability distribution over types and actions which is consistent with the prior distribution over types, such that when each player observes its type and action, the observed action is optimal and no further information about other players' types is obtained. Any such equilibrium can be implemented by a type-independent correlation device when players' observations may be type-dependent. The type correlated equilibrium correspondence is shown to be upperhemicontinuous with respect to player information.

Notes: Summary We identify a family of discounted dynamic optimization problems in which the immediate return function depends on current consumption, capital input and a taste parameter. The usual monotonicity and concavity assumptions on the return functions and the aggregative production function are verified. It is shown that the optimal transition functions are represented by the “quadratic family”, well-studied in the literature on chaotic dynamical systems. Hence, Jakobson's theorem can be used to throw light on the issues of robustness of ergodic chaos and sensitive dependence on initial conditions.

Notes: Summary This study constructs a class of dynamic models in which optimal paths are generated by nonlinear transition functions similar to a tent map. We provide a sufficient condition under which such a transition function is a chaotic map. This characterization provides a way to construct complex nonlinear dynamics in a broad range of dynamic economic models.

Notes: Summary We present an overlapping generations model of endogenous fertility and growth. The cost of child rearing and the effect of population size on total factor productivity determine the dynamics of competitive equilibrium path of our model. The non-linear dynamics of the model generates a plethora of outcomes (depending on the functional forms, parameters and initial conditions) that include not only the neo-classical steady state with exponential growth of population with constant per capita income and consumption, but also growth paths which do not converge to a steady state and are even chaotic. Exponential, and even super exponential, growth of per capita output are possible in some cases.

Notes: Summary It is shown that the solution of stochastic differential equation that describes Solow's model with uncertainty via the population dynamics converges in probability uniformly on bounded intervals to the classical deterministic solution as the variance of the population approaches zero. To achieve this, it was necessary to use methods pertaining to the realm of Ventsel' and Freidlin theory of small random perturbations of dynamical systems. We also show the convergence of the expectations of the steady-state as well as the vague convergence of the steady state distribution to the deterministic equilibrium and the degenerated distribution concentrated on the deterministic equilibrium respectively.

Notes: Summary We study equilibria in which agent's belief are rational in the sense of Kurz [1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an “amplification” of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such “amplification.”

Notes: Summary The paper proposes that the theory of expectations be reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy. Instead, we postulate that they can observe past data of the economy and form probability beliefs based on the data generated by the economy. Using past data agents can compute relative frequencies and the basic assumption of the theory is that the system which generates the data is stable in the sense that the empirically computed relative frequencies converge. It is then shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy. This probability is stationary. Abelief of an agent is a probability on the space of infinite sequences of the observable variables in the economy. Such a probability represents the “theory” or ∌ypothesis” of the agent about the mechanism which generates the data. A belief is said to becompatible with the data if under the proposed probability belief the economy would generate the same limit of the relative frequencies as computed from the real data. A theory which is “compatible with the data” is a theory which cannot be rejected by the data. A belief is said to be aRational Belief if it is (i) compatible with the data and (ii) satisfies a certain technical condition. The Main Theorem provides a characterization of all Rational Beliefs.

Notes: Summary This paper provides a new proof of Miyasawa's (1961) result showing the convergence of fictitious play in 2×2 games. The novelty of the approach used here is that it rests entirely on the geometric properties of the best-response correspondence. The geometric approach greatly shortens the exposition, and it suggests some possible extensions to more difficult convergence conjectures.

Notes: Summary Experimental games typically involve subjects playing the same game a number of times. In the absence of perfect rationality by all players, the subjects may use the behavior of their opponents in early rounds to learn about the extent of irrationality in the population they face. This makes the problem of finding the Bayes-Nash equilibrium of the experimental game much more complicated than finding the game-theoretic solution to the ideal game without irrationality. We propose and implement a computationally intensive algorithm for finding the equilibria of complicated games with irrationality via the minimization of an appropriate multi-variate function. We propose two hypotheses about how agents learn when playing experimental games. The first posits that they tend to learn about each opponent as they play it repeatedly, but do not learn about the population parameters through their observations of random opponents (myopic learning). The second posits that both types of learning take place (sequential learning). We introduce a computationally intensive sequential procedure to decide on the informational value of conducting additional experiments. With the help of that procedure, we decided after 12 experiments that our original model of irrationality was unsatisfactory for the purpose of discriminating between our two hypotheses. We changed our models, allowing for two different types of irrationality, reanalyzed the old data, and conducted 7 more experiments. The new model successfully discriminated between our two hypotheses about learning. After only 7 more experiments, our approximately optimal stopping rule led us to stop sampling and accept the model where both types of learning occur.

Notes: Summary A multi-person bargaining model based on sequential demands is studied for coalitional games with increasing returns to scale for cooperation. We show that for such games the (subgame perfect) equilibrium behavior leads to a payoff distribution which approaches the Shapley value as the money unit approaches 0. Subgame consistency and strategic equilibria are the main tools used in the analysis. The model is then applied to study a problem of public good consumption.

Notes: Summary This paper analyzes the effect of two fiscal policy regimes on the set of equilibria. A general equilibrium model with public goods is used to re-examine Friedman's [9] proposal for fiscal reform. The issue is whether a constraint upon fiscal policy requiring budget balance under all contingencies increases the stability of the economy. Stability is modelled in terms of neutralizing extrinsic uncertainty or sunspots. The government consists of bureaus providing public goods. The budgetary rules entail fixed shares of revenues and arrangements for budget balancing. Existence of equilibrium and properties of the equilibrium set are established. The Friedmanite rules permit extrinsic uncertainty to affect outcomes, while a policy that allows the bureaus greater discretion in the pursuit of their objectives neutralizes it.

Notes: Summary A representative-agent model with money holdings motivated by transactions costs, a fiscal authority that taxes and issues debt, no production, and a convenient functional form for agents' utility is presented. The model can be solved analytically, and illustrates the dependence of price determination on fiscal policy, the possibility of indeterminacy, even stochastic explosion, of the price level in the face of a monetary policy that holdsM fixed, and the possibility of a unique, stable price level in the face of a monetary policy that simply pegs the nominal interest rate at an arbitrary level. In a rational expectations, market-clearing equilibrium model with a costlessly-produced fiat money that is useful in transactions, the following things are true under broad assumptions. - A monetary policy that fixes the money stock may (depending on the transactions technology) be consistent with indeterminacy of the price level—indeed with stochastically fluctuating, explosive inflation. - A monetary policy that fixes the nominal interest rate, even if it holds the interest rate constant regardless of the observed rate of inflation or money growth rate, may deliver a uniquely determined price level. - The existence and uniqueness of the equilibrium price level cannot be determined from knowledge of monetary policy alone; fiscal policy plays an equally important role. Special case models with interest-bearing debt and no money are possible, just as are special cases with money and no interest-bearing debt. In each the price level may be uniquely determined. Determinacy of the price level under any policy depends on the public's beliefs about what the policy authority would do under conditions that are never observed in equilibrium. These points are not new. Eric Leeper [1991] has made most of them within a single coherent model. Woodford [1993], in a representative agent cash-in-advance model, has displayed the possibility of indeterminacy with a fixed quantity of money and the possibility of uniqueness with an interest-rate pegging policy. Aiyagari and Gertler [1985] use an overlapping generations model to make many of the points made in this paper, without discussing the possibility of stochastic sunspot equilibria. Sargent and Wallace [1981] and Obstfeld [1983] have also discussed related issues. This paper improves on Leeper by moving beyond his analysis of local linear approximations to the full model solution, as is essential if explosive sunspot equilibria are to be distinguished from explosive solutions to the Euler equations that can be ruled out as equilibria. It improves on the other cited work by pulling together into the context of one fairly transparent model discussion of phenomena previously discussed in isolation in very different models. We study a representative agent model in which there is no production or real savings, but transactions costs generate a demand for money. The government costlessly provides fiat money balances, imposes lump-sum taxes, and issues debt, but has no other role in the economy. We make restrictive assumptions about the form of the utility function and the form of a transactions cost term in the budget constraint. The model could be extended to include production, capital accumulation, non-neutral taxation, productive government expenditure, and a more general utility function without affecting the conclusions discussed in this paper. Indeed the model I informally matched to data in an earlier paper [1988] makes some such extensions. While such an extended model is more realistic, it is harder to solve. The version in my earlier paper [1988] was solved numerically and simulated. The bare-bones model of this paper allows an explicit analytic solution that may make its results easier to understand.

Notes: Summary The simple economics of a firm's decision to begin an in-house program of R&D is more complicated than appears at first blush. We utilize a multi-period search theoretic model to consider this decision when the firm's state of technological progress is fully described by a real-valued variable. By investing in R&D at the beginning of a period, the firm obtains an innovation whose value is revealed at the end of the period. Whereas there is a fixed cost of implementing a new innovation, the benefits include not only an increase in the flow rate of profits but also an increase in the efficiency of the firm's R&D efforts. Thus, an explicit complementarity between production and R&D is included. Because of this complementarity, a myopic decision rule—adopt an innovation only if the discounted value of the increase in the flow rate of profits (due to this one innovation) exceeds the fixed cost of adoption—is rarely optimal; furthermore, once begun the firm will not terminate its R&D program. Thus, a failure to account for this complementarity will lead to the oft-mentioned American under investment in R&D.

Notes: Summary The elasticity of substitution has been proposed as one factor in the generation of aggregate fluctuations in dynamic models with incomplete markets. We study the existence of periodic solutions in a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous agents. A dynamical system representing an equilibrium profile with only the most patient agent holding capital is analyzed when capital income is not an increasing function of total capital. Conditions for the linear approximation system at a steady state to have an eigenvalue of — 1 are found. A one-parameter family of maps based on a perturbation of the production function is introduced and the dynamical system is reduced to 1 dimension via an application of a center manifold theorem. Conditions for a stable flip bifurcation are shown to hold at the steady state.

Notes: Summary This paper examines the dynamic behavior of optimal consumption and investment policies in the aggregate stochastic growth model when utility depends on both consumption and the stock level. Such models arise in the study of renewable resources, monetary growth, and growth with public capital. The paper shows that there is a global convergence of optimal policies to a unique stationary distribution if (a) there is sufficient complementarity in the model, or (b) if there is sufficient randomness in production. Two examples illustrate the possibility of multiple stationary distributions. In one, multiple stochastic steady states exist for a generic class of production and utility functions.

Notes: Conclusion The direction of information with respect to the choice variable can easily change under a general class of distributions. The implication is that, when information is a function of the choice variable, the result of a model may be an outcome of the structure of the uncertainty and not of the existence of uncertainty. Thus, incomplete information does not always have such a clear effect on an agent's decision as previous models have suggested. If such results are key to the conclusions, then the structure of the model should be examined. The model presented here can be used to determine the relationship between information and the choice variable and to derive basic insights into the particular model being examined. It can also be used to eliminate the informational aspect of decisions so as to examine other aspects of a model, e.g., the incentive for information transmission (jamming) and other dynamic aspects (e.g., capital accumulation). Finally, the functional form of the unknown function as well as the error function are inportant in determining the direction of increased information, as the direction of increased noise can be the direction of experimentation.

Notes: Summary This exposition addresses three reasonable departures from fully maximizing behavior that exhibit important Keynesian features. These departures involve inertial, imitative, and error-conscious behaviors. A simple general frame-work is used to model the three departures in an otherwise fully optimizing model. This makes transparent the differences in the underlying mechanisms and the sources of the Keynesian results.

Notes: Summary This note analyzes a modified version of the standard repeated-offers bargaining game with one-sided incomplete information studied in Fudenberg, Levine and Tirole (1985), Gul, Sonnenschein and Wilson (1986) and Ausubel and Deneckere (1989). The modification, which is introduced in the extensive form, is that the (uninformed) seller can choose to withdraw her offer immediately after the (informed) buyer accepts it. This modification is important because it removes the (implicit) commitment assumption built into the standard model that the seller is committed not to withdraw her price offer. A main result obtained is, that whether or not there is a gap between the seller's valuation and the lowest possible buyer's valuation, any seller payoff between zero and the static monopoly profit can be supported by sequential equilibria. Thus, even in the “gap” case there exist equilibria that completely reverse the Coase conjecture.

Notes: Summary We extend the notion of the inner core of a finite economy to a large economy. We prove that competitive allocations and the core coincide with the inner core.

Notes: Summary I study the question on the convexity of the value function and Blackwell (1951)'s Theorem and relate this to the uniqueness of optimal policies. The main results will conclude that strict convexity and a strict inequality in Blackwell's Theorem will hold if and only if from different priors different optimal actions may be chosen.

Notes: Summary There is increasing interest in conducting monetary policy so as to achieve a given target inflation rate (or price level path). Several policies that have been advocated for this purpose are evaluated on the following criteria: (a) are they consistent with the existence of an equilibrium for a variety of targets? (b) do they support only equilibria with the desired price level behavior, or are other equilibria also possible? (c) even if only the desired price level path is possible, are indeterminacies avoided on other dimensions? (d) if there is a unique equilibrium, does it support an allocation that can be Pareto dominated in equilibrium by an alternative policy mechanism? None of the policies examined performs well on the basis of all these criteria.

Notes: Summary This note provides an elementary short proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley (K-K-M-S) Theorem based on Brouwer's fixed point theorem. The usefulness of the K-K-M-S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K-K-M-S Theorem and the Gale-Nikaido-Debreu Theorem can be proved by the same arguments.

Notes: Summary This paper investigates credit card rate stickiness using a screening model of consumer credit markets. In recent years, while the cost of funds has fallen, credit card rates have remained stubbornly high, spurring legislators to consider imposing interest rate ceilings on credit card rates. The model incorporates asymmetric information between consumers and banks, regarding consumers' future incomes. The unique equilibrium is one of two types: separating (in which low-risk consumers select a collateralized loan and high-risk consumers select a credit card loan), or pooling (in which both types of consumers choose credit card loans). I show that a change in the banks' cost of funds can have an ambiguous effect on the credit card rate, so that the credit card rate need not fall when the cost of funds does. Usury ceilings on credit card rates are detrimental to consumer welfare, so would be counter to their legislative intent.

Notes: Summary We report an exploratory study of the process of price formation in a speculative market in the absence of liquidity traders. Traders exchange a futures contract because they interpret information differently. We formulate trading as a sequence of anonymous double auctions and introduce a notion of bounded rationality in which traders use approximate models of market response in forming their bids. We prove existence of a perfect equilibrium in the sequential anonymous auctions game, and show that the equilibrium has a “no-regret” property. After learning the market price, a trader regrets neither the bid that he made nor the position that he holds. We show that trading volume is related to changes in the distribution of information in the economy. We also show that volume and expected change in price are related to two different attributes of the pattern of private information flow. Fundamentally, no particular relationship between the time series of these variables is always valid for all futures contracts. This point is emphasized by an example.

Notes: Summary Two-sided matching procedures are considered using the stable marriage model. There exist some matching procedures that, in spite of producing unstable matches, have nonetheless survived in practice; other such procedures have failed and been abandoned. The success or failure of these procedures may be linked to the amount of instability in the matchings they produce. We describe a way to measure the amount of instability likely to result from such algorithms, and use it to analyze the performance of a particular matching procedure much like those used by the United States Naval Academy and the National Football League. We also consider how favorable the matchings are likely to be from the standpoint of the agents, and examine how our results change when agents agree on some portion of their preference lists.

Notes: Summary We provide an elementary proof of the existence of equilibrium in a general equilibrium model allowing for non-convex production sets. It is shown that when firms follow upper hemicontinuous and convex-valued pricing rules with bounded losses, a price vector and an allocation exist, such that all agents are in equilibrium and all markets clear. The existence result presented in this paper is a particular case of that one in Bonnisseau & Cornet (1988, Th. 2.1′). In this respect our contribution consists of presenting an alternative proof which turns-out to be simpler and more intuitive.

Notes: Summary We examine a discrete-time aggregative model of discounted dynamic optimization where the felicity function depends on both consumption and capital stock. The need for studying such models has been stressed in the theory of optimal growth and also in the economics of natural resources. We identify conditions under which the optimal program is monotone. In our framework, the optimal program can exhibit cyclic behavior for all discount factors close to one. We also present an example to show that our model can exhibit optimal behavior which is chaotic in both topological and ergodic senses.

Notes: Summary In this paper we attempt to formalize the idea that a mechanism that involves multilateral communication between buyers and sellers may be dominated by one that involves simple bilateral communication. To do this we consider the well known problem in which a seller tries to sell a single unit of output to a group ofN buyers who have independently distributed private valuations. Our arguments hinge on two considerations. First, buyers communicate their willingness to negotiate with the seller sequentially, and second, buyers have the option of purchasing the good from some alternative supplier. It is shown that the seller cannot improve upon a procedure in which she offers the good to each buyer in turn at a fixed price. The seller reverts to multilateral communication if possible, only when no buyer is willing to pay the fixed price. In reasonable environments buyers will be too impatient to wait for the outcome of a multilateral negotiation and all communications will be bilateral. In many problems in mechanism design, informed traders have no alternative to participation in the mechanism that is offered by its designer. The best mechanism from the designer's point of view is then the one that is most efficient at extracting informational rents, that is, a simple auction. In a competitive environment it is likely to be costly for buyers to participate in an auction or any other multilateral selling scheme in which the seller must process information from many different buyers because alternative trading opportunities will be disappearing during the time that the seller is collecting this information. Buyers might be willing to participate in an auction, but only if they could be guaranteed that the competition that they face will not eliminate too much of their surplus. At the other extreme to the auction is a simple fixed price selling scheme 1. The seller simply waits until he meets a buyer whose valuation is high enough, given the opportunities that exist in the rest of the market, for him to be willing to pay this price. The seller extracts the minimum of the buyer's informational rents since the price that a buyer pays is independent of his valuation. Yet the seller might like this scheme if adding a second bidder to the process makes it very difficult for him to find a buyer with a valuation high enough to want to participate. In the presence of opportunity costs, the seller faces a trade-off between his ability to extract buyers informational rents and his ability to find buyers who are willing to participate in any competitive process. In practice this trade-off will impose structure on the method that is used to determine a price. In markets where there are auctions, limits are put on buyer participation. In tobacco auctions bids are submitted at a distinct point in time from buyers who are present at that time. In real estate auctions time limits are put on the amount of time the seller will wait before making a decision. These restrictions on participation are presumably endogenously selected by the seller (possibly in competition with other mechanism designers) with this trade-off in mind. On the other hand, markets in which objects appear to trade at a fixed price are rarely so simple. A baker with a fixed supply of fresh bagels is unlikely to collect bids from buyers and award the bagels to the high bidder at the end of the day. Buyers are unlikely to be willing to participate in such a scheme since they can buy fresh bagels from a competitor down the street. Yet despite the fact that bagels sell at a fixed price throughout the day, most bakers are more than willing to let it be known that they will discount price at the end of the day on any bagels that they have not yet sold. Selling used cars presents a similar problem. Each potential buyer for the used car is likely to have inspected a number of alternatives, and is likely to know the prices at which these alternative can be obtained. A seller who suggests that buyers submit a bid, then wait until the seller is sure that no higher offer will be submitted is asking buyers to forgo these alternative opportunities with no gain to themselves. To avoid the rigidity of the pure fixed price scheme most used cars are sold for a fixed price or best offer. These examples suggest that the best selling mechanism may involve a complex interplay between participation and surplus extraction considerations. The purpose of this paper is to provide a simple formalism within which the factors that determine the best contract can be evaluated. We consider the best known environment from the point of view of auction design in which there are a large number of buyers with independent private valuations for a unit of an indivisible commodity that is being sold by a single supplier who acts as the mechanism designer. We modify this standard problem in two critical ways. First, we assume that the seller meets the potential buyers sequentially rather than all at once. Secondly we assume that buyers have a valuable alternative that yields them a sure surplus. This creates a simple bidding cost that is effectively the expected loss in surplus (created by the disappearance of outside alternatives) that the buyer faces during the time that he spends negotiating with the seller. These simple assumptions allow us to calculate the impact of competition and communication costs using completely standard arguments from the mechanism design literature. We are able to show that with these assumptions the seller's expected surplus will be highest if the object is sold according to the following modified fixed price scheme: the seller contacts each of the potential buyers in turn and either offers to negotiate or announces that he no longer wishes to trade. If he offers to negotiate and the buyer agrees, the buyer immediately has the option of trading for sure with the seller at a fixed price set ex ante. If the buyer does not wish to pay this fixed price, he may submit an alternative bid. The seller will then continue to contact new buyers, returning to trade with the buyer only if no buyer wishes to pay the fixed price and no higher bid is submitted. It will be clear that in our environment, both the simple fixed price scheme and the simple auction are feasible. The simple auction prevails when the fixed price is set equal to the maximum possible valuation, while the simple fixed price scheme occurs when the fixed price is set so that buyers are willing to participate if and only if they are willing to pay the fixed price. Our results will show that a simple auction in never optimal for the seller. The seller can always strictly improve his payoff by moving to a scheme in which there is some strictly positive probability that trade will occur at the fixed price. On the other hand, there are reasonable circumstances in which the seller cannot achieve a higher payoff than the one she gets by selling at a fixed price. It is shown that for any positive participation cost, there is a large, but finite, number of potential buyers so that the seller cannot achieve a higher payoff than what she gets by selling at a fixed price. Two simple, but important continuity results are also illustrated. As the cost of participation in the mechanism increases (decreases), the probability with which the seller's unit of output is sold at a fixed price goes to one (zero) in the best modified fixed price mechanism for the seller. Our paper is not the first to generate such a modified fixed price scheme. Both McAfee and McMillan (1988) and Riley and Zeckhauser (1983) come up with similar schemes for the case in which the seller must bear a fixed cost for each new buyer that she contacts. There are two essential differences between our model and theirs. First, as the cost is interpreted as the opportunity cost of participation in the mechanism, it is reasonable to imagine that the seller advertises the mechanism ex ante. Another way

Notes: Summary This paper explores the possibility of designing strategy-proof mechanisms yielding satisfactory solutions to the marriage and to the college admissions problem. Our first result is negative. We prove that no strategy-proof mechanism can always choose marriages that are individually rational and Pareto efficient. This strengthens a result by Roth (1982) showing that strategy-proof mechanisms cannot always select stable marriages. The result also applies, a fortiori, to college admissions. Since finding difficulties with strategy-proofness is quite an expected result, we then address a second question which is classical within the incentives literature. Are there restrictions on the preferences of agents under which strategy-proof and stable mechanisms do exist? We identify a nontrivial restriction on the domain of preferences, to be called top dominance, under which there exist strategy-proof and stable mechanisms for both types of matching problems. The mechanisms turn out to be exactly those that derive from the most classical algorithms in the literature; namely, the women's optimal, the men's optimal and the student's optimal. Finally, top dominance is shown to be essentially necessary, as well as sufficient, for the existence of strategy-proof stable matching mechanisms.

Notes: Summary The paper considers the determinacy of the equilibrium price level in the cash-in-advance monetary economy of Lucas and Stokey (1983, 1987), in the case of deterministic “fundamentals”. The possibilities both of a multiplicity of perfect foresight equilibria and of “sunspot equilibria” are considered. Two types of monetary policy regimes are considered and compared, one in which the money supply grows at a given exogenous rate (that may be positive or negative), and one in which the nominal interest rate on one-period government debt is pegged at a given non-negative level. In the case of constant money growth rate regimes, it is shown that one can easily have both indeterminacy of perfect foresight equilibrium and existence of sunspot equilibria; indeed, in the case of negative rates of money growth (as called for by Friedman (1969)), both types of indeterminacy necessarily occur. On the other hand, sufficient conditions for uniqueness of equilibrium (and non-existence of equilibria other than a deterministic steady state) are also given, and a class of cases is identified in which a sufficiently high rate of money growth guarantees this. Thus there may be a conflict between the aims of choosing a rate of money growth that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium.) In the case of the interest rate pegging regimes, sufficient conditions are given for uniqueness of equilibrium (and impossibility of sunspot equilibria), and it is shown that these necessarily hold in the case of any low enough nominal interest rate. Thus the nominal interest rate peg allows simultaneous achievement of price level determinacy and a high level of welfare in the unique (steady state) equilibrium. In this paper I consider the consequences of alternative choices of the monetary policy regime for the determinacy of the rational expectations equilibrium value of money, and in particular for the existence or not of “sunspot” equilibria, i.e., rational expectations equilibria in which fluctuations in the price level occur in response to random events that represent no change in economic “fundamentals”, simply due to self-fulfilling revisions of people's expectations. I am interested in particular in making the point that a consideration of the complete set of possible equilibria associated with a given policy regime may alter one's evaluation of the relative desirability of alternative policies, relative to the conclusion that one might reach if one considered only a single possible equilibrium associated with each policy regime (perhaps a unique equilibrium involving a “minimum set of state variables”). In view of this I give particular attention to policy regimes of types that have sometimes been advocated as ways of reducing the inefficiency associated with a rate of return differential between money and other financial assets, and show that policies that might otherwise be desirable (policies that make possible a more desirable equilibrium than would otherwise be possible) can have the unfortunate consequence of rendering equilibrium indeterminate and making possible equilibrium fluctuations in response to “sunspot” events. Two classes of policy regimes are considered in particular: on the one hand, alternative constant rates of growth or contraction of the money supply, financed through lump sum taxes or transfers, with zero net government assets at all times; and on the other, alternative constant nominal interest rate pegs, to be maintained through open market operations between money and interest-bearing debt, with an exogenously fixed level of net transfer payments. The first class of policies is considered because of Friedman's (1969) well-known proposal that a constant contraction of the money supply of this sort would be welfare improving. I find that while thestationary equilibrium associated with the Friedman regime achieves the maximum possible level of utility for the representative consumer, and while the level of utility associated with stationary equilibrium may be monotonically decreasing in the rate of money growth, lower rates of money growth (in particular, rates near that called for by Friedman) are associated with indeterminacy of equilibrium and the existence of sunspot equilibria, while these problems need not arise in the case of higher rates of money growth. The second class of policies is considered because they represent an obvious alternative approach to the elimination of the same rate of return differential with which Friedman is concerned. Achievement of permanently low nominal interest rates through a simple interest rate peg is not often advocated; one reason is that it is often asserted that such a policy must result in price level indeterminacy. In fact, I find that if the interest rate pegging regime is properly specified, it results in aunique rational expectations equilibrium, regardless of the level at which interest rates are to be pegged. Thus not only does the interest rate peg not result in price level indeterminacy but it allows nominal interest rates to be maintained permanently at a level lower than that which can be obtained through a policy regime of the first sort without creating price level indeterminacy. It would hence appear, at least in the case of the kind of economy modeled here, that interest rate pegging is a more reliable way of trying to reduce the inefficiency associated with consumers being forced to “economize on liquidity”.

Notes: Summary Yannelis has shown that under very mild conditions on preferences, a 2-agent exchange economy has a nonempty α-core [4, Corollary 4.2]. The purpose of the present paper is to demonstrate that an exchange economy with three or more agents can have an empty α-core. Hence, Yannelis' result would not extend to three or more agents. Examples are provided with and without free disposal, and all preferences are described by linear utility functions. These results are compared with those of Scarf [3], who proved the existence of an α-core solution for a large class ofn-person games. The comparison is carried out on two levels. First, since Scarf [3] and Yannelis [4] use different definitions for the α-core of an exchange economy, we compare these definitions. Second, the present results show that a natural extension of Scarf's theorem forn-person games fails if certain feasibility constraints are incorporated.

Notes: Summary We give a simple proof of the K-K-M-S theorem based on the Kakutani fixed point theorem, the separation theorem for convex sets and the Berge maximum theorem.

Notes: Summary This paper provides simple proofs of a theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem.

Notes: Summary Given any problem involving assignment of indivisible objects and a sum of money among individuals, there is an efficient envyfree allocation (namely the minmax money allocation) which can be extended monotonically to a new efficient envyfree allocation for any object added or individual removed, and another (the maximin value allocation) extendable similarly for any object removed or person added. Still, the efficient envyfree solution is largely incompatible with the resource and population monotonicity axioms: The minmax money and maxmin value allocations are unique in being extendable.

Notes: Summary This paper addresses the question of distinguishing the output of a stochastic process from that of a deterministic process. An impossibility theorem is described which states that time a series resulting from deterministic B-processes is observationally equivalent to, and hence indistinguishable from, the output of a continuous time Markov process on a finite number of states.

Notes: Summary Consider an infinitely repeated normal form game where each player is characterized by a “type” which may be unknown to the other players of the game. Impose only two conditions on the behavior of the players. First, impose the Savage (1954) axioms; i.e., each player has some beliefs about the evolution of the game and maximizes its expected payoffs at each date given those beliefs. Second, suppose that any event which has probability zero under one player's beliefs also has probability zero under the other player's beliefs. We show that under these two conditions limit points of beliefs and of the empirical distributions (i.e., sample path averages or histograms) are correlated equilibria of the “true” game (i.e., the game characterized by the true vector of types).

Notes: Summary LetT denote a continuous time horizon and {G t :t∈T} be a net (generalized sequence) of Bayesian games. We show that: (i) if {x t : t∈T} is a net of Bayesian Nash Equilibrium (BNE) strategies for Gt we can extract a subsequence which converges to a limit full information BNE strategy for a one shot limit full information Bayesian game, (ii) If {x t : t∈T} is a net of approximate or εt-BNE strategies for the game Gt we can still extract a subsequence which converges to the one shot limit full information equilibrium BNE strategy, (iii) Given a limit full information BNE strategy of a one shot limit full information Bayesian game, we can find a net of εt-BNE strategies {x t : t∈T} in {G t :t∈T} which converges to the limit full information BNE strategy of the one shot game.

Notes: Abstract A theoretical model is developed in which the market for teachers is linked to the time path of fertility in the general population. The model is simple in its components but when the components are combined they form a complex long-memory dynamic system. Simulation experiments are carried out to investigate the effects of changes in fertility rates on supply/requirements imbalances in the teachers' market, the median age of teachers, and other variables. The model (and by implication, the real-world system) is found to be highly volatile in response to fertility variations.

Notes: Abstract Since the work of Pollak and Wales (1979), it is well-known that demand data are insufficient to identify a household cost function. Hence additional information is required. For that purpose I propose to employ direct measurement of feelings of well-being, elicited in surveys. In the paper I formally establish the connection between subjective measures and the cost function underlying the AID system. The subjective measures fully identify cost functions and the expenditure data do this partly. This makes it possible to test the null hypothesis that both types of data are consistent with one another, i.e. that they measure the same thing. I use two separate data sets to set up a test of this equivalence. The outcomes are somewhat mixed and indicate the need for further specification search. Finally, I discuss some implications of the outcomes.

Notes: Abstract The paper analyzes factors influencing the age of motherhood in Japan, using both cross-sectional and time-series data. Both hazard rate and time series analyses support the hypothesis that better women's earning opportunities, as indicated by their educational attainments and relative pay, encourage Japanese women to marry and become mothers later in their lives. But both these analyses indicate that the trend toward later marriage and motherhood in Japan cannot be fully accounted for by improvements in women's educational attainments and earning opportunities, and the hazard analysis indicates that the strength of the trend increases with a woman's educational attainment.

Notes: Abstract The remarkable shift from a limping United States recovery from the Great Depression of the 1930's to the relatively rapid and immensely successful World War II mobilization of the 1940's was far from an easy and orderly transition. The first official national income estimates in the United States were prepared in 1933 and were valuable in monitoring the recovery programs. They were especially helpful in determining the maximum potential resources for the wartime mobilization. This information was essential in setting goals that were both ambitious and feasible. Many difficulties were encountered in a feasibility dispute between civilian and military organizations and leaders. Changes in personnel, reorganizations and top level coordination led to massive production of armaments and truly making the United States the “Arsenal for Democracy.”

Notes: Abstract Over the last 20 years OECD countries have converged in terms of their innovations, in parallel to the process of economic convergence and catching up in technology. However, this has not led to a similarity in the sectoral strengths of the majority of countries. Applying a measure of ‘technological distance’ between pairs of countries based on patents, it is shown that nations have increased their technological specialization (i.e. their sectoral differences) over the 1980s. An apparent paradox is pointed out, as countries converge by becoming more different and grow by becoming more specialized.

Notes: Abstract In this note the stability of the rational expectations equilibrium for the Foster and Frierman (1990) version of the Blume and Easley (1982) model is investigated under the assumption that the learning mechanism used by economic agents is based on a selection mechanism on a class of competing models having a ‘physical’ meaning for the agent and not on the interpolation of models having no clear physical meaning, as it is often the case in the literature on learning rational expectations. It is found that, under the standard assumption that the rational expectations model is in the information set of the uninformed trader no matter his degree of rationality, convergence to it is less likely the higher the uninformed agent's degree of rationality, in a sense to be specified in the paper. Some comments on the result are also provided.

Notes: Abstract The paper presents an infinite horizon model of innovation and diffusion incorporating features from recent advances in evolutionary economics. A stochastic variant is explored which posits that technological knowledge is costly to obtain, requiring resource expenditure. There are heterogeneous agents: optimizing as well as non-optimizing agents. The optimizing agents incur an innovation cost. The return from inventive investment is random. The non-optimizing agents, operating existing technologies, behave solely adaptively. Cross-effects between those two types of agents give rise to the multiple equilibria, path-dependence, diversity of diffusion processes and a coexistence of different technologies. Some policy conclusions are drawn in the last section.

Notes: Abstract In this paper, I model technological change as an evolutionary process of generation and selection of economic activities in a highly path-dependent fashion. There are two key features of our approach. The first is that economic activities are conceived as points of a directed graph and endowed with a corresponding notion of technological distance which determines both the probability of invention of any new activity and the cost of learning it. The second feature is that agents are assumed rational and taken to choose optimally from among the available activities, given the status quo and the associated learning costs. In such a context, we focus on two economies that start off technologically close and evolve side by side with some extent of technological diffusion across them. It is shown that alternative assumptions on the speed of diffusion may have drastically different implications for the evolution of the process. I then argue that this theoretical analysis helps provide some insight on existing empirical evidence; in particular, on the conditions under which relative stagnation or technological catch-up may arise and become consolidated among different economies.

Notes: Abstract Adaptive (path dependent) processes of growth modeled by urn schemes are important for several fields of applications: biology, physics, chemistry, economics. In this paper we present a general introduction to urn schemes, together with some new results. We review the studies that have been done in the technological dynamics by means of such schemes. Also several other domains of economic dynamics are analysed by the same machinery and its new modifications allowing to tackle non-homogeneity of the phase space. We demonstrate the phenomena of multiple equilibria, different vonvergence rates for different limit patterns, locally positive and locally negative feedbacks, limit behavior associated with non-homogeneity of economic environment where producers (firms) are operating. It is also shown that the above urn processes represent a natural and convenient stochastic replicator dynamics which can be used in evolutionary games.

Notes: Abstract This paper reformulates several basic ideas introduced by Joseph Schumpeter to examine the correlation between productivity growth and technological change in order to explore why American productivity growth has been sluggish for the past two decades. Convetional growth theory maintains that a primary cause of low productivity growth is inadequate capital formation, which in turn is caused by low private domestic saving. This paper borrows concepts from cybernetics, formal information theory, and chaotic dynamic systems to describe the Schumpeterian process through which innovative “new combinations” of capital goods generate wealth, productivity increases, and income growth, and which in turn cause increased savings. It describes the process through which such fundamental technological changes are diffused by entrepreneurs throughout the economy, and concludes that the fundamental causes of America's relatively weak productivity growth are to be found in policies or practices that inhibit innovation and entrepreneurship.

Notes: Abstract This paper presents the basic ideas and methodologies of a set of contemporary contributions which are grouped under the general heading of “evolutionary economics”. Some achievements-especially with regard to the analysis of technological change and economic dynamics-are illustrated, some unresolved issues are discussed and a few promising topics of research are flagged.

Notes: Abstract This paper examines the effects of inter-firm variation in vintage equipment replacement policies on industry productivity and structure using an evolutionary model based on Nelson-Winter. Traditional industry productivity measures assume a graduated replacement policy with low variation across firms in the average age of the capital stock. This approach allows for inter-firm policy variation. The first part reviews the neoclassical treatment of vintage capital investment; the second part outlines an evolutionary model of vintage replacement in the context of industry growth; and the third part presents results of simulation experiments focused on the relationship between vintage replacement patterns and industry productivity growth. Findings suggest that inter-firm differences in vintage capital investment policies may account for significant shifts in the rates of industry productivity growth and changes in market structure.

Notes: Abstract We formulate a simple multiagent evolutionary scheme as a model of collective learning, i.e. a situation in which firms experiment, interact, and learn from each other. This scheme is then applied to a stylized endogenous growth economy in which firms have to determine how much to invest in R&D, where innovations are the stochastic product of their R&D activity, spillovers occur, but technological advantages are only relative and temporary and innovations actually diffuse, both at the intra and interfirm levels. The model demonstrates both the existence of a unique long-run growth attractor (in the linear case) and distinct growth phases on the road to that attractor. We also compare the long-run growth patterns for a linear and a logistic innovation function, and produce some evidence for a bifurcation in the latter case.

Notes: Abstract In this paper we study an industry in which there is an ongoing sequence of R&D races between two firms. Firms are engaged in product innovation. Products are horizontally and vertically differentiated. There are two key characteristics/dimensions to products, and the level at which these are embodied in products can be increased by R&D. At each time firms can spend R&D on improving their product in one or both dimensions. We allow the possibility of economies scope — so R&D undertaken in one dimension can spillover to the other. The question we are interested in is whether a firm that is ahead in a single dimension but behind in another will focus all its R&D effort in the area in which it is ahead (product specialisation), or whether it will try to do R&D in both dimensions in the hope that it might get ahead in both and end up with a superproduct that dominates in both characteristics. The outcome of this R&D competition determines a Markov transition probability matrix determining the evolution of the industry. We show that when the R&D technology is characterized by constant returns then the only steady-state outcome is one in which the economy stays forever in a position in which one firm produces a super-product and the other gives up doing R&D altogether. This outcome is unaffected by the degree of economies of scope. When the R&D technology is characterised by decreasing returns, then the industry will visit all states and so will exhibit both product specialisation and superproduct dominance at various times. Now the extent of economies of scope matters and we show that the greater the extent of economies of scope, the less likely is the industry to exhibit product dominance, and the more likely it is to exhibit product specialisation.

Notes: Abstract A disequilibrium model of endogenous innovation and growth is presented. The behaviour of the agents is supposed to be governed by routines, not by maximization. The entrepreneurs are assumed to invest a fraction of their operating profits in real capital accumulation, and another fraction in R&D. The latter leads to an increase in labour productivity via a R&D production function. In this ‘Schumpeterian’ model, not only the R&D processes of innovations are considered, but the diffusion processes as well. As in Schumpeter's theory of economic development the economic impact of technical change is considered a disequilibrium phenomenon. Thus, in a capitalist economy characterized by ongoing diffusion processes of innovations, time averages are more important than steady state values even in a long run perspective.

Notes: Abstract A two-sector growth model with endogenous technical change is presented. Concerning technical change, we assume that it is reflected by increases in the stock of human capital which are acquired through learning by doing. As a result, it turns out that transitory or, using the Hopf bifurcation theorem, persistent oscillations of the economic variables may be the outcome. Thus we are able to show that learning mechanisms alone may be sufficient to destroy the circular flow as described by Schumpeter.

Notes: Abstract A dynamic framework based on the process of firm selection and industry evolution is used to analyse the post-entry performance of new firms. In particular, it is hypothesized that, based on the stylized fact that virtually all new firms start at a very small scale of output, firm growth and survival are shaped by the need to attain an efficient level of output. The post-entry performance of more than 11,000 U.S. manufacturing firms established in 1976 is tracked throughout the subsequent tenyear period. Firm growth is found to be negatively influenced by firm size but positively related to the extent of scale economies, capital intensity, innovative activity, and market growth. By contrast, the likelihood of survival is identified as being positively influenced by firm size, market growth, and capital intensity, but negatively affected by the degree of scale economies in the industry. When viewed through the dynamic framework of firm selection and industry evolution, the empirical results shed considerable light on several paradoxes in the industrial organization literature, such as the continued persistence over time of an asymmetrical firm-size distribution consisting predominantely of suboptimal scale firms, and the failure of capital intensity and scale economies to substantially deter the entry and start-up of new firms.

Notes: Abstract What is the relation between the average level of complexity that characterizes a product's technology, and the degree of diversity of that technology across rival firms? Evolutionary theories of innovation and technical advance are consistent with either a direct or an inverse relation. The issue thus becomes an empirical one. This paper uses a unique database containing detailed quantitative data on the specifications of 12 high-tech product groups for the U.S., Japan and selected European countries, for 1982, for both products and processes. It is found that the more complex the technology, the less diverse is the technology of rival firms that produce the product. This is consistent with the following evolutionary process: Economies of scale and scope inherent in high-level technologies require firms who adopt them to dispose entirely of older technologies, in order to remain competitive; at the same time, older, simpler technologies continue to exist and permit wide diversities among firms who pursue “niche” market strategies.

Notes: Abstract In transition from command to market economies total privatization has proved to be impossible to achieve, and a substantial part of large enterprises are likely to remain in full or partial state ownership. Hasty privatization has in many cases even proved to be destructive. There is a need to reconsider the basic approach to transition. Contrary to conventional wisdom prevailing in mainstream economics state-owned enterprises (SOEs) are not necessarily inferior to private firms in economic efficiency. J. Kornai's soft-budget constraint is reconsidered. Two models are suggested under which SOEs may prove to be viable in the long run and serve to promote a smoother physical transition. Under Model One (which is the general case) SOEs are largely separated from the state and operate on the basis of profit maximization. Under Model Two (which applies to certain industries) different objective functions are chosen for purposes of economic efficiency. Finally, preserving SOEs is seen as an alternative means of reducing inequitable income distribution at the source where primary incomes are created.

Notes: Abstract This paper explores the relationship between increasing returns and structural change in the context of an explicitly evolutionary model. The central theme concerns the behaviour of a population of competing firms which is elaborated in terms of Fisher's Principle, the rate of change of the moments of this population distribution are functionally related to higher order moments of the. distribution. Different kinds of increasing returns are distinguished and it is shown how they influence the dynamics of selection. The basic principles here are those of replicator dynamic, systems, and it is shown how the Fisher Principle interacts with the more familiar Kaldor/Verdoorn principles of endogenous growth.

Notes: A FORUM ON FINANCIAL REPORTING

Notes: A FORUM ON FINANCIAL REPORTING

Notes: A FORUM ON FINANCIAL REPORTING

Notes: A FORUM ON ACCOUNTING FOR NOT-FOR-PROFIT ORGANIZATIONS

Notes: A FORUM ON ACCOUNTING FOR NOT-FOR-PROFIT ORGANIZATIONS

Notes: A FORUM ON ACCOUNTING FOR NOT-FOR-PROFIT ORGANIZATIONS