# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA

Phone: (203) 432-3702

Fax: (203) 432-6167

Web page: http://cowles.yale.edu/

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Phone: (203) 432-3702

Fax: (203) 432-6167

Web page: http://cowles.yale.edu/

More information through EDIRC

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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### 1972

**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**244 Pitfalls in Financial Model-Building***by*William C. Brainard & James Tobin**243 Quiz Show Problems***by*Joseph B. Kadane

### 1967

**242 A Re-Examination of the Modigliani Miller Theorem***by*Joseph E. Stiglitz**241 The Optimal Life of a Patent***by*William D. Nordhaus**240 Some Experimental Non-Constant-Sum Games Revisited. Part II***by*Martin Shubik & David H. Stern**239 Iterative Multi-Level Planning with Production Targets***by*Martin L. Weitzman**238 Distribution of Income and Wealth Among Individuals***by*Joseph E. Stiglitz**237 A Note on Taxation, Increasing Returns Due to Set-up Costs and Competitive Equilibrium***by*Martin Shubik**236 Some Experimental Non-Constant-Sum Games Revisited. Part I***by*Martin Shubik & David H. Stern**235 An Econometric Study of Cotton Production and Trade Before 1860***by*Gavin Wright**234 A Noncooperative View of Oligopoly***by*James W. Friedman**233 Price Strategy Oligopoly with Product Variation***by*Lloyd S. Shapley & Martin Shubik**232 On the Computation of Equilibrium Prices***by*Herbert E. Scarf**231 Cross-Section Analysis and Bank Dynamics***by*Donald D. Hester & James L. Pierce**230 Welfare, Static and Dynamic Solution Concepts***by*Martin Shubik**229 Maximizing Stationary Utility in a Constant Technology***by*Richard Beals & Tjalling C. Koopmans**228 Intertemporal Distribution and 'Optimal' Aggregate Economic Growth***by*Tjalling C. Koopmans**227 Part VII: The Nonsymmetric Game: The Generalized Beat-the-Average Solution***by*Levitan, Richard E. & Martin Shubik**226 Spectral Analysis of the Relation between Employment Changes and Output Changes***by*Daniel S. Hammermesh**225 Part V: The Nonsymmetric Game: Joint Maximum, Efficient Solution and Measures of Collusion and Welfare***by*Richard E. Levitan & Martin Shubik**224 The Cournot Equilibrium in a Nonsymmetric Oligopolistic Market (A Business Game for Teaching and Research Purposes: Part VI)***by*Richard E. Levitan & Martin Shubik**223 An Empirical Analysis of the Postwar Savings and Loan Industry***by*John E. Spencer**222 A Note on the Limit of the Core of an Exchange Economy***by*Terje Hansen**221 Distributed Lags and Unobserved Components in Economic Time Series***by*Marc Nerlove**220 The Role of the Neyman Pearson Lemma in the Theory of Discrete Search***by*Joseph B. Kadane**219 Part IV: Mathematical Structure and Analysis of the Nonsymmetric Game***by*Richard E. Levitan & Martin Shubik**218 An Impossibility Result Concerning the Theory of Decision-Making***by*Gerald H. Kramer**217 A Further Comparison of Some Models of Duopoly***by*Martin Shubik**216R The Approximation of Fixed Points of a Continuous Mapping***by*Herbert E. Scarf**203BR Simulation of Socio-Economic Systems. Part II: An Aggregative Socio-Economic Simulation of a Latin American Country***by*Martin Shubik

### 1966

**215 A Note on the Role of Money in Providing Sufficient Intermediation***by*David Cass & Menahem E. Yaari**214 Optimal Employment and Inflation over Time***by*Edmond S. Phelps**213 Structural Restrictions and Estimation Efficiency in Linear Econometric Models***by*Thomas J. Rothenberg**212 Objectives, Constraints and Outcomes in Optimal Growth Models***by*Tjalling C. Koopmans**211 An Algorithm for a Class of Nonconvex Programming Problems***by*Herbert E. Scarf**210 Estimation of A Fixed Coefficients Vintage Model of Production***by*Richard Attiyeh**209 Some Econometric Problems in the Analysis of Inventory Cycles***by*Kenneth F. Wallis**208 Notes on the Taxonomy of Problems Concerning Public Goods***by*Martin Shubik**207 Equal Profits as a Fair Division***by*James W. Friedman**206R Structure of Preference over Time***by*Tjalling C. Koopmans**205 Efficient Estimation with a priori Information: A Classical Approach***by*Thomas J. Rothenberg**204 Game Theory and Economic Behavior***by*Martin Shubik**203A Simulation of Socio-Economic Systems. Part I: General Considerations***by*Martin Shubik**202 Application of Signal Extraction Techniques in the Study of Economic Time Series***by*David M. Grether**201 An Empirical Analysis of Risk Taking by Firms in the Savings and Loan Industry***by*Donald D. Hester**200 Measurable, Transferable, Comparable Utility and Money***by*Martin Shubik

### 1965

**199 Quasi and Generalized Golden Rule Paths: A Study of Commanding Growth Paths***by*Edmond S. Phelps**198 Individual Saving, Aggregate Capital Accumulation, and Efficient Growth***by*David Cass & Menahem E. Yaari**197 Uncertainty and Diversification in International Trade***by*William C. Brainard & Richard N. Cooper**196 Axioms for Factor Augmenting Technical Progress***by*Edmond S. Phelps**195 A Re-Examination of the Pure Consumption Loans Model***by*David Cass & Menahem E. Yaari**194 The Ramsey Problem and the Golden Rule of Accumulation***by*Edmond S. Phelps**193 Random Measure Preserving Transformations***by*Robert J. Aumann**192 An Experimental Study of Cooperative Duopoly***by*James W. Friedman**191 Absorptive Capacity and the Golden Rule of Accumulation***by*Edmond S. Phelps**190 Investment in Humans, Technological Diffusion and the Golden Rule of Education***by*Edmond S. Phelps**189 Investment in Humans, Technological Diffusion and Economic Growth***by*Richard R. Nelson & Edmond S. Phelps**188 A Model of Fixed Capital without Substitution***by*Robert M. Solow & James Tobin & C.C. Von Weisazacker & Menahem E. Yaari**187 A Dynamic Model of the Competitive Firm***by*Edward Zabel**186 A Model of Induced Invention, Growth and Distribution***by*Emmanuel M. Drandakis & Edmond S. Phelps**185 Factor-Price-Frontier Estimation of a 'Vintage' Production Model of the Post-war U.S. Nonfarm Business Sector***by*Edmond S. Phelps & Charlotte Phelps**184 The Relation Between Bank Portfolios and Earnings: An Econometric Analysis***by*Donald D. Hester & John F. Zoellner**183 Optimal Output and Price Policies for General Distributed Lag Demand Equations***by*Robert L. Graves & Lester G. Telser**182R The Core of an N Person Game***by*Herbert E. Scarf

### 1964

**181 A Time Series Analysis of Interest Rates***by*David I. Fand**180 A Business Game for Teaching and Research Purposes. Part III. Discussion and Manual for Users***by*Martin Shubik**179 A Parametric Simplicial Formulation of Houthakker's Capacity Method***by*C. Van De Panne & Andrew B. Whinston**178 Optimum Economic Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem***by*David Cass**177 The Construction of Utility Functions from Expenditure Data***by*S.N. Afriat**176 Models of Technical Progress and the Golden Rule of Research***by*Edmond S. Phelps**175 Stock Market Indices: A Principal Components Analysis***by*George J. Feeney & Donald D. Hester**174 An Experimental Study in Oligopoly***by*James W. Friedman**173 Second Essay on the Golden Rule of Accumulation***by*Edmond S. Phelps**172 A Decomposition Algorithm for Quadratic Programming***by*Andrew B. Whinston**171 Convexity in the Theory of Choice under Risk***by*Menahem E. Yaari**170 An Informal Aggregative Socio-Economic Simulation of a Latin American Country***by*James W. Friedman & Martin Shubik**169 The Existence of a Competitive Equilibrium in a Monetary Economy***by*Emmanuel M. Drandakis**168 The Monetary Mechanism: Some Partial Relationships***by*James L. Pierce**167 Ownership and the Production Function***by*Lloyd S. Shapley & Martin Shubik**166 On Prices, Fiat Money, Credit and Transferable Utility. Part I***by*Martin Shubik**161R Anticipated Inflation and Economic Welfare in a Neoclassical Model***by*Edmond S. Phelps**156 Consumption-Saving Decisions When the Horizon is Random***by*Menahem E. Yaari

### 1963

**165 On an Asymptotic Non-Substitution Theorem in the Two-Sector Closed Production Model***by*Emmanuel M. Drandakis**164 A Two-Country, Three Commodity, Dynamic Model of International Trade***by*T.N. Srinivasan**163A Appendix to 'On the Concept of Optimal Economic Growth'***by*Tjalling C. Koopmans**163 On the Concept of Optimal Economic Growth***by*Tjalling C. Koopmans**162 Conjugate Functions and Symmetric Duality***by*Andrew B. Whinston**160b Alternative Fiscal Policies for Targeted Growth***by*T.N. Srinivasan**160a On the Feasibility of Targeted Growth Through Taxation and the Social Virtue of Private Thrift***by*Edmond S. Phelps**159 Commercial Banks as Creators of 'Money'***by*James Tobin**158 On the Existence of an Optimal Plan in a Continuous-Time Allocation Process***by*Menahem E. Yaari**157 A Test of the Specification of the Aggregate Production Function***by*Ronald G. Bodkin**155 On the Consumer's Lifetime Allocation Process***by*Menahem E. Yaari**154R Factor Substitution in the Two-Sector Growth Model***by*Emmanuel M. Drandakis**153 Properties of Efficient Accumulation Paths in a Closed Production Model***by*Emmanuel M. Drandakis**152 Proportional Growth and Turnpike Theorems***by*Tjalling C. Koopmans**151 Seasonal Adjustment of Economic Time Series and Multiple Regression***by*Michael C. Lovell

### 1962

**63R Financial Intermediaries and the Effectiveness of Monetary Controls***by*James Tobin & William C. Brainard**150 On Flexibility of Future Preference***by*Tjalling C. Koopmans