Lecture 1 Introduction, motivation and the Arrow-Debreu model

  

1.1 The Field of Microeconomics

 

 

 

See Journal of Economic Literature 'Classification System' for Articles and is available at http://www.aeaweb.org/journal/jel_class_system.php

 

 

 

            This standard classification may give you some idea of the scope of the subject.

 

 

 

1.2 The Framework of Microeconomics

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), Microeconomic Theory, Oxford, pp. 3-4.

 

 

 

            Very brief introduction to and overview of the nature and structure of Microeconomics.

 

 

 

D. Kreps (1990),  A Course in Microeconomic Theory, Harvester-Wheatsheaf, Ch. 1.

 

 

 

            Introduces the “Actors, behaviour, institutions and outcomes” picture, which can be a very useful organising device.

 

 

 

M. Blad and H. Keiding (1990), Microeconomics: Institutions, Equilibrium and Optimality,  Ch. 1.

 

 

 

Gives an overview of Microeconomics with particular emphasis on the environment in which agents are imagined to be operating and introduces some of the available equilibrium concepts by which their behaviour might be modelled.

 

 

 

 

 

Frank Hahn (2003), “Macro foundations of micro-economics” Economic Theory 21, 227–232

 

 

 

No this is not  typo – he actually called the paper this. It is worth reading for the elegance of expression alone – but also for the context it gives to the study we are about to undertake.

 

 

 

1.3 Methodology and Scientific Method

 

 

 

E. Silberberg (1978), The Structure of Economics, pp. 1-20.

 

 

 

Introduces the idea that Microeconomics exploits the information contained in the maximisation hypothesis to make predictions about the comparative statics of economic agents, (‘the Samuelson program’).

 

 

 

 

 

A. Jehle (1992), Advanced Microeconomics, pp. 1-3.

 

 

 

            Useful summary of basic scientific method.

 

 

 

C.W.J. Granger (1992), "Fellows Opinion: Evaluating Economic Theory",   Journal of Econometrics, pp 3-5.

 

 

 

Presents an interesting perspective on 'testing the theory'.

 

 1.4 The Framework of the Arrow-Debreu Model

 Mas-Colell, Whinston and Green (1995), pp. 511-513.

 

 Very brief introduction to the A-D model and the field of general equilibrium theory.

 

 J. Geanakoplos (2008), “Arrow-Debreu model of general equilibrium”, (in) NPDE2.

 

 

 

A very useful guide to the Arrow-Debreu model. At this stage it is probably easiest for you to          read just the first three pages and glance at the rest. You might like to retain the article as a           map of             where we are going.

 

 

Lecture 2 Arrow-Debreu Consumers I (Choice Theory)

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 5-9, 17-22, 40-50.

 

This introduces the basic notions of “commodity”, “preference relation”, “budget set” and   “utility function”.

 

 

 

L. W. McKenzie (2002), pp. 13 – 15.

 

           

 

This section presents a nice discussion of the classic Sonnenschein theorem on choice without transitivity. Such discussions are hard to find outside the research literature and this one in particular would repay careful study.

 

 

 

C. Blackorby (2008), “Lexicographic orderings”, (in) NPDE2.

 

Nice discussion of an interesting (and widespread?) class of preferences.

 

Lecture 3 Arrow-Debreu Consumers II (Demand Theory)

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 50-56, 23-28.

 

This section presents some of the basic results which make up neo-classical or Arrow-Debreu consumer demand theory.           

 

L. W. McKenzie (2002), pp. 15 – 22.

 

Gives a very nice, compact treatment of demand theory via what we have called the ‘primal’ approach. Includes a neat derivation of the Slutsky equation. See also pp. 36 – 38 for a discussion of the remarkable Mitiushin-Polterovich theorem.

 

M. Blad and H. Keiding (1990), Ch. 2.

 

Defines the notion of a “consumer”; writes down neoclassical choice theory  and derives the             comparative statics of neoclassical consumers acting in an Arrow-Debreu environment.

 

 

 

Lecture 4 Arrow-Debreu Consumers III (Duality and Revealed Preference Theory)

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 28-36, (optional pp. 91-92).

 

Presents information about the Slutsky matrix and also introduces the Weak Axiom of          Revealed Preference (and optionally the Strong Axiom of Revealed Preference).

 

L. W. McKenzie (2002), pp. 22 – 25.

 

Gives a thorough and uncluttered account of the revealed preference approach.       

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 56-63 and 67-75 (pp. 64-67 optional).

 

This introduces the “Duality” approach to consumer theory. There are in a sense no new results here, but there are number of new techniques which are now pervasive in economic analysis.

 

           

 

L. W. McKenzie (2002), pp. 1 – 13.

 

 

 

Discusses the dual approach to consumer demand. Note there are some notational differences between the approach of McKenzie and that of Mas-Collell et. al., Varian and co.

 

 

 

 

 

V. Bohm and H. Halker (2008), "Demand theory", (in) NPDE2.

 

 

 

            Compliment to Mas-Colell, Whinston and Green and gives a very complete (reference level)            account of consumer choice and demand theory.

 

 

 

 

 

E. Silberberg (2008), “Hicksian and Marshallian Demand Curves”, (in) NPDE2.

 

 

 

            A nice account of Arrow – Debreu consumer theory.

 

 

 

 

 

Lecture 5 Arrow-Debreu Producers

 

 

 

Mas-Colell, M. Whinston and J. Green (1995), pp. 127-154.

 

 

 

            An account of Arrow-Debreu producer theory from the “Primal” and “Dual” points of view.

 

 

 

M. Blad and H. Keiding (1990), Ch. 3.

 

 

 

            Presents the theory of production in an Arrow-Debreu environment from the set theoretic,    production function and dual points of view. Notice the attention given to the question of the     existence of profit maximising decisions.  

 

G. Debreu (1959), Theory of Value, Ch. 3.

 

 

 

Classic and fairly easy to follow treatment of firm behaviour in an Arrow-Debreu environment written by the second part of the famous team.

 

 

 

D. W. Jorgensen (2008), “Production functions”, (in) NPDE2.

 

 

 

            A nice presentation of producer theory from the ‘primal’ point of view.

 

 

 

W. E. Diewert (2008), “Cost Functions” (in) NPDE2.

 

 

 

Surveys producer theory with particular emphasis on the duality between production, cost and profit functions. Also contains some interesting material on ‘empirical testing’ that we will return to later in the course.

 

 

 

 

 

Lecture 6 Existence of Market Equilibrium

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 578-589 (optionally pp. 632-641).

 

 

 

            Introduction to the basic existence question for market or Walrasian equilibrium.

 

 

 

H. Varian (1992), Microeconomic Analysis, (3rd. Edition) pp. 313-323.

 

 

 

Gives an account of an approach to the existence question, originally due to Arrow and Hahn (1971), which exploits the properties of the excess demand map in an Arrow-Debreu economy to achieve an existence result. Note that Varians' approach appears to be for the exchange case, but as we will see in the lectures, it easily generalises to the production case.

 

           

 

M. Allingham (1987), "Excess Demand and Supply", NPDE1 (2), pp. 201-222.

 

 

 

            Also comes at the existence problem from the “excess demand end”.

 

 

 

M. Blad and H. Keiding (1990), pp. 156-162.

 

 

 

            Existence from the “primitives” point of view.

 

 

 

G. Debreu (2008), "Existence of General Equilibrium", NPDE2.

 

 

 

            A nice account of the existence problem which allows you to get a feel for what has to be    assumed about the primitives of the economy if an existence argument is to go through.

 

 

 

W. D. A . Bryant (1997), “Conditions for the existence of market equilibrium” Journal of Economic Education, 28(3), pp. 230-254.

 

           

 

            This is a critical survey of the available sufficient conditions for the existence of market      equilibrium, in particular the conditions which appear in the ‘third level’ proofs of the          equilibrium existence theorem. The paper also discusses an apparently little known necessary    condition due to Arrow and Debreu (1954) as well as providing an introduction to the recent    and emerging literature on necessary and sufficient conditions for the existence of market             equilibrium.

 

 

 

L. W. McKenzie (2002), pp. 189 – 214.

 

 

 

Has an extensive discussion of issues associated with the existence of competitive equilibrium. Also discusses in detail some of the issues discussed in Bryant (1997).         

 

 

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 598-606 (optionally Chapter 4.)

 

 

 

A fundamental result which tells us something about the “aggregate” implications of Arrow-Debreu Microeconomics and also conditions the search for conditions which yield Uniqueness, Stability and Comparative Static properties of market equilibrium.

 

 

 

 

 

M. Blad and H. Keiding (1990), pp.173-176.

 

 

 

            Nice treatment of the classic Sonnenschein-Mantel-Debreu theorem, which apart from being            interesting in its own right, underpins a lot of the work to be discussed in the sections to            follow.

 

 

 

L. W. McKenzie (2002), pp. 25 – 33.

 

 

 

Contains a discussion of the properties of market demand functions that is slightly more accessible than that presented in Mas- Colell, Whinston and Green (1995).

 

 

 

W. D. A. Bryant (2010), Ch 2 and 3.

 

 

 

Presents more detail on sufficient, necessary and necessary and sufficient conditions for the existence of equilibrium. Recommended reading only if you are having trouble sleeping!

 

 

 

 

 

 

 

 

 

 

 

 

 

Lecture 7 Uniqueness and Stability of Market Equilibrium

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 589 - 615.

 

 

 

Presents a thorough analysis of the conditions needed for uniqueness (and local uniqueness) and does so from a number of “angles”. Also gives a thorough account of the remaekable  ‘Sonnenschein-Mantel-Debreu Theorem’.

 

 

 

 

 

 

 

M. Blad and H. Keiding (1990), pp. 162-166.

 

 

 

            Gives a nice introduction to the “conditions on excess demand functions” approach to the    uniqueness question.

 

 

 

H. Varian (1992), pp. 394-397.

 

 

 

            Presents a reasonably accessible summary of the modern “index analysis” approach to the   uniqueness question.

 

 

 

L. W. McKenzie (2002), pp. 229 – 235.

 

 

 

            Provides a unified view of some relatively recent work on the uniqueness of equilibrium.

 

 

 

W. D. A. Bryant (2010), Ch 7.

 

 

 

Gives and overview of the uniqueness problem, particularly in a production context – and suggests a potentially new approach to getting uniqueness conditions via contraction mappings.

 

           

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 620-626.

 

 

 

            Interesting account of price and quantity adjustment processes.

 

 

 

M. Blad and H. Keiding (1990), pp. 169-173.

 

 

 

            Are there forces at work in the economy that will take the prevailing price vector to equilibrium, supposing that one exists? This is the “stability question” for market equilibrium

 

            and in these pages Blad and Keiding present an introduction to the field of answers to this    question.

 

 

 

H. Varian (1992), pp. 398-402.

 

 

 

            Gives an account parallel to that in Blad and Keiding for the first few pages, but then           introduces the important 'Non-Tatonnement' adjustment processes.

 

 

 

           

 

 

 

 

 

F. H. Hahn (2008), “Auctioneer”, (in) NPDE2.

 

 

 

In teresting discussion of the stability problem. Also, if you get interested in this problem, then a place where you might start a serious study is         Hahn (1982), both for details about known results and for 'attitude'.

 

 

 

D.G. Saari and C.T. Simon (1978), "Effective price mechanisms", Econometrica, pp. 1097-1125.

 

 

 

This is an extremely important paper in the Stability literature. A summary of the main conclusion will be presented in lectures.

 

 

 

L. W. McKenzie (2002), pp. 45 – 96.

 

 

 

            Proides a unified treatment of numerous important issues in stability analysis.

 

 

 

W. D. A. Bryant (2010), Ch 8.

 

 

 

Provides a discussion of the stability properties of some tatonnement, non-tatonnement and ‘agent driven’ adjustment processes, in a GE context.           

 

 

 

 

 

Lecture 8 Comparative Statics of Market Equilibrium

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 616-620.

 

 

 

What happens to (equilibrium) prices and quantities if the economy is “shocked” (¹ morally outraged) by a variation in the parameters which define it, in particular, tastes, endowments and technologies? This is a fundamental applied issue and also one of considerable theoretical and “methodological” significance.

 

 

 

M. Blad and H. Keiding (1990), pp. 166-168.

 

 

 

            If we are serious about the “Samuelson-program” and also if we want to make bread and     butter predictions about the effects on prices and quantities traded of various parameter            changes, then we need to be able to extract from our multi-market models, so called         comparative static predictions. Blad and Keiding give an introduction to the circumstances in    which this might be possible.

 

           

 

J. Nachbar (2010), "Comparative Statics" NPDE2.

 

 

 

Excellent survey of what is involved in obtaining comparative static results in disaggregated systems.

 

 

 

L. W. McKenzie (2002), pp. 133 – 153.

 

 

 

Ties up a number of the issues associated with comparative statics in GE systems as well as providing an introduction to some of the emerging modern techniques for tackling this task.

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 652-673.

 

 

 

When does price taking behaviour make sense and what precisely is meant by the term “competitive”? A fundamental result due to Aumann answered these questions and that answer            and the associated extensions is presented here.

 

 

 

 

 

W. D. A. Bryant (2010), Ch 10.

 

 

 

            Discusses the major approaches to, and results for, comparative statics in a GE context.

 

 

 

 

 

Lecture 9 Optimality of Market Equilibrium and the Welfare Theorems

 

 

 

A. Mas-Colell, M Whinston and J. Green (1995), (background: pp. 515-525; see also the course notes.)

 

 

 

            Provides the geometric intuition for what is going on with the Welfare Theorems.

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 545-566.

 

 

 

            Extensive account of the First and Second Fundamental Theorems of Welfare Economics.

 

 

 

M. Blad and H. Keiding (1990), Ch. 4.

 

 

 

            Market or Walrasian equilibrium might be an interesting solution concept for certain abstract            games and even a way of understanding market prices, trades and sometimes a vehicle for         obtaining comparative static predictions.  Possibly even more interesting is the fact that under       certain conditions Walrasian equilibrium decentralises a Pareto optimal allocation.  This            chapter deals with the optimality of equilibrium.

 

 

 

G. Debreu (1959), Ch. 6.

 

 

 

            Classic treatment of the first and second fundamental theorems of Welfare Economics.  Note           in particular the hypotheses and conclusions of these theorems.

 

 

 

L. W. McKenzie (2002), pp. 165 – 171.

 

 

 

            Gives a very nice account of the Welfare theorems and their context.

 

 

 

 

 

W. D. A Bryant (1994), "Misinterpretations of the Second Fundamental Theorem of Welfare Economics", Journal of Economic Education, 25(1), pp. 75 – 80.

 

 

 

The informal and semi-formal literature which interprets the SFTWE often claims more than the theorem does.  “Support” is not analogous in English to “achieve”.  This distinction matters when policy design is considered.

 

 

 

L. Kaplow (2008), “Pareto principle”, (in) NPDE2.

 

           

 

An interesting and insightful discussion of the optimality principle that has come to dominate thinking about welfare economics, at least at the undergraduate level.

 

 

 

W. D. A. Bryant (2010), Ch 9.

 

 

 

Discusses both the First and Second welfare theorems. Explores some circumstances where they hold and also some circumstances where they fail.

 

 

 

 

 

 

 

Lecture 10 Some Applications of the Arrow-Debreu Model

 

 

 

This LECTURE aims to show that far from being an arcane piece of theory, Arrow-Debreu microeconomics informs a great deal of economic analysis – both ‘pure’ and ‘applied’.

 

 

 

Application 1: The first application involves a relatively careful anlysis of The Gains from Trade Proposition.

 

 

 

M. Kemp (1987), "Gains from Trade", NPDE1 (2), pp. 453-454.

 

 

 

            There are numerous applications of Arrow-Debreu model.  Here Kemp shows how the         model underpins standard “gains from trade” arguments.

 

 

 

M. Kemp and K. Shimomura (1997), “Trade gains: A unified exposition based on duality”, The Japanese Economic Review, Volume 48, No. 2, pp. 121 – 131.

 

 

 

This paper provides an in depth look at the propositions which constitute the gains from trade proposition in international trade.

 

 

 

Newbery, D. and J. Stiglitz (1984), “Pareto inferior trade”, The Review of Economic Studies, 51(1), pp.

 

1 – 12.

 

 

 

Shy, O. (1988), “A general equilibrium model of Pareto inferior trade”, Journal of International Economics, 25(1/2), pp. 143 – 154.

 

 

 

Shy, O. (1989), “External effects and Pareto inferior trade”, Southern Economic Journal, 56(1), pp. 56 – 63.

 

 

 

Willmann, Gerald (2004), “Pareto gains from trade: a dynamic counterexample” Economics Letters Volume 83, Issue 2, Pages 199-204.

 

 

 

Grandmont, J. M. and D. McFadden (1972), “A technical note on the classical gains from trade”, Journal of International Economics, 2, pp. 109 – 125.

 

 

 

Grinols E. (1991), “Increasing returns and the gains from trade”, International Economic Review, 32(4), pp. 973 – 984.

 

 

 

Kemp, Murray C. and Koji Shimomura (2002), “Recent Challenges to the Classical Gains-from-Trade Proposition”, German Economic Review, November 2002, v. 3, iss. 4, pp. 485-89.

 

 

 

Fachini G. and G. Willmann (2001), “Pareto gains from trade”, Economia et Politica, 18(2), pp. 207 – 215.

 

 

 

Calvo-Pardo, Hector (2009), “Are the Antiglobalists Right? Gains-from-Trade without a Walrasian Auctioneer”, Economic Theory, v. 38, iss. 3, pp. 561-92

 

 

 

Application 2: The second application involves studying the fascinating subject of Picemeal reform. This approach to economic policy formulation turns out to be widely applicable to task of finding welfare improving policies. This LECTURE provides a discussion of the foundations of the approach in Arrow-Debreu microeconomics, along with some applications.

 

 

 

Debreu, G. (1951), “The coefficient of resource utilization”, Econometrica, 19, 273 – 92.

 

 

 

Dixit, A. (1975), “Welfare effects of price changes”, Journal of Public Economics, 4, pp. 103 – 25.

 

 

 

Dixit, A. (1979), “Price changes and optimum taxation in a many-consumer economy”, Journal of Public Economics, 11, pp. 143 – 57.

 

 

 

Dixit, Avinash (1987), “On Pareto-Improving Redistributions of Aggregate Economic Gains”, Journal of Economic Theory, February 1987, v. 41, iss. 1, pp. 133-53.

 

 

 

Rader, T. (1976), “The Welfare Loss from Price Distortions”, Econometrica, 44, pp. 1253 – 57.

 

 

 

Guesnerie, R. (1977), ”On the direction of tax reform”, Journal of Public Economics, 7, pp. 179 – 202.

 

 

 

A. Woodland (1982), International Trade and Resource Allocation, pp. 341-344.

 

 

 

            Presents an introduction to the tax and tariff reform literature which uses the Arrow-Debreu             model as its laboratory.

 

           

 

A. Turenen-Red and A. Woodland (1991), "Tariff Reform in a Small Open Multi -  Household Economy with Domestic Distortions and Nontraded Goods", International Economic Review, pp. 937-957.

 

 

 

Advanced contribution to the Arrow-Debreu tariff reform literature, which relaxes some of the assumptions previously made in the literature.

 

Quiggin, John (1998), “Micro Gains from Micro Reform”, Economic Analysis and Policy, March 1998, v. 28, iss. 1, pp. 1-16

 

 

 

Ju, Jiandong and Kala Krishna (2000), “Necessary conditions for welfare improving reforms” Economics Letters Volume 67, Issue 2, Pages 121-237

 

 

 

Serra, Pablo (1988), “The excess utility functions and the welfare adjustment process”, Economics Letters, Volume 26, Issue 1, Pages 1-5

 

 

 

Yun, Kwan Koo (2010), “Efficient, Pareto-improving processes”, Journal of Mathematical Economics, Volume 46, Issue 3, Pages 326-331

 

 

 

Carvajal, Andrés and H.M. Polemarchakis (2008), “Identification of Pareto-improving policies: Information as the real invisible hand” Journal of Mathematical Economics Volume 44, Issue 2, Pages 167-179

 

 

 

Acocella, N. and G. Di Bartolomeo (2006), “Tinbergen and Theil meet Nash: Controllability in policy games” Economics Letters Volume 90, Issue 2, Pages 213-218.

 

 

 

Turunen-Red, Arja H. (1990), “On the Hatta Normality Condition and Tax Reforms”, Journal of Public Economics, v. 43, iss. 2, pp. 253-62

 

 

 

Nakanishi, Noritsugu (1993), “Welfare Analysis of Tariff Change with and without International Transfers” Journal of International Economics, November 1993, v. 35, iss. 3-4, pp. 377-87.

 

 

 

Konishi, H. (1995), “Pareto-improving commodity tax reform under a smooth non-linear income tax”, Journal of Public Economic, 56, 413 – 46.

 

 

 

Mandler, Michael (1999), “Simple Pareto-Improving Policies”, Journal of Economic Theory, v. 84, iss. 1, pp. 120-33.

 

 

 

 

 

Application 3: In LECTURE 8 on Comparative Statics, we developed a general expression for the variation in prices associated with particular changes in the parameters that define the economy. One such parameter is the size, composition and distribution of endowments among consumers in the economy. It is of some interest to study what happens when agents are transferred between agents. Our third application of Arrow-Debreu microeconomics therefore considers endowment transfers, endowment manipulation and The Transfer Problem and the transfer paradox. Academic interest in the transfer problem, grew out of a debate between Ohlin and Keynes about the likely effects of post WW1 German reparations. Here we outline the classic transfer problem and explore the various ‘manipulation via endowments’ results that have appeared in the literature.

 

 

 

M. Rao (1992), "On the transfer and advantageous reallocation paradoxes"  Social Choice and Welfare, pp. 131-139.

 

 

 

            Presents a nice account of the so-called 'Transfer Paradox', which although it appears to be a            highly academic question, actually has historical antecedents in the debates (between Keynes          and Ohlin among others) about the appropriate size of post WW1 German reparations. Can      be applied in many contemporary situations also..

 

 

 

Kemp, Murray C. and Koji Shimomura (2002), “A Theory of Voluntary Unrequited International Transfers”,  Japanese Economic Review, v. 53, iss. 3, pp. 290-300

 

 

 

Safra, Z. (1987), “Strategic reallocation of resources”, NPDE1, Vol 4., pp. 516 – 518.

 

 

 

Donsimoni, M. P. and H. Polemarchakis(1994), “Redistribution and welfare”, Journal of Mathematical Economics, 23, 235 – 42.

 

 

 

Galor, O. and H. Polemarchakis (1987), “Intertemporal equilibrium and the transfer paradox”, Review of Economic Studies, 54, pp. 147 – 56.

 

 

 

Dixit, A. (1995), “The multi-country transfer problem”, in International Trade, Volume 1: Welfare and Trade Policy, (ed.) J. P. Neary, Edward Elgar, Aldershot.

 

 

 

Goenka, Aditya and Stefano Matta (2008), “Manipulation of endowments and sunspot equilibria” Economic Theory 36, pp. 267 – 82.

 

 

 

Hens, Thorsten and Beate Pilgrim (2004), “Sunspot Equilibria and the Transfer Paradox”, Economic Theory, Vol. 24, No. 3, pp. 583-602.

 

 

 

Lane, Philip R. and Gian Maria Milesi-Ferretti (2004), “The transfer problem revisited: net foreign assets and real exchange rates”, Review of Economics &Statistics, Vol. 86 Issue 4, p841-857.

 

 

 

Brock, P. (2008),Transfer problem”, in New Palgrave Dictionary of Economics, 2^nd Edition, S. Durlauf and L. Blume (eds.), Palgrave Macmillan, London.

 

 

 

Yano, M. and J. Nugent (1999), “Aid, nontraded goods and the transfer paradox in small countries”, American Economic Review, 89, pp. 431 – 49.

 

 

 

Application 4: Our fourth application is to optimal taxation.

 

 

 

Atkinson, A. and J. E. Stiglitz (1972), “The structure of indirect taxes and economic efficiency”, Journal of Public Economics, 1, pp. 97 – 119.

 

 

 

Atkinson, A. and N. Stern (1980), “The switch from direct to indirect taxation”, Journal of Public Economics, 14, pp. 195 – 224.

 

 

 

Sandmo, A. (1974), “A note on the structure of optimal taxation”,  American Economic Review, 64, pp. 701 – 06.

 

 

 

Sandmo, A. (1976), “”Optimal taxation- - an introduction to the literature”, Journal of Public Economics, 6, pp. 37 – 54.

 

 

 

Sandmo, A. (1987), “A reinterpretation of elasticity formula in optimum tax theory”, Economica, 54, pp. 89 – 96.

 

 

 

Stiglitz, J. E. (1987), “The theory of Pareto efficient and optimal redistributive taxation”, in P. G. Hare (ed.), Surveys in Public Sector Economics, Blackwell Publishers, Oxford, pp. 71 – 114.

 

 

 

Saez, E. (2000), “Optimal Income Tax Rates and Elasticities: A Summary”, Proceedings: Ninetysecond Annual Conference on Taxation, Atlanta, Georgia, October 24-26, 1999, pp. 64-71, Washington, D.C.: National Tax Association

 

 

 

Saez, E. (2001), “Using Elasticities to Derive Optimal Income Tax Rates”, Review of Economic Studies, v. 68, iss. 1, pp. 205-29.

 

 

 

Laroque, G. R. (2005), “Indirect Taxation Is Superfluous under Separability and Taste Homogeneity: A Simple Proof”, Economics Letters, 87, pp. 141 – 44.

 

 

 

Hellwig, Martin F. (2010), “A generalization of the Atkinson–Stiglitz (1976) theorem on the undesirability of nonuniform excise taxation” Economics Letters, Volume 108, Issue 2,  Pages 156-158.

 

 

 

Robledo, Julio R. and Andreas Wagener (2007), “No spurious welfare gains from taxation: A further argument for the equivalent variation”, Economics Letters Volume 96, Issue 3, Pages 325-330.

 

 

 

Facchini, Giovanni, Peter J. Hammond and Hiroyuki Nakata (2001), “Spurious deadweight gains”, Economics Letters Volume 72, Issue 1, Pages 33-37

 

 

 

Keen, Michael and David Wildasin (2004), “Pareto-Efficient International Taxation”, American Economic Review, Vol. 94, No. 1, pp. 259-275.

 

 

 

Application 5: Thanks to a result known a Sperner’s Lemma, is a close relative of Brouwer’s Fixed Point Theorem, it is possible to compute Arrow-Debreu prices (and quantities). Our sixth application will explore and explain some of what is involved in the computation of equilibrium prices and quantities.

 

 

 

Scarf, H. E. (2008), “Computation of general equilibria”, in The New Palgrave Dictionary of Economics, 2nd Edition (rds.), S. Durlauf and L. Blume, Palgrave MacMllan, London.

 

 

 

Richter, Marcel K. and Kam-Chau Wong (1999), “Non-computability of Competitive Equilibrium”, Economic Theory, v. 14, iss. 1, pp. 1-27.

 

 

 

Brocker, Johannes (1998), “Operational Spatial Computable General Equilibrium Modeling”, Annals of Regional Science, v. 32, iss. 3, pp. 367-87

 

 

 

Caucutt, Elizabeth M. (2001), “Peer Group Effects in Applied General Equilibrium”, Economic Theory, Vol. 17, No. 1, pp. 25-51

 

 

 

Deng, Xiaotie and Ye Du (2008), “The computation of approximate competitive equilibrium is PPADhard”, Information Processing Letters, Vol. 108 Issue 6, p369-373.

 

 

 

Kubler, F. (2008), “Computation of general equilibrium (new developments)”, (in) New Palgrave Dictionary of Economics, 2nd Edition (eds.), S. Durlauf and L. Blume, Palgrave MacMillan, London.

 

 

 

Chia N. and J. Whalley (1997), “A numerical example showing globally welfare worsening liberalisation of international trade in banking services”, Journal of Policy Modeling, 19(2), pp. 119 – 127.

 

 

 

 

 

Lecture 11 Testing Arrow-Debreu Theory

 

 

 

F. Kleibergen (2008), “Testing”, (in) NPDE2.

 

 

 

          Interesting discussion of the testing in an economics context.

 

 

 

 

 

(Testing Arrow-Debreu Consumer Theory)

 

 

 

A. Deaton (1984), "Demand Analysis", Handbook of Econometrics, Vol. 3, Ch. 30.

 

 

 

            Presents a summary of the outcome of testing Neoclassical consumer demand theory and     some background material on how to conduct such tests.

 

J. Sabelhaus (1990), "Testing Neoclassical Consumer Theory with Aggregate and Household Data",  Applied Economics, pp. 1471-1479.

 

 

 

            Presents a test of Neoclassical consumer demand theory using the AID demand system and draws attention to the contrast between results for aggregate and  individual data.

 

 

 

R. Cooper and K. McLaren (1992), "An empirically oriented demand system with improved regularity properties",  Canadian Journal of Economics, pp.652-            68.

 

 

 

            An important development in the methodology of testing A-D consumer theory is presented             here along with an interesting empirical application.

 

 

 

M. Familari (1995), “A household-based non-parametric test of Demand    Theory”, Review of Economics and Statistics, pp. 372-382.

 

 

 

            A non-parametric test of consumer theory.

 

 

 

A. P. Barten (2003) “The empirical content of consumer theory”, Journal of Agricultural and Applied Economics, Supplement 2003, v. 35, pp. 7-17

 

 

 

Falsification of nontrivial empirical statements, of a statistical nature or not, is basically destructive. No wonder that it is rarely practiced. Rather than then abandoning a rejected null hypothesis, one tries to salvage it by looking for reasons why the rejection of an otherwise credible, plausible hypothesis occurs. One then attempts to modify the set-up in such a manner that formal rejection is avoided. Testing, in general, but specifically of nonnested hypotheses, can be seen as a kind of model selection. These issues are illustrated with examples from applied demand analysis: the testing of the homogeneity condition and of Slutsky symmetry and the choice of functional form for demand systems.

 

 

 

W. D. A. Bryant (2010), pp. 356 – 76.

 

 

 

Provides a survey of tests of consumer theory.

 

 

 

 

 

(Testing Arrow-Debreu Producer Theory)

 

 

 

K. Conrad and R. Unger (1987), "Expost Tests for Short - and Long-Run Optimisation", Journal of Econometrics, pp. 339-1479.

 

 

 

Tests Neoclassical producer theory by exploiting consequences of various dual equivalence’s.

 

 

 

J. Pencaval and B. Craig (1994), “Empirical Performance of Orthodox Models       of the Firm: Conventional Firms and Worker Co-operatives.” Journal of Political Economy, pp. 718-744.

 

 

 

            Cleverly does (at least) two things: (i) See’s how well the standard price taking, profit maximising   model of the firm performs as far as predicting how firms will react to changes in their economic           environment and (ii) check to see how different this behaviour is from that which one observes in      firms which have objectives other than straight profit maximisation. Also claims to be doing this work                 without appeal to restrictive assumptions about returns to scale.

 

Barnett, WilliamA. (2002), “Tastes and technology: Curvature is not enough for regularity”, Journal of Econometrics, May 2002, v. 108, iss. 1, pp. 199-202

 

 

 

An interesting discussion of  some basic issues in the econometrics of testing producer (and consumer) theory.

 

 

 

W. D. A. Bryant (2010), pp. 377 – 86

 

 

 

Provides a survey of tests of producer theory.

 

 

 

(Testing The Market Clearing Hypothesis)

 

 

 

G. Rudebusch (1989), "An Empirical Disequilibrium Model of Labor, Consumption and Investment", International Economic Review, pp. 633-654.

 

 

 

            Tests the Walrasian-equilibrium hypothesis using a disaggregated model of the US economy             and aggregate data.

 

 

 

Mishra, D. and D. Talman (2006), “Overdemand and underdemand in economies with invisible goods and unit demands”, Tilburg University, Center for Economic Research, Discussion Paper No. 84.

 

 

 

Considers the possibility of disequilibrium on markets due to various sorts of indivisibilities. Also presents some informal evidence in this direction.

 

 

 

W. D. A. Bryant (2010), pp. 386 – 401.

 

 

 

Presents some empirical evidence derived from tests of market clearing.

 

 

 

Lecture 12 Arrow – Debreu and Uncertainty

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 167-207.

 

 

 

            Detailed introduction to the theory of individual behaviour under uncertainty, including a     review of some of the modern developments in the field.

 

 

 

D. Kreps (1990), Ch. 3.

 

 

 

            There are many ways to model the choice, by an individual, of an action when there is an    uncertain connection between any particular action and the resulting outcomes. Kreps provides an introduction and useful discussion of one of the most heavily investigated models      of choice under uncertainty, that due to von Neumann and Morgenstern.

 

 

 

 

 

P. P. Wakker (2008), “Uncertainty”, (in) NPDE2.

 

 

 

            Provides a very nice treatment of choice under uncertainty.

 

 

 

Lecture 13 Arrow – Debreu and Uncertainty (cont’d)

 

 

 

 

 

G. Debreu (1959), Ch.7.

 

 

 

            Provides a classic treatment of the results obtainable about an economy in which there is a   complete set of contingent markets.

 

 

 

A. Mas-Colell, M. Whinston and J. Green (1995), pp. 167-207.

 

 

 

            Detailed introduction to the theory of individual behaviour under uncertainty, including a     review of some of the modern developments in the field.

 

 

 

Summary and Revision

 

 F. Hahn (1982), "Reflections on the Invisible Hand", Lloyds Bank Review, pp. 1-21.

A delightful summary of much of what we have seen, presented with flair and great “attitude”.

 

 

 

W. D. A. Bryant (2010), Ch 12.

An attempts a reflection on some of what GET  has to teach us.

 

Teaching Week	Lecture	Other things happening
1	Lecture 1: Microeconomics and the Arrow–Debreu model.
2	Lecture 2: Arrow–Debreu Consumers I (Choice).	Tute 1 due
3	Lecture 3: Arrow–Debreu Consumers II (Demand).	Tute 2 due
4	Lecture 4: Arrow–Debreu Consumers III (Duality and Revealed Preference).	Tute 3 due
5	Lecture 5: Arrow–Debreu Producers.	Tute 4 due
6	Lecture 6: The Existence of equilibrium.	Tute 5 due
7	Lectute 7: Uniqueness and Stability of equilibrium.	Tute 6 due
8	Lecture 8: Comparative Statics of equilibrium.	Tute 7 due
9	Lecture 9: Optimality and the Welfare Theorems.	Tute 8 due
10	Lecture 10: Some applications of Arrow–Debreu general equilibrium theory.	Tute 9 due
11	Lecture 11: Testing Arrow–Debreu consumer, producer and equilibrium theory.	Tute 10 due
12	Lecture 12: Arrow–Debreu and Uncertainty	Tute 11 due
13	Lecture 13: Arrow–Debreu and Uncertainty (cont’d) + Revision.	Tute 12 due

 

___________________________________________________________________________

 

                                    FIRST WEEK OF EXAMINATIONS

 

                                    SECOND WEEK OF EXAMINATIONS

 

 

 

All the best and I hope you learn something from the course.