The supply side in a post-Keynesian two-sector model

Summary In order to avoid missing the wood for trees a brief summary of the results having been obtained above appears to be appropriate.Firstly, we regard it as a result in itself of the present paper to have presented a two-sector model encapsulating a Kaleckian (and Kaldorian) vision of a capitalist economy, a model in which supply conditions of primary products take up a prominent position.Secondly, it belongs to the main results of the paper that it has laid bare, through the model presented, an astoundingly simple pattern in the way economic key-concepts such as activity, employment and distributive shares are affected by on one hand the demand side (which has so far captured an excessive amount of attention in macroeconomic modelling) and on the other hand the largely neglected supply side of the economy.Thirdly, by means of an arbitrary but not implausible numerical example we have attempted to indicate how changes in activity and distributive shares caused by exogeneous changes on the demand and supply side of the economy, respectively, are in themselves crucially dependent on (the assumptions concerning) the supply elasticity of primary products.The notation applied will be as follows C consumption - C ⁰ autonomous element of the consumption function - I investment (gross) - A autonomous expenditure - S savings (gross) - U stock of the primary product - Q real output (not necessarily real income) (gross) - Y income (gross) - W wage bill - L employment - w money wage rate - p price level - mark-up factor - level parameter of the production function pertaining to the primary sector - a labour-input coefficient of the industrial sector - b raw-material input coefficient of the industrial sector - s _w marginal propensity to save out of wages - s marginal propensity to save out of profits - s (weighted) average ofS _w ands - (unit) raw material costs as a proportion of total (unit) prime costs - share of wages in total income - E _{y, x} partial or total elasticity ofY with respect toX. I am most grateful to Søren Gammelgård, Peter Guldager, Erik Strøjer Madsen, Jørgen Ulff-Møller Nielsen, Kurt Pedersen and an anonymous referee for their valuable suggestions and helpful comments on an earlier draft of this paper.     

On the hellwig method of feasible portfolio construction

The work feasible portfolio is built into the work, that is, the k-dimensional Q column vector with components q_i where q_i 0 for i=1,...,k and q₁+...+q_k=1. We define i=1,...,k in the following way:

A law of large numbers for large economies

Summary LetX(i),i[0; 1] be a collection of identically distributed and pairwise uncorrelated random variables with common finite mean and variance ². This paper shows the law of large numbers, i.e. the fact that ₀ ¹ X(i)di=. It does so by interpreting the integral as a Pettis-integral. Studying Riemann sums, the paper first provides a simple proof involving no more than the calculation of variances, and demonstrates, that the measurability problem pointed out by Judd (1985) is avoided by requiring convergence in mean square rather than convergence almost everywhere. We raise the issue of when a random continuum economy is a good abstraction for a large finite economy and give an example in which it is not.I am indebted to Hugo Hopenhayn. Furthermore I would like to thank Dilip Abreu, Glenn Donaldson, Ed Green, Ramon Marimon, Nabil Al-Najjar, Victor Rios-Rull, Timothy van Zandt and the editor for useful comments. The first version of this paper was written in 1987.     

Numerical Computation of Equilibrium Bid Functions in a First-Price Auction with Heterogeneous Risk Attitudes

We use numerical methods to compute Nash equilibrium (NE) bid functions for four agents bidding in a first-price auction. Each bidderi is randomly assigned:r _i [0,r _max], where 1 –r _i is the Arrow-Pratt measure of constant relative risk aversion. Eachr _i is independently drawn from the cumulative distribution function (·), a beta distribution on [0,r _max]. For various values of the maximum propensity to seek risk,r _max, the expected value of any bidder's risk characteristic,E (r _i ), and the probability that any bidder is risk seeking,P (r _i > 1), we determine the nonlinear characteristics of the (NE) bid functions.     

Exact equivalence of instrumental variable estimators in an error component structural system

The paper establishes an equivalence result in the context of anm-equation error component structural system, whose disturbances have the usual three-component structure, and whose equations feature explanatory variables of the formz _i, z_t andz _it; the latter vary (respectively) only over individuals, only over time, and over both. Under the stochastic specification assumed, it is shown that the alternative instrumental variables (IV) estimators commonly used in the special cases of this system are all equivalent (numerically identical); the result is a generalization of the equivalences established previously for the special cases. In the single equation (m=1) context, the equivalence requires that the IV set contain variables of the formz _i and/orz _t, and further, in numbers determined by the ranks of (respectively) the individuals-mean and time-mean matrices of the instruments. If such an IV set is common to all equations, the equivalence also holds for the system under joint estimation. The result is used to recommend a couple of estimators for use in panel data, on grounds of computational simplicity.This is a revision of the December 1990 draft with the same title, and is a substantial revision of the April 1990 version entitled: Analysis of an error component structural system. This revision has benefited from comments received from a referee and a editor of this journal. I came to know from an anonymous reader that the equivalence criterion developed in my 1990 a article, used here and the two earlier versions, was infact obtained previously in an unpublished paper by Balestra (1988). Balestra's paper, which was made available to me by Badi Baltagi at the time of this revision, and subsequently by Balestra, considers the equivalence of ^b, ^c and one other estimator which differs from our ^a. Errors, if any, are my responsibility.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.     

Anonymous sequential games: Existence and characterization of equilibria

Summary In this paper we consider Anonymous Sequential Games with Aggregate Uncertainty. We prove existence of equilibrium when there is a general state space representing aggregate uncertainty. When the economy is stationary and the underlying process governing aggregate uncertainty Markov, we provide Markov representations of the equilibria.Table of notation Agents' characteristics space ( ) - A Action space of each agent (aA) - Y Y = x A - Aggregate distribution on agents' characteristics - (X) Space of probability measures onX - C(X) Space of continuous functions onX - _X Family of Borel sets ofX - State space of aggregate uncertainty ( ) - x _t=1 aggregate uncertainty for the infinite game - = (₁,₂,...,_t,...) - ^{t t} (₁, ₂,..., _t) - L₁(^t,C ×A),v _t Normed space of measurable functions from ^t toC( x A) - 8o(^t,( x A)) Space of measurable functions from ^tto( x A) - X^t X^t= x _s=1 ^t X - _X ^t Borel field onX ^t - v Distribution on - v_t Marginal distribution of v on ^t - v(^t)((¦^t)) Conditional distribution on given ^t - v^t(^s)(v_t(¦^s)) Conditional distribution on ^t given ^s (wheres) - _t Periodt distributional strategy - Distributional strategy for all periods =(₁,₂,...,_t,...) - _t Transition process for agents' types - ( _t,^t,y)(P _t+1(, _t , ^t ,y)) Transition function associated with _t - u _t Utility function - V _t (, a, , ^t) Value function for each collection (, a, , ^t ) - W _t (, , ^t ) Value function given optimal action a - C() Consistency correspondence. Distributions consistent with and characteristics transition functions - B() Best response correspondence (which also satisfy consistency) - E Set of equilibrium distributional strategies - x _t=1 ( ^t , (x A)) - S Expanded state space for Markov construction - (, a, ) Value function for Markov construction - P( _t ^* , _t y)(P(, _t ^* , _t , _y )) Invariant characteristics transition function for Markov game We wish to acknowledge very helpful conversations with C. d'Aspremont, B. Lipman, A. McLennan and J-F. Mertens. The financial support of the SSHRCC and the ARC at Queen's University is gratefully acknowledged. This paper was begun while the first author visited CORE. The financial support of CORE and the excellent research environment is gratefully acknowledged. The usual disclaimer applies.     

Joint production in teams

Consider Holmström's moral hazard in teams problem when there are n agents, each agent i has an a_i-dimensional strategy space and output is m-dimensional. We show that a compensation mechanism that satisfies budget balance, limited liability and implements an efficient allocation generically exists if and only if . Moreover, under a weak additional condition, the equilibrium implemented by this mechanism is unique in the class of pure strategy Coalition-Proof equilibria.     

Phillips-Kurve und Bargaining-Theorie

Ohne ZusammenfassungSymbole N Beschäftigung - F (N) Produktionsfunktion (F>0,F <0) - Substitutionselastizität - Arbeitsangebot=Arbeitskräftepotential - Reallohnsatz - w Nominallohnsatz - p Preisniveau - T Zykluslänge - s Kosten der Erhöhung vonv (gemessen in Einheiten der Lohnsumme/Periode) - I Investition (konstant) - s_p (s_w) Sparquote aus Profiten (Löhnen) - Nutzendiskontrate - q Schattenpreis der Erhöhung von     

The closedness of the free-disposal hull of a production set

Summary Assume thatL is a topological vector lattice andY is a closed subset ofL ₊ ×R ^N, whereR ^N denotes theN-dimensional Euclidean space. It is shown that the setY–L ₊ ×R ₊ ^N is closed ifY has appropriate monotonicity properties. The result is applicable to the case ofL equal toL with the Mackey topology, (L ,L ¹).     

The Swedish industrial support program of the 1970s revisited

The economy-wide dynamic cost-benefit study of the Swedish industrial subsidy program 1976 through 1984 (Carlsson et al. Res Policy 10(43):336–354 1981; Carlsson J Ind Econ 32(1):9–14, 1983a, b) is revisited in light of later economic development. Since the Swedish Micro to Macro model (Eliasson Am Econ Rev 67(1):277–281 1977a, 2017a) was used for quantification, this article is both (1) a study on the calibration of high dimensional micro-based and nonlinear economic systems models, and (2) a post inquiry into the empirical credibility of the cost-benefit calculations performed. We find that the Micro-based Macro model represents the minimum of detailed resolution necessary for the dynamic cost benefit calculations of the micro interventions in the Swedish economy we study. Even though the increased model complexity meant significant parameter calibration difficulties, a thoroughly researched model specification with exactly defined policy interfaces (with the markets of the economy) should take priority over parameter estimation problems, and always be preferred to estimating the parameters of a wrongly specified model perfectly. The oil price shocks of the 1970s caused radical market disorder in the western economies, bankrupting some 35% of Swedish manufacturing and threatening the Swedish government with massive unemployment. We confirm the earlier results that the government choice of a radical employment rescue policy came at enormous social cost in the form of economic stagnation, and still did not prevent the unemployment of the rest of OECD Europe from hitting Sweden a decade later, and persisting well into the next millennium. According to an alternative simulated policy scenario on the model, had the subsidies been replaced with a general lowering of the payroll tax of the same magnitude and the consequent increase in unemployment taken immediately during 1976–1980, production structures would have been radically and rapidly reorganized, normal employment would have been rapidly restored, and neither the stagnation nor the radical increase in unemployment of the early 1990s would have occurred. In retrospect we see no reason to worry about the empirical credibility of this computed dynamic trade off between Keynesian demand and Schumpeterian supply effects (caused by resource reallocations and endogenous structural change due to the price change), as we did then. We conclude with certainty that this trade-off would not even have been discovered as a possibility had we used a traditional model that did not embody these micro-macro linkages.     

Asymptotical behavior of finite and possible discontinuous economies

We consider a finite economy in which the data are depending on an exogenous parameter and the utilities satisfy a condition, previously introduced by the authors and called sequential pseudocontinuity, weaker than sequential lower semicontinuity and than sequential upper semicontinuity. We show that the economy has a nice asymptotical behavior, that is: for any sequence (x _n ) _n of exogenous parameters converging to x _o , any convergent subsequence of a sequence of approximate competitive equilibria of converges to an exact equilibrium of .      

Asymmetric Factor Substitutability and Indeterminacy

We consider a discrete-time two-sector CES economy with sector specific external effects in which factor substitutability differs across sectors. For this general model, we provide sufficient conditions on the elasticities of capital/labor substitution for local indeterminacy of equilibria.Acknowledgement We would like to thank two anonymous referees, the editor Dieter Bös and Tapan Mitra for comments on an earlier version of this paper, previously entitled Capital Depreciation, Factors Substitutability and Indeterminacy, which allowed us to improve considerably the results.     

Fertility,income and welfare in an OLG model with regulated wages

We analyse the effects of the regulation of wages in a standard one-sector OLG model of neoclassical growth extended to account for endogenous fertility decisions of households and unemployment benefit policies financed at balanced budget. In contrast with the prevailing literature, which has failed to pay due attention to inter-temporal contexts, our conclusion is that minimum wages may be introduced not only for equity reasons, that is, to increase the income of low-paid workers, but under suitable conditions—i.e., if production is sufficiently capital oriented and the unemployment benefits are high enough—minimum wage legislation might be considered as a source of increased economic performance despite unemployment, i.e. a regulated-wage economy performs better than a market-wage economy. As a consequence, since higher minimum wages raise per capita income together with increasing unemployment, our results imply that a positive correlation between unemployment and long-run income per-capita may exist. Further, the lifetime welfare of the representative generation may be increased as well. Finally, the wage rate may also be treated as a policy instrument for the control of population growth.

Energy conservation, unemployment and the direction of technical change

This paper extends the model by Smulders and de Nooij (Resour Energy Econ 25:59–79, 2003), where technical change can be biased towards labour or energy, by assuming a monopolistic union and a government which pays unemployment benefits, collects wage taxes and sells emission permits. The extended model is applied to the analysis of environmental tax reforms. A reduction in the level of energy use yields a double dividend by lowering pollution and unemployment, while temporarily inducing energy-saving technical change. It moves the economy to a new balanced growth path where unemployment is permanently lower, but long-run growth is not affected. A reduction in the growth rate of energy use induces a persistent bias in technical change towards labour and reduces long-run growth.     

On the theory of cost sharing

This paper investigates efficiency and equitability issues given a cost sharing method in an economy with a public commodity. We study the concept of a -cost share equilibrium and examine the set of all equilibrium allocations. Finally, we devise a mechanism to implement -cost share equilibria as strong equilibria of an associated non-cooperative game.This paper was written while Shlomo Weber was visiting the University of Bonn. Financial support from theSonderforschungsbereich 303 is gratefully acknowledged. We also would like to thank Dieter Bös for valuable comments.     

Convergence and approximation results for non-cooperative Bayesian games: Learning theorems

Summary LetT denote a continuous time horizon and {G ^t :tT} be a net (generalized sequence) of Bayesian games. We show that: (i) if {x ^t : tT} is a net of Bayesian Nash Equilibrium (BNE) strategies for G^t 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 : tT} is a net of approximate or _t-BNE strategies for the game G^t 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 _t-BNE strategies {x ^t : tT} in {G ^t :tT} which converges to the limit full information BNE strategy of the one shot game.We wish to thank Larry Blume, Mark Feldman, Jim Jordan, Charlie Kahn, Stefan Krasa, Gregory Michalopoulos, Wayne Shafer, Bart Taub, and Anne Villamil for several useful discussions. The financial support of the University of Illinois at Urbana-Champaign Campus Research Board is gratefully acknowledged.     

Evolutionary stable stock markets

Summary. This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbents expense. This mutant portfolio rule changes the asset valuation in the course of time. The stochastic wealth dynamics in our evolutionary stock market model is formulated as a random dynamical system. Applying this theory, necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs follow a stationary Markov process. These local stability conditions lead to a unique evolutionary stable portfolio rule according to which assets are evaluated by expected relative dividends (with respect to the objective probabilities).Received: 7 October 2003, Revised: 18 January 2005, JEL Classification Numbers: G11, D52, D81. Correspondence to: Klaus Reiner Schenk-HoppéWe are grateful to Jarrod Wilcox and William Ziemba for valuable comments. Financial support by the national center of competence in research Financial Valuation and Risk Management is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities.     

The joint dynamics of inflation, unemployment and interest rate in the United States since 1980

In this paper, by using a combination of long-run and short-run restrictions, we identify a small structural VECM which includes inflation, unemployment and the federal funds rate and study the dynamic interactions at different frequencies among these variables. Our results show that: (a) in accordance with the traditional view of economic fluctuations, aggregate demand shocks and monetary policy shocks push inflation and unemployment in opposite directions in the short run; (b) the permanent supply shock explains the long-run movement of inflation and unemployment. These conclusions are at odds with the prediction of “natural-rate” models but are consistent with the idea of a propagation mechanism which links productivity shocks to inflation and unemployment at medium and low frequencies. Thus, with respect to some recent studies (e.g. Beyer and Farmer, ECB Working Paper 121, 2002, and Ireland, J Monet Econ 44:279–291, 1999), we offer a different interpretation of the low-frequency comovements between inflation and unemployment characterizing the US economy in the last decades.

Judging quality by price,snob appeal,and the new consumer theory

Conclusion The analysis contained in this paper has served two purposes. First, it has demonstrated the richness of the new consumer theory by showing how this new approach can incorporate the questions of judging quality by price and price-snob appeal. And second, the paper has derived analytically the conditions under which these phenomena will yield a positively sloping demand curve in a two-commodity, two-attribute world.In traditional theory the consumer's response to a change in the price of a good is conceptually divided into an income effect and a substitution effect. The new approach to consumer theory partitions the consumer's response differently, namely, into an efficiency substitution and a utility substitution. When a general price attribute is introduced each of these divisions retains its individual validity. The conclusion that the efficiency substitution is always non-positive also remains valid. But, the traditional substitution effect may now be positive and of sufficient magnitude to make theentire response to an own-price changepositive,x _i /p _i >0. We have shown analytically, then, as the verbal discussions of traditional consumer theory lead us to believe, that judgment of quality by price and price-snob appeal can result in positively sloped demand curves.The research described in this paper was supported in part by the Econometric Research Program at Princeton University. The authors would like to thank Professors W. J. Baumol, O. Morgenstern, and R. E. Quandt, Messrs. F. D. Gately and R. J. Sweeney, and other members of the Seminar on Research in Progress, Department of Economics, Princeton University, for their helpful comments and suggestions. Of course, any errors that may remain are solely our responsibility.