# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

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### 1968

**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**203B Simulation of Socio-Economic Systems. Part II: An Aggregative Socio-Economic Simulation of a Latin American Country***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**149 An Analysis of the Effects of Transitory Income on Expenditure of Norwegian Households***by*Harold W. Watts**148 The Demand for Cash and Working Balances of Corporations***by*Alan W. Heston**147 The Wage-Price Productivity Nexus***by*Ronald G. Bodkin**146 Welfare Economics and the Theory of Second Best***by*Otto A. Davis & Andrew B. Whinston**145 Non-Existence of Consistent Estimator Sequences and Unbiased Estimates: A Practical Example***by*H.S. Konijn**144 On a Theorem of Halmos Concerning Unbiased Estimation of Moments***by*H.S. Konijn**143 On the Existence of a Subinvariant Measure***by*Tjalling C. Koopmans & Richard E. Williamson**142 Stationary Utility and Time Preference***by*Peter A. Diamond & Tjalling C. Koopmans & Richard E. Williamson**141 Price Guides in Decentralized Organization***by*Andrew B. Whinston**140 Models of the Joint Demand for Cash and for an Interest-Bearing Asset. Part One***by*Tore Johansen**139R On a Two Sector Model of Growth***by*T.N. Srinivasan**138 Part I: Price-Quantity Markets***by*George J. Feeney**137 Size of Firm, Market Structure, and Innovation***by*Edwin Mansfield**136 The Expenditures of the Firm on Research and Development***by*Edwin Mansfield**135 An Empirical Evaluation of Theories of Saving***by*Harold W. Guthrie**134R The Speed of Response of Firms to New Techniques***by*Edwin Mansfield**133 Substitution, Fixed Proportions, Growth and Distribution***by*Edmond S. Phelps**132R Intrafirm Rates of Diffusion of an Innovation***by*Edwin Mansfield**131 Inventory Investment***by*Michael C. Lovell

### 1961

**89R Buffer Stocks, Sales Expectations, and Stability: A Multi-Sector Theory of the Inventory Cycle***by*Michael C. Lovell**130 On a Theorem of Scarf***by*Gerard Debreu**129 New Concepts and Techniques for Equilibrium Analysis***by*Gerard Debreu**128 An Inter-City Consumption Function***by*Harold W. Watts**127 Corporate Cash and Security Holdings: An Empirical Study of Cash, Securities and Other Current Accounts of Large Corporations***by*Alan W. Heston**126 Entry, Gibrat's Law, Innovation, and the Growth of Firms***by*Edwin Mansfield**125 Monetary Policy, Debt Management and Interest Rates: A Quantitative Appraisal***by*Arthur M. Okun**124 A Note on Uncertainty, Bayesian Inference and Competitive Behavior***by*Phoebus J. Dhrymes**123 Some Empirical Estimates of Short Run Price and Output Policies***by*Edwin S. Mills**122 On Devising Unbiased Estimators for the Parameters of a Cobb Douglas Production Function***by*Phoebus J. Dhrymes**121 Spatial Distribution of Industry***by*H.C. Bos**120 Economic Growth and Wicksell's Cumulative Process***by*Martin J. Beckmann**119 Administered Prices and Imports: The Steel Industry***by*Lawrence B. Krause**118 Input-Output and Activity Analysis in Industrial Concerns***by*Alan S. Manne**117 Investment Criteria and Choice of Techniques of Production***by*T.N. Srinivasan**116 The Growth of Television Ownership in the United Kingdom***by*Andrew D. Bain**115R3 A Business Game for Teaching and Research Purposes***by*Martin Shubik**115R2 A Business Game for Teaching and Research Purposes***by*Martin Shubik**115R1 A Business Game for Teaching and Research Purposes***by*Martin Shubik**114 Output, Sales and Inventory Policy in the Competitive Firm and the Stability of a Competitive Market***by*Edwin S. Mills**113 Some Informal Comments on Models of Decision Processes Under Uncertainty***by*Martin Shubik**112 Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing***by*Martin Shubik**111 An Empirical Examination of a Commercial Bank Loan Offer Function***by*Donald D. Hester**110R An Analysis of the New View of Investment***by*Edmond S. Phelps**109 The Accumulation of Risky Capital: A Discrete-Time Sequential Utility Analysis***by*Edmond S. Phelps**108 Estimation in the Linear Decision Model***by*Walter D. Fisher**107 Extended Edgeworth Bargaining Games and Competitive Equilibrium***by*Martin Shubik**105 Some Experimental Non-Zero Sum Games With Lack of Information about the Rules***by*Martin Shubik**104 Objective Functions and Models of Corporate Optimization***by*Martin Shubik

### 1960

**99 An Objective Permanent Income Concept for the Household***by*Harold W. Watts**98 Inter-Generation Transfers of Wealth and the Theory of Saving***by*James Tobin & Harold W. Guthrie**97 Partial Trace Correlation Theory***by*John W. Hooper**96 Programming of Economic Development***by*Alan S. Manne**95 Product-Mix Alternatives: Flood Control, Electric Power, and Irrigation***by*Alan S. Manne**94 Corporation Dividend Payout Ratios and Target Ratios -- Their Significance and Determination***by*Guy Stevens**93 Demand for Tourists' Goods and Services in a World Market***by*Harold W. Guthrie**92 A New Technique in Equilibrium Analysis***by*Gerard Debreu**91 A Keynesian Model Extended by Explicit Demand and Supply Functions for Investment-Goods***by*Bjorn Thalberg**90R Forced Saving in a Keynesian Economy: An Analysis of Demand-Pull Inflation***by*Michael C. Lovell**88 A Model of Bank Portfolio Selection***by*Richard C. Porter**85R Investment, Replacement, and an Index of Technology***by*Benton F. Massell**106 Comparative Advantage and Development Policy***by*Hollis B. Chenery**103 Factors Affecting the Occupational Migration of Labor from Agriculture***by*Charles H. Berry**102 Patterns of United States Imports, 1947-1958***by*Lawrence B. Krause**101 Capital Risk and Household Consumption: A Sequential Utility Analysis***by*Edmond S. Phelps**100 Approaches to the Study of Decision-Making Relevant to the Firm***by*Martin Shubik

### 1959

**87 On the Appraisal of Cyclical Turning Point Predictors***by*Arthur M. Okun**86 Manufacturers' Inventories, Sales Expectations, and the Acceleration Principle***by*Michael C. Lovell**84 Comment on 'Interindustry Economics' by Chenery and Clark***by*Alan S. Manne**83 Analysis of a Production Problem by Dynamic Programming***by*Martin J. Beckmann**82 Theory of an Efficient Several-Person Firm***by*Jacob Marschak**81 Stationary Ordinal Utility and Impatience***by*Tjalling C. Koopmans**80 Lagrange Multipliers Revisited***by*Morton Slater**79 Some Examples of Global Instability of the Competitive Equilibrium***by*Herbert E. Scarf**78 Consumers' Propensities to Hold Liquid Assets***by*Harold W. Guthrie**77R The Error of Forecast for Multivariate Regression Models***by*John W. Hooper & Arnold Zellner**76 Topological Methods in Cardinal Utility Theory***by*Gerard Debreu**75 Some Team Models of a Sales Organization***by*C.B. McGuire**74 Binary Choice Constraints on Random Utility Indicators***by*Jacob Marschak**73 On the Job Shop Scheduling Problem***by*Alan S. Manne**72 On 'An Identity in Arithmetic'***by*Gerard Debreu**71 Comparisons of Information Structures***by*C.B. McGuire**70 Remarks on the Economics of Information***by*Jacob Marschak**69 Consumer Expenditures and the Capital Account***by*James Tobin & Harold W. Watts**68 A Dynamic Programming Model of the Consumption Function***by*Martin J. Beckmann**67 A Few Remarks on the Assortment Problem***by*Wieslaw Sadowski**66 Random Orderings and Stochastic Theories of Response***by*H.D. Block & Jacob Marschak**65 Efficient and Viable Organizational Forms***by*Jacob Marschak**64 A Capital-Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators***by*Robert Summers**62 Linear Programming and Sequential Decision Models***by*Alan S. Manne

### 1958

**61 Testing for Neutrality of Technological Change. (Is Technological Change Neutral?)***by*Sidney G. Winter**60 A Theory of Life Insurance Company Portfolio Selection***by*Leroy S. Wehrle**59e Economic Theory of Teams. Chapter 5***by*Jacob Marschak & Roy Radner**59c Economic Theory of Teams. Chapter 3***by*Jacob Marschak & Roy Radner

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