# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

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### 1977

**445 Logrolling and Budget Allocation Games***by*Martin Shubik & Ludo Van der Heyden**444 An Extension of the Brown-Robinson Equivalence Theorem***by*Donald J. Brown & M. Ali Khan**443 Strategies for the Control of Carbon Dioxide***by*William D. Nordhaus**442 Can the Government Affect Real Output?: A Critique of Models with Rational Expectations***by*Ray C. Fair

### 1976

**441 Theory of Money and Financial Institutions. Part 34. A Multiperiod Trading Economy with Fiat Money, Bank Money and an Optimal Bankruptcy Rule***by*Martin Shubik**440 Probabilistic Generalizations of the Shapley Value***by*Pradeep Dubey**439 A Theory of Money and Financial Institutions. Part 33. On the Value of Market Information***by*Martin Shubik**438 Wages, the Terms of Trade, and the Exchange Rate Regime***by*Douglas D. Purvis**437 Price Information and the Economics of Consumerism: A Model of Stochastic Equilibrium***by*John Sutton**436 A Theory of Extramarital Affairs***by*Ray C. Fair**435 Economic Growth and Climate: The Carbon Dioxide Problem***by*William D. Nordhaus**434 A Note on the Computation of the Tobit Estimator***by*Ray C. Fair**433 The Small-Disturbance-Asymptotic Moments of the Instrumental Variables and Ordinary Least Squares Estimators for a Dynamic Equation with Correlated Errors***by*Jon K. Peck**432 A Model of Insurance Markets with Asymmetric Information***by*Charles Wilson**431 A Dynamic Economy with Shares, Fiat, Bank and Accounting Money***by*Joseph J.M. Evers & Martin Shubik**430 A Model of the World Economy***by*Ray C. Fair**429 A Closed Economic System with Production and Exchange Modelled as a Game of Strategy***by*Pradeep Dubey & Martin Shubik**428 The Linear Exchange Model and Induced Welfare Optima***by*Rolf R. Mantel**427 Asset Markets and the Cost of Capital***by*James Tobin & William C. Brainard**426 A Short-Run Two-Commodity Macroeconomic Model***by*Gary Smith & William Starnes**424R A Theory of Money and Financial Institutions. Part 30 (revised). The Optimal Bankruptcy Rule in a Trading Economy Using Fiat Money***by*Martin Shubik & Charles Wilson**423 On Disequilibrium Economic Dynamics. Part IV. The Theory of Long-Run Phillips Curve***by*Katsuhito Iwai**422 A Theory of Money and Financial Institutions. Part 28. The Noncooperative Equilibria of a Closed Trading Economy with Market Supply and Bidding Strategies***by*Pradeep Dubey & Martin Shubik**421 Concepts of Optimality and Their Uses***by*Tjalling C. Koopmans**420 The Use of Optimal Control Techniques to Measure Economic Performance***by*Ray C. Fair**419 On a General Approach to Optimality in Game Theory***by*Eduardas Vilkas**418 The Effects of Economic Events on Votes for President***by*Ray C. Fair**417 A Theory of Money and Financial Institutions. Part 27. Beyond General Equilibrium***by*Martin Shubik**416 A Theory of Money and Financial Institutions. Part 26. On the Number of Types of Markets with Trade in Money***by*Martin Shubik**415 Inflation Theory and Policy***by*William D. Nordhaus

### 1975

**414 A Theory of Money and Financial Institutions. Part 25. A Closed Economy with Exogenous Uncertainty, Different Levels of Information, Money, Futures and Spot Markets***by*Pradeep Dubey & Martin Shubik**413 A General Equilibrium Model of World Trade. Part II. The Empirical Specification***by*Victor Ginsburgh & Jean Waelbroeck**412 A General Equilibrium Model of World Trade. Part I. Full Format Computation of Economic Equilibria***by*Victor Ginsburgh & Jean Waelbroeck**411 On Disequilibrium Economic Dynamics. Part III. A Keynesian Theory of Money Wage Adjustment***by*Katsuhito Iwai**410R A Theory of Money and Financial Institutions. Part 24. Trade and Prices in a Closed Economy with Exogenous Uncertainty, Different Levels of Information, Money and No Futures Markets***by*Pradeep Dubey & Martin Shubik**409 Implications of Microeconomic Theory for Community Excess Demand Functions***by*Rolf R. Mantel**408 Examples of Production Relations Based on Microdata***by*Tjalling C. Koopmans**407 The Influence of Interest Rates on Resource Prices***by*Geoffrey M. Heal**406 The Values of a Nonstandard Competitive Allocation***by*Donald J. Brown & Peter A. Loeb**405 The Demand for Energy: An International Perspective***by*William D. Nordhaus**404 The Estimation of a Dynamic Equation Following a Preliminary Test for Autocorrelation***by*Jon K. Peck**403 Price Taking or Price Making Behavior: An Alternative to Full Cost Price Functions***by*Victor Ginsburgh & Israel Zang**402 A Critical Analysis of Ridge Regression***by*Frank Campbell & Gary Smith**401 Invariant Competitive Equilibrium in an Infinity-Horizon Economy with Negotiable Shares***by*Joseph J.M. Evers**400 A Control Variable Investigation of the Properties of Autoregressive Instrumental Variables Estimators for Dynamic Systems***by*David F. Hendry & Frank Srba**399 The Limiting Distribution of Inconsistent Instrumental Variables Estimators in a Class of Stationary Stochastic Systems***by*David F. Hendry**398 Testing Dynamic Specification in Small Simultaneous Systems: An Application to a Model of Building Society Behavior in the United Kingdom***by*David F. Hendry & Gordon J. Anderson**397 On Controlling the Economy to Win Elections***by*Ray C. Fair**396 A Dynamical Model of Political Equilibrium***by*Gerald H. Kramer**395 A Theory of Money and Financial Institutions. Part 23. Fiat Money, Bank Money, the Force of the Rate of Interest and the Vanishing Float***by*Martin Shubik**394 A Theory of Money and Financial Institutions. Part 21. Fiat Money, Bank Money, the Float and the Money Rate of Interest***by*Martin Shubik**393 Collective Rationality***by*Donald J. Brown**392 A Duality Theory for Convex Infinite-Horizon Programming***by*Joseph J.M. Evers**391 Acyclic Aggregation over Finite Sets of Alternatives***by*Donald J. Brown**390 The Solution of Systems of Piecewise Linear Equations***by*B. Curtis Eaves & Herbert E. Scarf**389 A Finite Algorithm for the Linear Exchange Model***by*B. Curtis Eaves**388 Oligopoly, Theory, Communication and Information***by*Martin Shubik**387 Keynesian Models of Recession and Depression***by*James Tobin**386 On Disequilibrium Economic Dynamics. Part II. Wicksellian Disequilibrium Dynamics, Say's Law and the End of the Natural Rate Theory of Unemployment***by*Katsuhito Iwai

### 1974

**385 On Disequilibrium Economic Dynamics. Part I. Microfoundations of Wicksellian Disequilibrium Dynamics***by*Katsuhito Iwai**384 Long Run Effects of Fiscal and Monetary Policy on Aggregate Demand***by*James Tobin & Willem H. Buiter**383 Multicollinearity and Forecasting***by*Gary Smith**382 The Value of a priori Information in Estimating a Financial Model***by*Gary Smith & William C. Brainard**381 Further Notes on the Misuse of R^2***by*Gary Smith**380 Okun's Law Revisited***by*Gary Smith**379 Competitive Equilibrium Contingent Commodities and Information***by*Martin Shubik**378 Global Analysis and Economics VI. Geometric Analysis of Pareto Optima and Price Equilibria under Classical Hypotheses***by*Steve Smale**377 A Theory of Money and Financial Institutions. Part XVI. Mathematical Models for a Theory of Money and Financial Institutions***by*Martin Shubik**376 Fiscal Capacity, Equalization and Public Expenditure for Education***by*Susan J. Lepper**375 Equilibrium Wage Distributions***by*Joseph E. Stiglitz**374 A Theory of Money and Financial Institutions. Part XVIII. A Noncooperative Model of a Closed Trading Economy with Many Traders and Two Bankers***by*Martin Shubik**373 The Walrasian and Von Neumann Equilibria: A Comparison***by*Jerzy Los & Maria Wycech-Los**372 Transactions Technology and the Use of Intermediary Agents***by*Ross M. Starr**371 On the Role of Numbers and Information in Competition***by*Martin Shubik**370 The Moments of the 3SLS Estimates of the Structural Coefficients of a Simultaneous Equation Model***by*J.D. Sargan**369 Towards Keynesian Micro-Dynamics of Price, Wage, Sales and Employment***by*Katsuhito Iwai**368 A Theory of Money and Financial Institutions. Part XV. A Trading Model to Avoid Tatonnement Metaphysics***by*Martin Shubik**367 A Theory of Money and Financial Institutions. Part XVII. On the Eight Basic Units of a Dynamic Economy with Spot and Futures Markets***by*Martin Shubik

### 1973

**366 A Theory of Money and Financial Institutions. Part XIII. Trade with Spot Markets, Fiat Money and Internal Banking***by*Martin Shubik**365 The General Equilibrium Model is the Wrong Model and a Noncooperative Strategic Process Model is a Satisfactory Model for the Reconciliation of Micro and Macroeconomic Theory***by*Martin Shubik**364 A Theory of Money and Financial Institutions. Part XII. A Dynamic Economy with Fiat Money Without Banking and With and Without Production Goods***by*Martin Shubik**363 A Theory of Money and Financial Institutions. Part XI. Trade with Fiat Money but No Individual Trust. A Preliminary Stage towards Banking***by*Martin Shubik**362 Regulation of Natural Monopolies and the Fair Rate of Return***by*Hayne E. Leland**361 Production Theory and the Stock Market***by*Hayne E. Leland**360 Acyclic Choice***by*Donald J. Brown**359 The General Equilibrium Model with Joint Ownership of the Corporation (Voting Stock and the Core)***by*Martin Shubik**358 Some Problems of Centralized Economy***by*N.N. Moiseev & A.G. Schmidt**357 Alternative Theories of Wage Determination and Unemployment in L.D.C.'s: II. The Efficiency Wage Model***by*Joseph E. Stiglitz**356 Some Observations on 'Optimal' Economic Growth and Exhaustible Resources***by*Tjalling C. Koopmans**355 Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game)***by*Martin Shubik & Ward Whitt**354 The Theory of 'Screening', Education, and the Distribution of Income***by*Joseph E. Stiglitz**353 Incentives and Risk-Sharing in Sharecropping***by*Joseph E. Stiglitz**352 Voting, Preference Orderings and Cooperative Games***by*Martin Shubik**351 Game Theory and Political Science***by*Martin Shubik**350 A Note on the Shape of the Pareto Optimal Surface***by*Gordon H. Bradley & Martin Shubik**349 Money and the Decentralization of Exchange***by*Joseph M. Ostroy & Ross M. Starr

### 1972

**348 Technological Development and Employment***by*James Tobin**347 Information, Duopoly and Competitive Markets: A Sensitivity Analysis***by*Martin Shubik**346 Input Quality, Obsolescence and Unemployment***by*J. Kirker Stephens**345 Social Choice on Pollution Management: The GENOSSENSCHAFTEN***by*Alvin K. Klevorick & Gerald H. Kramer**344 Some Further Results on the Measurement of Inequality***by*Michael Rothschild & Joseph E. Stiglitz**343 Existence of a 'Local' Cooperative Equilibrium in a Class of Voting Games***by*Gerald H. Kramer & Alvin K. Klevorick**342 Existence of a Competitive Equilibrium in a Nonstandard Exchange Economy***by*Donald J. Brown**341 Voting Behavior and Aggregate Policy Targets***by*Susan J. Lepper**340 Benefit-Cost Analysis and Trade Policies***by*Partha Dasgupta & Joseph E. Stiglitz**339 On the Irrelevance of Corporate Financial Policy***by*Joseph E. Stiglitz**338 A Theory of Money and Financial Institutions. Part V. The Rate of Interest on Fiat Money in a Closed Economy***by*Martin Shubik**337 A Theory of Money and Financial Institutions. Part IX. Competitive and Controlled Price Economies: The Arrow Debreu Model Revisited***by*Martin Shubik**336 A Theory of Money and Financial Institutions. Part VIII. Transactions Costs in a Market Economy***by*Martin Shubik**335 Alternative Theories of Wage Determination and Unemployment in L.D.C.'s: I. The Labor Turn-Over Model***by*Joseph E. Stiglitz**334 A Theory of Money and Financial Institutions. Part VI. The Rate of Interest, Noncooperative Equilibrium and Bankruptcy***by*Lloyd S. Shapley & Martin Shubik**333 Notes on Transactions Costs and the Analysis of Microeconomic Monetary Theory***by*William D. Nordhaus**332 Notes on Transactions Costs and the Analysis of Microeconomic Theory***by*Ross M. Starr**331 A Theory of Money and Financial Institutions. Part VII. Money, Trust and Equilibrium Points in Games in Extensive Form***by*Martin Shubik**330 A Theory of Money and Financial Institutions. Part IV. Fiat Money and Noncooperative Equilibrium in a Closed Economy***by*Martin Shubik**329 The Effects of Inflation on the Distribution of Economic Welfare***by*William D. Nordhaus**328 A General Equilibrium Calculation of the Effects of Differential Taxation of Income from Capital in the U.S***by*John B. Shoven & John Whalley**327 The Marginal Revolution After One Hundred Years***by*Ronald G. Bodkin**326 The Cores of Large Standard Exchange Economies***by*Donald J. Brown & Abraham Robinson**325 A Comparison of Alternative Estimators for a Dynamic Relationship Estimated from a Time Series of Cross-Sections When the Disturbances Are Small***by*Jon K. Peck**313R On the Definition and Computation of a Capital Stock Invariant Under Optimization***by*Terje Hansen & Tjalling C. Koopmans

### 1971

**324 A Theory of Money and Financial Institutions. Part III. The Missing Degree of Freedom: Commodity Money and Oligopoly in a General Equilibrium Model***by*Martin Shubik**323 Alternative Management of Common Property Resources under Free Access and Private Ownership***by*Martin L. Weitzman**322 A Theory of Money and Financial Institutions: Part II. On the Paradox of the Efficient Price System in a Completely Centralized Economy and in a Capitalist Individual Ownership Economy***by*Martin Shubik**321 A New Measure of Income from Wealth***by*Donald A. Nichols**320 A Theory of Money and Financial Institutions. Part I. The General Approach Adopted***by*Martin Shubik**319 Is Growth Obsolete?***by*William D. Nordhaus & James Tobin**318 On the Scope of Gaming***by*Martin Shubik**317 Duality Theory of Convex Programming for Infinite Horizon Economic Models***by*Martin L. Weitzman**316 Competitive Equilibrium and Game Theory Solutions: Part I. The Core and Value***by*Lloyd S. Shapley & Martin Shubik**315 Summary Comment***by*James Tobin**314 Wealth, Liquidity, and the Propensity to Consume***by*James Tobin**312 Systems of Indirect Management in a Planned Economy: Effectiveness Models and Their Applications in Poland***by*Witold Trzeciakowski**311 Wealth, Liquidity, and Consumption***by*Walter Dolde & James Tobin**310 The Price of Money in a Pure Exchange Monetary Economy***by*Ross M. Starr**309 Friedman's Theoretical Framework***by*James Tobin**308 Nonstandard Exchange Economies***by*Donald J. Brown & Abraham Robinson**307 An Estimate of Racial Discrimination in Rental Housing***by*Thomas King & Peter M. Mieszkowski**306 On Transitions between Steady States***by*Joseph E. Stiglitz

### 1970

**305 Taxation, Risk-Taking, and the Allocation of Investment***by*Joseph E. Stiglitz**304 The Property Tax: An Excise Tax or a Profits Tax?***by*Peter M. Mieszkowski**303 The Badly Behaved Economy with the Well Behaved Production Function***by*Joseph E. Stiglitz**302 On Durbin's Test for Serial Correlation in Distributed Lag Models***by*G.S. Maddala & A.S. Rao**301 On the Asymptotic Properties of Certain Two-Step Procedures Commonly Used in the Estimation of Distributed Lag Models***by*David M. Grether & G.S. Maddala**300 Equilibrium and Demand for Media of Exchange in a Pure Exchange Economy with Transactions Costs***by*Ross M. Starr**299 Differential Taxation, Public Goods, and Economic Efficiency***by*Joseph E. Stiglitz & Partha Dasgupta**298 Non-Linear Time Series Regression***by*E.J. Hannan**297 An Econometric Model of Postwar Japan***by*Fumimasa Hamada**296 Recent Developments in Price Dynamics***by*William D. Nordhaus**295 The Structure of Exchange in Barter and Monetary Economies***by*Ross M. Starr**294 Time Series Regression with Linear Constraints***by*E.J. Hannan & R.D. Terrell**293 On the Existence of a Cooperative Solution for a General Class of N-Person Games***by*Herbert E. Scarf**292 Aggregation and Disaggregation in the Pure Theory of Capital and Growth: A New Parable***by*Martin L. Weitzman**291 The Estimation of Mixed Regression, Autoregression, Moving Average and Distributed Lag Models***by*E.J. Hannan & D.F. Nichols**290 Food Prices in Relation to Income Levels in New York City***by*Roger E. Alcaly & Alvin K. Klevorick**289 Duopoly with Price and Quantity as Strategic Variables***by*Richard E. Levitan & Martin Shubik**288 Pecuniary Externalities: A Game Theoretic Analysis***by*Martin Shubik**287 Price Duopoly and Capacity Constraints***by*Richard E. Levitan & Martin Shubik

### 1969

**286 Material Balances under Uncertainty***by*Martin L. Weitzman**285 Investment, Savings and Employment in the Long-Run***by*David M.C. Newbery & A.B. Atkinson**284 On a Class of Equilibrium Conditions for Majority Rule***by*Gerald H. Kramer**283 Money and Income: Post Hoc Ergo Propter Hoc?***by*James Tobin**282 Borrowing-Lending Interest Rate Differentials and the Time Allocation of Consumption***by*Thayer H. Watkins**281 An Analysis of the Importance of the Malleable Capital Assumption in Optimal Growth Models***by*David M.C. Newbery**280 Economic Aspects of Information***by*Luigi M. Tomasini**279 Distributed Lags, Prediction, and Signal Extraction***by*David M. Grether**278 The Choice of Techniques in a Dual Economy***by*David M.C. Newbery**277 A Fixed Point Algorithm for Approximating the Optimal Solution of a Concave Programming Problem***by*Terje Hansen**276 An Example of an Algorithm for Calculating General Equilibrium***by*Herbert E. Scarf**275 Increasing Risk: A Definition and Its Economic Consequences***by*Michael Rothschild & Joseph E. Stiglitz**274 Game Theory, Behavior and the Paradox of the Prisoners Dilemma -- 3 Solutions***by*Martin Shubik**273 Optimal Growth with Scale Economies in Overhead Capital***by*Martin L. Weitzman**272 On The Applications of a Recent Combinatorial Algorithm***by*Terje Hensen & Herbert E. Scarf**271 A Note on a Variance-Components Model Useful in the Study of Cross-Sections over Time***by*Marc Nerlove**270 Price Variation Duopoly with Differentiated Products and Random Demand***by*Richard E. Levitan & Martin Shubik**269 Comparison of k-Class Estimators When the Disturbances Are Small***by*Joseph B. Kadane**268 Risk Aversion over Time and a Capital-Budgeting Problem***by*Alvin K. Klevorick**267 The 'Bridge Game' Economy***by*Martin Shubik**266 Shiftable vs. Non-Shiftable Capital: A Synthesis***by*Martin L. Weitzman**265 An Economic Theory of Technological Change***by*William D. Nordhaus**264 The Time Allocation of Consumption under Debt Limitations***by*Thayer H. Watkins**263 Money and Permanent Income: Some Empirical Tests***by*James Tobin & Craig Swan**262 A Note on Behavior towards Risk with Many Commodities***by*Joseph E. Stiglitz

### 1968

**261 Some Properties of 'Optimal' Seasonal Adjustment***by*David M. Grether & Marc Nerlove**260 Optimal Entrepreneurial Decisions in a Completely Stochastic Environment***by*Nils H. Hakansson**259 A Long-Run Cost Function for the Local Service Airline Industry: An Experiment on Non-Linear Estimation***by*George Eads & Marc Nerlove & William Raduchel**258 Countably Additive Measures in Cores of Games***by*Yakar Kannai**257 Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross-Sections***by*Marc Nerlove**256 Soviet Postwar Economic Growth and Capital Labor Substitution***by*Martin L. Weitzman**255 Regularity in the Distribution of Participation in Group Discussions***by*Joseph B. Kadane & Gordon H. Lewis**254 Stochastic Theories of Participation***by*Joseph B. Kadane & Gordon H. Lewis & John G. Ramage**253 Money Illusion, Price Expectations, and the Aggregate Consumption Function***by*William H. Branson & Alvin K. Klevorick**252 Theory of Liquidity Preference and the Term Structure of Interest Rates***by*Joseph E. Stiglitz**251 The Distribution, When the Residuals Are Small, of Statistics Testing Overidentifying Restrictions***by*Joseph B. Kadane**250 Lags in Fiscal and Monetary Impacts on Investment in Producers Durable Equipment***by*Charles W. Bischoff**249 A Note on a Simulated Stock Market***by*Martin Shubik**248 The Effects of Income, Wealth, and Capital Gains Taxation on Risk Taking***by*Joseph E. Stiglitz**247 Some Experimental Non-Constant-Sum Games Revisited. Perception of Opponent's Payoffs. Part III***by*Martin Shubik & David H. Stern**246 An Experimental Research in Oligopoly***by*James W. Friedman**245 Notes on Optimal Monetary Growth***by*James Tobin

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