Table Of Content

MACRO-ECONOMIC THEORY A Mathematical Treatment Some Other ELBS Low-Priced Editions Allen MATHEMATICAL ANALYSIS FOR ECONOMISTS Macmillan Allen MATHEMATICAL ECONOMICS Macmillan Bridger and FAMINE IN RETREAT? Dent de Soissons Dasgupta and COST-BENEFIT ANALYSIS Macmillan Pearce Giles MARKETING Macdonald & Evans Hague MANAGERIAL ECONOMICS Longman Hanson A DICTIONARY OF ECONOMICS AND COMMERCE Macdonald & Evans Hanson MONETARY THEORY AND PRACTICE Macdonald & Evans Hanson TEXTBOOK OF ECONOMICS Macdonald & Evans Hicks VALUE AND CAPITAL Oxford University Press Lipsey AN INTRODUCTION TO POSITIVE ECONOMICS Weidenfeld Meade THE THEORY OF INTERNATIONAL Oxford ECONOMIC POLICY, Vols. I and II University Press Marshall PRINCIPLES OF ECONOMICS Macmillan Paish and Culyer BENHAM'S ECONOMICS Pitman Prest PUBLIC FINANCE IN THEORY AND PRACTICE Weidenfeld Robinson THE ACCUMULATION OF CAPITAL Macmillan Stafford MATHEMATICS FOR ECONOMISTS Macdonald & Evans Stillwell, Lipsey WORKBOOK TO ACCOMPANY THE and Clarke FOURTH EDITION OF 'AN INTRODUCTION TO POSITIVE ECONOMICS' Weidenfeld Stone and Stone NATIONAL INCOME AND EXPENDITURE Bowes & Bowes Stonier and Hague A TEXTBOOK OF ECONOMIC THEORY Longman Thirlwall GROWTH AND DEVELOPMENT Macmillan Second Edition MACRO-ECONOMIC THEORY A M athelnatical Treatnzent R.G.D.ALLEN [Jj[5J ~ Palgrave Macmillan © R. G. D. Allen 1967 All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. First edition 1967 Reprinted 1968, (with corrections) 1970, (with corrections) 1973 ELBS edition first published 1973 Reprinted 1975, 1979 Published by THE MACMILLAN PRESS LTD London and Basingstoke Associated companies in Delhi Dublin Hong Kong Johannesburg Lagos Melbourne New York Singapore and Tokyo ISBN 978-1-349-81543-2 ISBN 978-1-349-81541-8 (eBook) DOI 10.1007/978-1-349-81541-8 The paperback edition of this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or other wise circulated without the publishers' prior consent in any fonn of binding or cover other than that in which it is published and without a similar con dition including this condition being imposed on the subsequent purchaser. Contents Preface Me xi 1 Introduction 1.1 Macro-Economics 1 1.2 Stocks and Flows: Time Dimensions 2 1.3 Fonnulation of Models 4 1.4 Continuous versus Period Analysis 5 1.5 Necessary and Sufficient Conditions 7 1.6 Variables of the Models 10 1.7 Plan of Text 12 Exercises 14 THE TOOLS 2 Consumption and Saving Functions 2.1 The Circular Flow of Income 16 2.2 The Consumption Function 19 2.3 Lagged Consumption Functions 20 2.4 The Product Market: Flow Conditions 23 2.5 The Relation of Saving to Investment 24 2.6 The Multiplier 25 2.7 Particular Forms of the Saving Function 29 Exercises 31 3 The Technology of the Economy 3.1 Capital and Output-Capital Ratios 33 3.2 Fixed Coefficients 35 3.3 Linear Programming Fonn 37 3.4 Production Functions 41 3.5 Distribution of the Product 44- 3.6 Elasticity of Substitution between Factors 48 3.7 The Cobb-Douglas Production Function 49 3.8 The C.E.S. Production Function 52 Exercises 55 4 Investment Functions 4.1 Detenninants of Investment 57 4.2 The Rate of Return: Discounting 58 4.3 Varying Rates of Return 61 4.4 Investment and the Rate of Interest 62 4.5 D.C.F. versus Fixed Pay-off Period 66 4.6 Investment and Income 68 4.7 The Acceleration Principle 70 4.8 Investment and Profits 73 Exercises 75 vi CONTENTS 5 Economic Dynamics page 5.1 Statics and Dynamics 76 5.2 A Simple Illustration 79 5.3 Methods of Economic Dynamics 84 5.4 Lags: Period Analysis 86 5.5 Lags: Continuous Analysis 88 5.6 Error-Adjustment Conditions 94 5.7 Consumption and Investment Lags 95 5.8 Closed-Loop Systems: Block Diagrams 97 Exercises 100 SHORT-PERIOD EQUILIBRIUM: KEYNES AND THE CLASSICS 6 Classical Macro-Economic Theory 6.1 The Short-Period Problem 101 6.2 A Classical Model of Income and Employment 102 6.3 A Particular Case 105 6.4 Saving and Investment 106 6.5 The Marginal Efficiency of Investment 108 6.6 Diagrammatic Representation 109 Exercises 112 7 Keynesian Models 7.1 Income as the Central Variable 113 7.2 Simple Keynesian Model: the Multiplier 114 7.3 The Keynesian Theory of Income Determination 116 7.4 Diagrammatic Representation 120 7.5 The Labour Market 123 7.6 The Complete Keynesian Model 126 7.7 Unemployment 130 7.8 Keynes and the Classics 131 Exercises 134 8 Aggregate Demand 8.1 Government Expenditure and Taxation 136 8.2 Government: the Multiplier 138 8.3 Government: the IS and LM Schedules 140 8.4 Diagrammatic Representation 142 8.5 Taxes Varying with Income 145 8.6 Inflation 147 8.7 A Two-Sector Model 150 Exercises 154 9 The Dynamic Multiplier 9.1 Keynesian Dynamics 156 9.2 The Dynamic Multiplier: Period Analysis 157 9.3 Diagrammatic Representation 160 9.4 Variable Autonomous Investment 161 9.5 Continuous Analysis 163 9.6 Inventory Cycles 166 9.7 Fixed versus Working Capital 168 Exercises 172 CONTENTS vii LONG-PERIOD EQUILIBRIUM: GROWTH MODELS 10 Capital Accumulation page 10.1 Growth 174 10.2 Fixed Cofficients: Continuous Analysis 176 10.3 Autonomous Expenditure and the Stationary State 179 10.4 Fixed Cofficients: Period Analysis 181 10.5 Stability: the Knife-Edge Problem 184 10.6 Stability: Continuous Analysis 187 10.7 Stability: Period Analysis 190 10.8 The Parameters and their Values 192 Exercises 195 11 Simple Growth Models 11.1 Basic Harrod-Domar Model 197 11.2 Continuous Analysis: Fixed-Coefficients Version 198 11.3 Multiplier-Accelerator Version 201 11.4 Period Analysis 203 11.5 Variants of the Harrod-Domar Model 207 11.6 A Linear Programming Model 209 11. 7 Basic Neo-Classical Model 211 11.8 Basic Kaldor (Keynesian) Model 215 Exercises 218 12 Two-Sector Growth Models 12.1 Price Equations 220 12.2 Quantity Equations 223 12.3 Basic Two-Sector Model 224 12.4 Case: Classical Saving Function 227 12.5 Case: Proportional Saving Function 229 12.6 Stability 231 Exercises 234 13 Technical Progress 13.1 Various Forms of Technical Progress 236 13.2 Neutrality of Disembodied Technical Progress 237 13.3 Constant Returns 240 13.4 Case: Fixed Coefficients 245 13.5 Case: Cobb-Douglas Production Function 248 13.6 Non-Constant Returns 251 13.7 Technical Progress Functions 252 13.8 Embodied Technical Progress 254 Exercises 257 14 N eo-Classical Growth Models 14.1 The Neo-Classical Approach 259 14.2 A General Neo-Classical Model 260 14.3 Constant Returns 262 14.4 Diagrammatic Representation 264 14.5 Model with Differential Saving 266 14.6 Particular Production Functions 269 14.7 Stability 272 14.8 A Neo-Classical Two-Sector Model 274 Exercises 279 viii CONTENTS 15 Vintage Models page 15.1 Models with Embodied Technical Progress 281 15.2 Vintage Capital with Factor Substitution 283 15.3 The Aggregate Production Function 285 15.4 Vintage Model: Factor Substitution 286 15.5 The Capital Stock and its Valuation 290 15.6 Vintage Model: Fixed Labour Requirements 292 15.7 Obsolescence 294 15.8 Vintage Model: Fixed Coefficients 299 Exercises 303 16 Kaldor (Keynesian) Models 16.1 Development of the Basic Model 305 16.2 Kaldor's Non-Vintage Model 306 16.3 Steady-State Solution 307 16.4 Case: Classical Saving Function 311 16.5 Kaldor's Vintage Model 312 16.6 Steady-State Solution 314 16.7 Valuation of the Capital Stock 317 16.8 Summary 318 Exercises 319 MEDIUM-PERIOD DISEQUILIBRIUM: CYCLE MODELS 17 Multiplier-Accelerator Models 17.1 Disequilibrium Models 321 17.2 Formulation: Continuous Analysis 322 17.3 Parameters of Multiplier-Accelerator Models 324 17.4 Case: Investment Lag Only 325 17.5 Phillips' Model 328 17.6 Period Analysis 333 17.7 Samuelson-Hicks Model: Elementary Case 336 Exercises 340 18 Economic Regulation 18.1 Autonomous Expenditure 342 18.2 Intrinsic and Forced Oscillations 347 18.3 Stabilisation Policy 350 18.4 Stabilisation in the Multiplier Model 353 18.5 Stabilisation in the Multiplier-Accelerator Model 356 18.6 Solution by Laplace Transforms 357 18.7 Numerical Examples 359 Exercises 362 19 Trade-Cycle Theory 19.1 Oscillations and the Trade Cycle 364 19.2 Some Theory of the Trade Cycle 366 19.3 A Mixed Difference-Differential Model 369 19.4 Solution of the Model 372 19.5 A Non-Linear Accelerator 374 19.6 Goodwin's Non-Linear Model 378 Exercises 383 CONTENTS ix 20 Models of Cyclical Growth page 20.1 Cycles and Growth 385 20.2 Phillips'Model: Product Market 388 20.3 Product and Money Markets 391 20.4 Solution: Steady-State Growth 394 20.5 Cyclical Growth 397 20.6 Bergstrom's Model 400 20.7 Differential Equation of the Model 403 20.8 Solution: Growth and Cycles 405 Exercises 409 Exercises: Solutions 411 Index 416