INTERNATIONAL SCHOOL OF ECONOMIC RESEARCH

XII Workshop

GENERAL EQUILIBRIUM: PROBLEMS, PROSPECTS AND ALTERNATIVES

Existence of General Equilibrium: are the cases of non existence a cause of serious worry?
Elvio Accinelli                                                 download preliminary draft
In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocations sets. To obtain existence and efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.

Reading List
Debreu, G. (74)`` Mathematical Theory of Economic Problem''. Mathematical Economics, Twenty Papers of Gerard Debreu 217-231. Ed.a by Hanh F. Econometric Society Monograph, 4.
Mas-Colell, A.; Zame, W.R.}``Equilibrium Theory in Infinite Dimensional Spaces''. Handbook of Mathematical Economics, IV 1835 -1898 (1991)
Aliprantis, C. D, Border, K.C. ``Infinite Dimensional Analysis'' {\em Berlin, Springer-Verlag} (1994).
Aliprantis, C.D.; Brown, D.J.; Burkinshow, O. ``Existence And Optimality of Competitive Equilibrium'', Berlin, Springer-Verlag. (1989).
Bewley, T.Existence of Equilibria in Economies with Infinitely Many Commodities. Journal of Economic Theory 43 514-540 (1972)
Mas-Colell (86) ``The Price Equilibrium Existence Problem in Topological Vector Lattices'', Econometrica 54, 1039 - 1053.
Araujo, A.; Monteiro, P.K. (93)`` The General Existence of Extended Price Equilibria with Infinitely Many Commodities'' Journal of Economic Theory 63 408-426 (1993).
Accinelli, E.``Existence and Uniqueness of the Equilibrium for Infinite Dimensional Economies''. Revista de Estudios Economicos; colmex.

Stability and dynamics in General Equilibrium systems
Franklin M. Fisher                                          download abstract and download preliminary draft
Economic theory is an equilibrium subject. But the theory and its policy recommendations are incomplete without an adequate treatment of how -- and whether -- a competitive economy converges to equilibrium through the actions of rational, maximizing agents. Models relying on price adjustment alone (tâtonnement) found stability only under special conditions. Models allowing disequilibrium trading were more successful. A full model of arbitrage and disequilibrium is required to study the actions of rational agents faced with disequilibrium-generated opportunities. While stability becomes difficult, insights are gained as to the role of money, the relation of non-Walrasian equilibria to perceptions of market power and other subjects.

Reading List
While there is an old literature on this subject, it is generally summarized and extended in
Fisher, F.M., Disequilibrium Foundations of Equilibrium Economics. Cambridge:
Cambridge University Press, 1983.

Statistical equilibrium and Financial Arbitrage
Duncan Foley                                                 download abstract and download preliminary draft
Statistical equilibrium represents agents in a market as facing a uniform scalar field of probabilities over transactions, rather than a budget constraint defined by an equilibrium price vector. Different agents with the same resources, tastes, and technology, experience different realizations in terms of market transactions, and the same agent entering the market on successive trials experiences fluctuations in transactions outcomes governed by the probability laws. Under the assumption of a set of equally likely feasible and Pareto-improving transactions, the statistical equilibrium probability field is the Gibbs distribution governed by entropy prices, which are analogous to the inverse temperature of a physical system in thermodynamic equilibrium. Because statistical equilibrium takes explicit account of actual transactions possibilities, it incorporates a natural measure of the thickness or liquidity of markets. The formalism of statistical equilibrium is applied to a simple model of an asset market to explain the phenomenon of arbitrage profits, and the accompanying endogenous fluctuation in arbitrage positions that put firm capital at risk.

Reading List
The basic theory of statistical equilibrium is set out in:
Foley, Duncan K. 1994. A statistical equilibrium theory of markets. Journal of Economic Theory, 62(2), 321-345
An application to a simple model of the labor market can be found in:
Foley, Duncan K. 1996. Statistical equilibrium in a simple labor market. Metroeconomica 47(2) (June) 125-47.
A discussion of approaches to interpreting statistical equilibrium models is in:
Foley, Duncan K. 1996. Statistical Equilibrium Models in Economics. Paper presented at the Summer Meetings of the Econometric Society.
This paper is available in Acrobat Reader format at http://www.columbia.edu/~dkf2.
In my view the most useful survey of the application of statistical equilibrium reasoning in the physical sciences is:
Jaynes, E. T. 1978. Where do we stand on maximum entropy? Reprinted in R. D. Rosenkrantz, ed., E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics, Reidel, Dordrecht, 1982.
The interested reader may want to look at other papers in this volume as well.
A survey of maximum entropy modeling techniques can be found in:
Kapur, Jagat N. and Hiremaglur K. Kesavan. 1992. Entropy Optimization Principles with Applications. San Diego:Academic Press
A survey of the formally related topic of maximum entropy approaches to econometric estimation is:
A. Golan, G. G. Judge and D. Miller. 1996. Maximum Entropy Econometrics: Robust Estimation With Limited Data, John Wiley & Sons.

Endogenous Contract Enforcement and General Equilibrium Theory
Herbert Gintis                                               download preliminary draft

General Equilibrium and Macroeconomics
Frank Hahn
In this paper it is argued that the project of producing microeconomic foundations for macro-economics has resulted in there being nothing but microeconomics. In physics there is a micro-theory consistent with macro but different. Not so in our case. Strictly speaking there is no macro-theory at all.
I then ask whether we have not got it the wrong way round and whether we should not be looking for macro-economic foundations of micro theory. I answer in the affirmative. As an example with a good pedigree I consider search theory in the labour market. Whichever variant one considers the searching worker and firm need to know, or have beliefs concerning, total unemployment and vacancies. These are macroeconomic variables. But I combine these arguments with the strong belief that one needs a macroeconomics of the short period if one wants to avoid the ad hoc postulate of rational expectations. (This postulate is useful if one is interested in laboratory conditions of the sort which eliminate the influence of mistaken expectations). The short period is also the context in which to study learning and possible convergence to long run equilibrium. (An appendix provides an example of a simple dynamic model of a succession of short period equilibria.)
So far I have had the Arrow-Debreu model in mind as the paradigm of microeconomics. I argue that we need this model in sequence form if it is to be any help. This in turn implies incomplete markets with consequences for the definition of the "representative" house hold. It also of course has the implication that macro models which imply Pareto efficiency will not wash. I then turn to the neglected questions of the transactions technology and the role of and demand for money. I notice that the TOTAL money stock is another macro variable which affects micro behaviour. I conclude with some brief remarks on imperfect competition and its relation to macro theory, in particular I note the intrinsic externalities in an imperfectly competitive economy.

Endogenous Uncertainty and Rational Belief Equilibrium: A Unified Theory of Market Volatility
Mordecai Kurz                                               download abstract and teaching material
Endogenous Uncertainty is that component of economic risk which is propagated within the economy by the beliefs and actions of agents. The theory of Rational Belief permits rational agents to hold diverse beliefs and a Rational Belief Equilibrium (RBE) may exhibit diverse patterns of Endogenous Uncertainty. This survey paper provides a short exposition of the theory of RBE and reviews the various applications of the RBE model. It argues that most of the observed volatility in financial markets is expectations generated and diverse market puzzles are driven by the distribution of beliefs in the market. Focusing on the examination of market phenomena which have been viewed as general equilibrium empirical "anomalies", the paper reviews an RBE model which was constructed for the study of market volatility in general and of these phenomena in particular. Computer simulations show that this dynamic RBE model predicts the correct order of magnitude of:
(i) the long term mean and standard deviation of the price\dividend ratio;
(ii) the long term mean and standard deviation of the risky rate of return on equities;
(iii) the long term mean and standard deviation of the riskless rate;
(iv) the long term mean equity premium.
The model also predicts
(v) the GARCH property of risky asset returns;
(vi) the Forward Discount Bias in foreign exchange markets.
The paper offers an intuitively simple, common economic explanation for these phenomena.

(II.1) Papers Directly Related
Black, S. [1997], The Forward Discount Puzzle in a Rational Beliefs Framework. Working paper, Department of Economics, Stanford University, May.
Brock, W.A., LeBaron, B.D. [1996], "A Dynamic Structural Model for Stock Return Volatility and Trading Volume". The Review of Economics and Statistics 78 , 94 -110.
Morris, S.[1995],The Common Prior Assumption in Economic Theory. Economics and Philosophy 11, 227-253.
Kurz, M. [1994], On the Structure and Diversity of Rational Beliefs. Economic Theory 4, pp. 877 - 900. (An edited version appears as Chapter 2 of Kurz [1997])
Kurz, M.(ed) [1997], Endogenous Economic Fluctuations: Studies in the Theory of Rational Belief. Studies in Economic Theory No.6, Berlin and New York: Springer-Verlag.
Kurz, M., Beltratti, A. [1997], The Equity Premium is No Puzzle. In: Kurz, M. (ed.) Endogenous Economic Fluctuations: Studies in the Theory of Rational Belief, Chapter 11. Studies in Economic Theory No. 6, Berlin and New York: Springer-Verlag.
Note: The model developed in this paper is publicly available and can be downloaded as a Pdf file from http://www.stanford.edu//~mordecai/
Kurz, M., Schneider, M. [1996], Coordination and Correlation in Markov Rational Belief Equilibria. Economic Theory 8, pp. 489 - 520. (An edited version appears as Chapter 10 of Kurz [1997]).
Kurz, M., Motolese, M. [1999], Endogenous Uncertainty and Market Volatility. Research Report, Stanford University Department of Economics. Pdf file can be downloaded from http://www.stanford.edu//~mordecai/

(II.1) Additional Related Papers
Campbell, J.Y., Cochrane, J.H. [1995], "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior". Discussion Paper Number 1708, Harvard Institute of Economic Research, Harvard University, Massachusetts, January.
Constantinides, G. [1990], "Habit Formation: A Resolution of the Equity Premium Puzzle". Journal of Political Economy 98, 519 - 543.
Engel, C.M. [1996], "The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence". Journal of Empirical Finance 3, 123 - 192.
Epstein, L.G., Zin, S.E. [1990], " "First-Order" Risk Aversion and the Equity Premium Puzzle". Journal of Monetary Economics 26, 387 - 407.
Froot, K.A. [1990], "Short Rates and Expected Asset Returns". Working paper no. 3247, National Bureau of Economic Research, Cambridge, MA.
Froot, K.A., Thaler, R.A.[1990], "Anomalies: Foreign Exchange". Journal of Economic Perspectives 4, (Summer) 179-192.
Kurz, M. [1974], The Kesten-Stigum Model and the Treatment of Uncertainty in Equilibrium Theory. pp. 389-399 in Balch, M.S., McFadden, D.L., Wu, S.Y., (ed.), Essays on Economic Behavior Under Uncertainty, pp. 389-399, Amsterdam: North Holland.
Kurz, M. [1997a], Endogenous Economic Fluctuations and Rational Beliefs: A General Perspective. In: Kurz, M. (ed.) Endogenous Economic Fluctuations: Studies in the Theory of Rational Belief, Chapter 1. Studies in Economic Theory No. 6, Berlin and New York: Springer-Verlag.
Kurz, M.[1997b], On the Volatility of Foreign Exchange Rates. In: Kurz, M. (ed.) Endogenous Economic Fluctuations: Studies in the Theory of Rational Belief, Chapter 12. Studies in Economic Theory No. 6, Berlin and New York: Springer-Verlag.
Mankiw, G. N. [1986], "The Equity Premium and the Concentration of Aggregate Shocks". Journal of Monetary Economics, 15, 145 - 161.
Mehra, R., Prescott, E.C. [1985], "The Equity Premium: A Puzzle". Journal of Monetary Economics 15, pp. 145-162.
Nielsen, C.K. [1996], Rational Belief Structures and Rational Belief Equilibria. Economic Theory 8, 399 - 422. (Reproduced as Chapter 6 of Kurz [1997]).
Reitz, T.A. [1988], "The Equity Premium: A Solution". Journal of Monetary Economics 22, 117 - 133.
Siegel, J. J, [1994], Stocks for the Long Run: A Guide to Selecting Markets for Long Term Growth. New York: Irwin Professional Publishing.
Weil, P. [1989], "The Equity Premium Puzzle and the Riskfree Rate Puzzle". Journal of Monetary Economics 24, 401 - 422.

Is there a 'classical' theory of value and distribution?
Heinz Kurz & Neri Salvadori                                          download abstract and download preliminary draft

Incentive Role of the Stock Market
Michael Magill                                                 download abstract
The object of this lecture is to show how the analytical framework of the theory of incomplete markets (as developed e.g. in Magill-Quinzii (1996)) can be used to study how markets cope simultaneously with incentives and risk sharing in settings involving moral hazard. While the problem of incentives has traditionally been studied as a bilateral problem of design of contract between a principal and an agent, this lecture will show how the equity and option markets, by a combination of signals and anticipations, can serve to create appropriate incentives for managers of firms.

Reading List
(References with an asterisk are especially recommended as background preparation for the lecture.)
Models with Incomplete Markets and Production
Diamond, P.A., "The Role of a Stock Market in a General Equilibrium Model with Technological Uncertainty", American Economic Review, 1967, 57, pp. 759-773.
Drèze, J, "Investment under Private Ownership: Optimality, Equilibrium and Stability", in J. Drèze, Allocation Under Uncertainty: Equilibrium and Optimality, New York: Wiley, 1974.
Ekern, S. and R. Wilson , "On The Theory of the Firm in an Economy with Incomplete Markets", Bell Journal of Economics and Management Science, 1974, , pp. 171-180.
Grossman, S. and O. Hart (1979), "A Theory of Competitive Equilibrium in Stock Market Economies", Econometrica, 47, 293-330.
*Magill, M. and M. Quinzii, Theory of Incomplete Markets, Volume 1, Chapter 6, Cambridge: MIT Press, 1996.
Principal Agent Problem
Ross, S.A., "The Economic Theory of Agency: the Principal's Problem", American Economic Review, 1973, 63, pp. 134-139.
Holmström. B., "Moral Hazard and Observability", The Bell Journal of Economics, 1979, 57, pp. 74-91.
Rogerson, W.P., "The First Order Approach to Principal-Agent Problems", Econometrica, 1985, 53, pp. 1357-1367.
Jewitt, I., "Justifying the First-Order Approach to Principal-Agent Problems", Econometrica, 1988, 56, pp. 1177-1190.Managerial Incentives
Berle, A.A. and G.C. Means, The Modern Corporation and Private Property, New York: Harcourt, Brace and World, 1932.
*Jensen, M.C. and W.H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs, and Capital Structure", Journal of Financial Economics, 1976, pp. 305-360.
Murphy, K.J., "Executive Compensation", forthcoming in: Handbook of Labor Economics, Volume 3, O. Ashenfelter and D. Card eds, Amsterdam: North-Holland, 1998.
Incentives and Capital Structure of Firms: Partial Equilibrium Models
Grossman, S. and O. Hart, "Corporate Financial Structure and Managerial Incentives", in: J. McCall, ed., The Economics of Information and Uncertainty, Chicago: University of Chicago Press, 1982, pp. 107-137.
Brander, J.A. and B.J. Spencer, "Moral Hazard and Limited Liability: Implications for the Theory of the Firm", International Economic Review, 1989, pp. 833-849.
Harris, M. and A. Raviv, "Financial Contracting Theory", in Jean-Jacques Laffont ed., Advances in Economic Theory: Sixth World Congress, Volume II, Cambridge: Cambridge University Press, 1992, pp. 64-150.
Incentives and Capital Structure of Firms: General Equilibrium Models
Magill, M. and M. Quinzii, "Incentives and Risk Sharing in a Stock Market Equilibrium", in A. Alkan, C.D Aliprantis and N. Yannelis eds.: Current Trends in Economics: Theory and Applications, Springer-Verlag, 1999, forthcoming.
Magill, M. and M. Quinzii, "Equity, Options and Efficiency in the Presence of Moral Hazard", mimeo, 1998.
Spanning Role of Options
*Ross, S.A., "Options and Efficiency", Quarterly Journal of Economics, 1976, 90, pp. 75-89.
Cox, J.C. and M. Rubinstein, Options Markets, 1985, Englewood Cliffs: Prentice Hall.

Schumpeter and General Equilibrium
Michio Morishima                                               download teaching material and preliminary draft

Reading List
I
L. Walras, Elements of Pure Economics, 1954. J.. R. Hicks, Value and Capital, 1939.
G. La Volpe, Studies on the Theory of General Dynamic Economic Equilibrium, 1993.
M. Morishima, Walras' Economics, 1977. Dynamic Economic Theory, 1996.
P. Sraffa, Product,ion of Commodities by Means of Commodities, 1960.
II
J. A. Schumpeter, Das Wesen und der Hauptinhalt der theoretische Nationaloekonomie, 1908.
Theorie der wirtschaftlichen Entwichlung, 1926. , Capitalism, Socialism and Democracy, 1942.
III
E. von Boehm-Bawerk, Positive Theorie des Kapitales, 1921.
A. de Pietri-Tonelli and G. H. Bousquet, Vifredo Pareto: Neoclassical Synthesis of Economics and Sociology, 1994.
J. A. Schumpeter and Y. Takata, Power or Pure Economics?, 1998.
V. Pareto, The Mind and Society [Trattato di Sociologia generale], 1935.

Long-period versus short-period theories of distribution and growth
Fabio Petri                                                 download abstract download preliminary draft
Non-neoclassical approaches to distribution and growth. Part 1: Why non-neoclassical approaches to distribution and growth appear necessary: some fundamental deficiencies of the neoclassical approach.
1.1. The basic difference between the neoclassical and the classical approach lies in the presence, in the neoclassical approach, of a conception of the production process as a cooperation, in the production of utility, of factors of production directly or indirectly substitutable one for another. This conception makes it possible to argue with some plausibility in favour of the existence of a stable equilibrium on factor markets, what also implies Say's Law the moment capital is introduced among the factors and the investment schedule is seen as reflecting the demand curve for capital.
1.2. The neoclassical attempt to determine long-period equilibria requires an untenable conception of capital as a single factor whose 'form' i.e. composition is endogenously determined by the equilibrium. This conception has been shown to be indefensible by reswitching.
1.3. Modern General Equilibrium theories attempt to do without the traditional conception of capital as a single factor; they are then obliged to take as given the vector of endowments of capital goods, and as a result they run against an impermanence problem (their data change during disequilibra), an insufficient-substitutability problem, and an indefiniteness problem (due to the arbitrariness of the assumptions as to expectations); furthermore, the impossibility to base Say's Law on the decreasing demand curve for 'capital' makes the assumption, that full-employment savings will be absorbed by investment, arbitrary. Therefore their equilibria can advance no claim to being a guide to the actual behaviour of market economies.
1.4. Neoclassical macroeconomics can therefore rely, for a microfoundation of the decreasing demand curve for labour, or for a microfoundation of the decreasing investment schedule, neither on the long-period nor on the contemporary versions of GE theory. We need therefore a different theory of the real wage, and a different theory of aggregate investment - i.e. a different theory of distribution and a different theory of employment and growth.
Part 2: Some alternatives.
2.1. For the theory of relative prices, the traditional approach of Adam Smith, Marx, Marshall, Wicksell, the early Walras, etc. appears quite solid: competitive product prices can be assumed to gravitate to long-period prices yielding a uniform rate of return on supply price. Some negative results on the stability of long-period prices (Nikaido, cross-dual dynamics) are based on unacceptable assumptions.
2.2. For the theory of wages, the classical approach of Adam Smith appears to be a good starting point, to be integrated with the historical evidence since then, and with the elements pointed out by the institutionalist tradition. Richard Goodwin's Ricardian Lotka-Volterra cycle appears a bit too simple. The theory of efficiency wages also appears insufficient. Explaining the level and variation of real wages must be seen as a question not so different from explaining the French Revolution. Game-theory-based theoretical analyses of wage rigidities such as by Solow or De Francesco can only suggest starting points for analyses which must also consider a wealth of political influences.
2.3. For the theory of employment and growth, we have an excellent starting point in the theories of the multiplier and of the (flexible) accelerator. The Keynesian message is strengthened by the abandonment of the neoclassical elements surviving in his analyses. There remain to inquire in greater detail on the elements influencing aggregate investment. The importance of government policies, both industrial, monetary, fiscal, infrastructural, and versus the labour markets, suggests that here too all applied analyses will have to be very specific and alive to political influences. Kalecki can be a suggestive starting point for his empirical observations, although theoretically he is often criticisable. The theory of growth will have to admit that it is not saving propensities but rather the rate of growth of autonomous expenditure that determines growth, even in the very long run; and that very often it is false that, in order to increase the rate of growth, the average propensity to save must be increased.

Reading List
Minimal readings, highly recommended to fellows new to these topics:
P. Garegnani, "Sraffa: Classical versus marginalist analysis", in K. Bharadwaj, B. Schefold, eds., Essays on Piero Sraffa, Routledge, 1990.
P. Garegnani and A. Palumbo, "Accumulation of Capital", in H. D. Kurz, N. Salvadori, eds., The Elgar Companion to Classical Economics, Edward Elgar, 1998
M. Kalecki, "Political Aspects of Full Employment", Political Quarterly, vol. 14, 1943; reprinted in id., Selected Essays on the Dynamics of the Capitalist Economy, Cambridge University Press, 1971.
F. Petri, "The difference between long-period and short-period general equilibrium and the capital theory controversy", Australian Economic Papers, Dec. 1978, 246-260.
F. Petri, "On the theory of aggregate investment as a function of the rate of interest", Quaderno no. 215, Dipartimento di Economia Politica, Università di Siena, 1997 (printable from the Web site of the Dipartimento)
Further readings, recommended for a more in-depth understanding of the issues:
P. Garegnani, "Quantity of Capital", in J. Eatwell, M. Milgate, P. Newman, eds., Capital Theory, Macmillan, 1990.
P. Garegnani, "Notes on consumption, investment and effective demand", and id., "On a Change in the Notion of Equilibrium", in J. Eatwell, M. Milgate, eds., Keynes's Economics and the Theory of Value and Distribution, Oxford University Press, 1983.
M. De Francesco, "Norme sociali, rigidità dei salari e disoccupazione involontaria", Economia Politica, 1993
F. Petri, "The Golden Age, Investment, Efficiency Wages: a Review Article", Economic Notes, 1994.
F. Petri, "Hicks's recantation of the temporary equilibrium method", Review of Political Economy, 1991.

The Stock Market and Intergenerational Transfers
Martine Quinzii                                               download abstract
This lecture studies the conditions under which financial markets or a process of intermediation ensure that the equilibrium trajectories of an overlapping generations (OLG) model converge to a long-run efficient steady state (the Golden Rule). To set the stage we recall the classical exchange models of Samuelson (1958) and Gale (1973) and the production model of Diamond (1965) which define the set of economies for which the propensity to save is "low" (underaccumulation) or "high" (overaccumulation). We examine an economy in which capital once installed is firm specific so that firms are transferred as financial entities through a stock market rather than as physical entities via the (second-hand) capital goods market. We show that, for almost all initial conditions, economies characterized by underaccumulation converge to the Golden Rule. The stock market does not however solve the problem of overaccumulation. We argue that in this case financial markets are unlikely to ensure that the requisite transversality condition is satisfied, so that the only robust solution to long-run inefficiency involves a process of intermediation via a social security system.

Reading List
(References with an asterisk are especially recommended as background preparation for the lecture)
The OLG Model of Exchange Economy
*Samuelson, P.A. (1958), "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money", Journal of Political Economy, 66, 467-482.
*Gale, D. (1973), "Pure Exchange Equilibrium of Dynamic Economic Models", Journal of Economic Theory, 6, 12-36.
Geanakoplos, J. and H. Polemarchakis (1991), "Overlapping Generations", in: Handbook of Mathematical Economics, Volume IV, W. Hildenbrand and H. Sonnenschein eds, Amsterdam: North-Holland.
The OLG Model of Production Economy
Diamond, P.A. (1965), "National Debt in a Neoclassical Growth Model", American Economic Review, 55, 1126-1150.
Barro, R.J. (1974), "Are Government Bond Net Wealth", Journal of Political Economy, 82, 1095-1117.
Abel, A.B. (1987), Operative Gift and Bequest Motives, American Economic Review, 77, 1037-1047.
Abel, A. B., Mankiw N.G., Summers L.H. and R. J. Zeckhauser (1989), "Assessing Dynamic Efficiency: Theory and Evidence", Review of Economic Studies, 56, 1-20.
*Blanchard, O.J. and S. Fischer (1989), Lectures on Macroeconomics, Chapter 3, Cambridge, Mass.: MIT Press
Galor, O. and H.E. Ryder (1989), "Existence, Uniqueness and Stability of Equilibrium in an Overlapping Generations Model with Productive Capital", Journal of Economic Theory, 49, 360-375.
Magill, M. and M. Quinzii (1999) "Efficiency of Stock Market in an OLG Model with Production", Working paper, University of Southern California.
The Problem of Overaccumulation and Proposed Solutions
Samuelson, P.A. (1975), "Optimum Social Security in a Life-cycle Growth Model", International Economic Review, 16, 539-544.
Scheinkman, J.A. (1980), "Notes on Asset Trading in an Overlapping Generations Model", Working Paper, University of Chicago.
Tirole, J. (1985), "Asset Bubbles and Overlapping Generations", Econometrica, 53, 1499-1528.
McCallum, Bennett T. (1987), "The Optimal Inflation Rate in an Overlapping-Generations Economy with Land", in: New Approaches to Monetary Economics, W. A. Barnett and K. J. Singleton eds, Cambridge: Cambridge University Press.
Rhee, C. (1991), "Dynamic Inefficiency in an Economy with Land", Review of Economic Studies, 58, 791-797.
Pingle, M. and L. Tesfatsion (1998), "Active Intermediation in Overlapping Generations Economies with Production and Unsecured Debt", Macroeconomic Dynamics, 2, 183-212.
Market Structure and the Saddle-Point Property
Hahn, F.H. (1966), Equilibrium Dynamics with Heterogeneous Capital Goods", Quarterly Journal of Economics, 80, 65-94
Samuelson, P.A. (1967), "Indeterminacy of Development in a Heterogeneous-Capital Model with Constant Saving Propensity", in: Essays on the Theory of Optimal Economic Growth, K. Shell ed., Cambridge: Cambridge University Press.
Shell, K. and J.E. Stiglitz (1967), "The Allocation of Investment in a Dynamic Economy", Quarterly Journal of Economics, 81, 592-609.
Foley, D.K., Shell, K. and M. Sidrauski (1969), "Optimal Fiscal and Monetary Policy", Journal of Political Economy", 77, 698-719.
Tobin’s q
Tobin, J. (1969), "A General Equilibrium Approach to Monetary Theory", Journal of Money, Credit and Banking, 1, 15-29.
Blanchard O., Rhee C. and L. Summers (1993), "The Stock Market, Profit and Investment", Quarterly Journal of Economics, 108, 114-135.
Lewellen W. G. and S.G. Badrinath (1997), "On the Measurement of Tobin’s q", Journal of Financial Economics, 44, 77-122.

Applications of the classical approach
Bertram Schefold
The applications of the classical approach in a broad sense have been many, starting with the classical authors themselves, and present-day economists often use a methodology which is closer to that of the classicals than to that of the neoclassicals without being aware of it. The relationship between intertemporal general equilibrium and models of prices of production deserves to be clarified in this context. More specific applications include the extensions of input-output models to long-run prices and distribution, the analysis of joint production, with special extensions to energy analysis, to exhaustible resources and others. Finally, historical applications concern the analysis of technical progress and different economic systems.

Reading List
The lecture will mainly be based on the papers assembled in:
Schefold, Bertram: Normal Prices, Technical Change and Accumulation. London: Macmillan 1997, XV, 577 pp. (Studies in Political Economy) (with bibliography) See chapter 1 (Introduction) for a survey. Chapters 2, 11, 13, 14, 18.2 will be most relevant.
Schefold, Bertram: Mr. Sraffa on Joint Production and other Essays. London: Unwin & Hyman 1989, XII, 378 pp. Chapters I 9-11, II 196, III 6.
Other works:
Bidard, Christian: Prix, reproduction, rareté. Paris: Dunod 1991.
Kurz, Heinz and Neri Salvadori: Theory of Production. A Long-Period Analysis. Cambridge: University Press 1995 (with extensive bibliography).