Ⅰ MATHEMATICS IN THE SOCIAL SCIENCES 1
1.INTRODUCTION 1
2.STRUCTURE AND CHANGE 3
a.Births and survivals 3
b.Marriage and descent 6
c.Class structure and social mobility 7
d.Group interaction 8
e.Social accounting 9
f.The national accounts and a model of pro-duction growth 10
g.Industrial inputs and outputs 12
h.Education and training 13
i.Teachers and graduates 14
3.DECISIONS 16
a.Single-stage decisions under certainty 17
b.Multi-stage decisions under certainty 21
c.Decisions under uncertainty 23
4.SYSTEMS ANALYSIS 28
Ⅱ THE A PRIORI AND THE EMPIRICAL IN ECONOMICS 36
1.INTRODUCTION 36
2.THE A PRIORI AND THE EMPIRICAL 37
3.DEMAND THEORY AND CONSUMERS BEHAVIOUR 40
4.IDENTIFICATION AND SIMULTANEOUS RELATIONSHIPS 50
5.INFINITE HORIZONS AND THE PROBLEM OF PLANNING 57
6.CONCLUSION 62
Ⅲ THE HOUSEKEEPER AND THE STEERSMAN 63
1.SUBCONSCIOUS CYBERNETICS 63
a.Equilibrium in isolated markets 67
2.CONSCIOUS CYBERNETICS 67
b.Macro-dynamic models 69
c.Economic control 71
3.CYBERNETICS IN ECONOMIC ANALYSIS AND POLICY 73
a.Economic planning 74
b.Shadow prices 75
c.Computers 76
d.The human element 76
4.CONCLUSION 77
Ⅳ MISERY AND BLISS 79
1.INTRODUCTION 79
2.POSITIVE THEORY 84
b.The production function 85
a.The accounting identities 85
c.The maintenance of assets per head with steady growth of population 87
d.The saving function 88
e.The influence of the standard of living on population growth 89
f.A summary and interpretation of the positive theory 89
3.NORMATIVE THEORY 92
4.POLICY PRESCRIPTION 96
a.Ramsey s saving principle 97
b.A saving principle for a growing economy 101
c.Foreign aid and domestic saving 103
5.CONCLUSIONS 104
Ⅴ THREE MODELS OF ECONOMIC GROWTH 106
1.INTRODUCTION 106
2.THE MULTIPLIER-ACCELERATOR MODEL 108
3.A TWO-SECTOR MODEL FOR INVESTMENT PLANNING 110
4.AN OPTIMIZING ALLOCATION MODEL 112
5.SOME COMMENTS ON THE OPTIMIZING MODEL 121
6.CONCLUSIONS 124
Ⅵ MODELS OF THE NATIONAL ECONOMY FOR PLANNING PURPOSES 127
1.INTRODUCTION 127
2.A SLICE OF LIFE 128
3.OPERATIONAL RESEARCH AND MODELS OF THE NATIONAL ECONOMY 137
a.Taxonomy 138
b.Basic data 138
c.Relationships 139
d.Reviewing results 140
e.Linking models 141
4.CONCLUSIONS 142
1.INTRODUCTION 144
Ⅶ A DEMONSTRATION MODEL OF ECO-NOMIC GROWTH 144
2.THE CONSUMPTION FUNCTIONS 145
3.CURRENT OUTPUT REQUIREMENTS FOR GROWTH IN CONSUMPTION 149
4.THE PRODUCTION FUNCTIONS 151
5.THE DETERMINATION OF PRICES 153
6.THE SOLUTION OF THE MODEL 153
7.THE DETERMINATION OF PARAMETERS AND INITIAL VALUES 154
8.SOME REALISTIC COMPLICATIONS 157
9.THE MODEL AND ITS PURPOSE 159
Ⅷ TRANSITIONAL PLANNING 163
1.INTRODUCTION 163
2.ASSUMPTIONS 166
3.CONSTRAINTS 169
4.A MAXIMAND 171
5.A LINEAR PROGRAMME 172
6.SOME RELAXATIONS 174
a.The parameters，b and c，of the consum-ption functions 174
b.The replacement of capital goods 175
c.The matrix，A，of current input-output coefficients 175
d.The matrix，K，of capital input-output coefficients 178
e.Differences in investment lags 179
f.Changes in the productivity of labour，f 183
g.Foreign trade 184
h.Future shadow prices 186
7.CONCLUSION 190
Ⅸ A MODEL OF THE EDUCATIONAL SYSTEM 192
1.INTRODUCTION 192
2.THE STRUCTURE OF EDUCATIONAL PROCESSES 196
3.BIRTHS AND SURVIVALS 203
4.THE DEMAND FOR PLACES 206
5.THE INFLUENCE OF ECONOMIC PROSPECTS 210
6.ECONOMIC INPUTS INTO EDUCATION 213
7.TECHNOLOGIAL CHANGE IN EDUCATION 215
8.THE SUPPLY OF ECONOMIC INPUTS 215
9.THE NEXT STEPS 217
Ⅹ SOCIAL ACCOUNTS AT THE REGIONAL LEVEL:A SURVEY 219
1.INTRODUCTION 219
2.SINGLE INDICATORS FOR EACH REGION 223
3.REGIONAL ACCOUNTS 227
4.DIRECT AND INDIRECT ESTIMATION AND THE ADJUSTMENT OF OBSERVATIONS 236
5.FURTHER USES FOR THE ALL REGIONS ACCOUNTS 240
6.A NUMERICAL EXAMPLE OF REGIONAL ACCOUNTING 242
7.PRICE AND QUANTITY COMPARISONS BETWEEN REGIONS 252
8.STRUCTURAL ANALYSIS OF REGIONS 255
9.PARTIAL ANALYSIS WITH REGIONAL DATA 259
10.NATIONAL ACCOUNTING MODELS WITH REGIONAL DATA 261
11.EXTENDED ACCOUNTING MODELS:REGIONAL INPUT-OUTPUT 263
12.A CENTRALLY CONNECTED REGIONAL MODEL 265
13.VARIABLE COST STRUCTURES AND BILATERALLY FIXED TRADING PATTERNS 266
14.LOCAL AND REGIONAL INPUT-OUTPUT STUDIES 269
15.FURTHER DEVELOPMENTS AND CONCLUSIONS 273
APPENDIX:BRIEF NOTES ON THE CONSTRUCTION OF TABLE 10 277
Ⅺ A COMPARISON OF THE ECONOMIC STRUCTURE OF REGIONS BASED ON THE CONCEPT OF‘DISTANCE’ 282
1.INTRODUCTION 282
2.THE PROBLEM 283
3.THE DATA 285
4.THE METHOD 285
5.DISTANCE AND FACTORS 290
6.APPLICATIONS 293
7.CONCLUSIONS 310
Ⅻ POPULATION MATHEMATICS，DEMAND ANALYSIS AND INVESTMENT PLANNING 313
1.INTRODUCTION 313
2.THE SIMPLEST CASE:FUTURE DEMAND CONSTANT 314
3.THE SECOND CASE:EXPONENTIAL GROWTH OF FUTURE DEMAND 317
4.THE THIRD CASE:SATURATION IN THE GROWTH OF FUTURE DEMAND 319
5.A SUMMARY OF THE TRANSITION MATRICES 321
6.TRANSITION MATRICES AND DEMAND ANALYSIS 322
7.A RELAXATION OF THE ASSUMPTIONS 324
1.INTRODUCTION 326
ⅩⅢ A DYNAMIC MODEL OF DEMAND 326
2.A DYNAMIC MODEL OF THE DEMAND FOR A DURABLE GOOD 328
3.GENERALIZATIONS 333
a.The case of perishable goods 333
b.Time lags in the determining variables 333
c.A variable rate of adjustment 334
d.Allowance for scrapping 335
e.A system of demand relationships 337
f.The aggregate consumption function 337
g.A generalization of the input-output model of Leontief 338
4.CALCULATIONS 338
a.The calculation of stocks from past purchases 338
b.The relationship of m to n 339
e.The combination of data with different time units 340
c.The time taken for a good to depreciate through use to 10 per cent of its original amount 340
d.Internal estimates of 1/n 340
5.APPLICATIONS 341
a.Analyses for individual groups of durable goods 341
b.Comparison of pre-war and post-war de-mand structures 343
c.Dynamic systems of demand relationships 343
6.SUMMARY AND CONCLUSIONS 344
ⅩⅣ THE CHANGING PATTERN OF CONSUMP-TION 346
1.INTRODUCTION 346
2.THE ECONOMICS OF THE SYSTEM 347
3.THE STATISTICS OF THE SYSTEM 352
a.The computing sequence 352
b.The analysis of subgroups 354
c.Cross-section data and time series 356
4.SOME RESULTS OF THE MODEL 358
5.CONCLUSIONS 367
ⅩⅤ PRIVATE SAVING IN BRITAIN，PAST，PRESENT AND FUTURE 369
1.INTRODUCTION 369
2.A MODEL OF SAVING 370
3.ANNUAL MODELS OF PERSONAL SAVING 373
4.A QUARTERLY MODEL OF PERSONAL GROSS SAVING 379
5.SHORT-TERM FORECASTS OF PERSONAL GROSS SAVING 382
a.The 1962 prediction 382
b.A prediction for 1964 383
6.ANNUAL MODELS OF COMPANY SAVING 384
a.All companies 385
b.Quoted companies in manufacturing and distribution 386
7.RATIONS AND STEADY GROWTH 388
8.CONCLUSIONS 394
APPENDIX Ⅰ:THE MATHEMATICAL MODEL 396
a.The basic model 397
b.Non-homogeneity 399
c.Exogenous influences 399
d.The subdivision of income 400
e.Time units 401
f.Statistical methods 402
g.Steady-state ratios 402
APPENDIX Ⅱ:THE STATISTICAL DATA AND RESULTS 404
ⅩⅥ MULTIPLE CLASSIFICATIONS IN SOCIAL ACCOUNTING 411
1.INTRODUCTION 411
2.CRITERIA OF CLASSIFICATION FOR A PROPER SOLUTION 413
3.A SIMPLE EXAMPLE:INDUSTRIES AND COMMODITIES 418
4.A SECOND EXAMPLE:A CLASSIFICATION CONVERTER FOR FINANCIAL FLOWS 421
5.REAL-FINANCIAL CONVERTERS 423
6.A NUMERICAL EXAMPLE:THE ACCOUNTING FRAME-WORK OF THE CAMBRIDGE GROWTH MODEL 423
7.CONCLUSIONS 428
APPENDIX:FURTHER DETAILS OF THE ACCOUNTING FRAMEWORK OF THE CAMBRIDGE GROWTH MODEL 431
1.A LIST OF ACCOUNTS 431
2.THE ENTRIES IN THE ACCOUNTS 435
3.A PROVISIONAL TABLE FOR 1959 447
ⅩⅦ BRITISH ECONOMIC BALANCES IN 1970:A TRIAL RUN ON ROCKET 448
1.INTRODUCTION 448
2.THE FRAMEWORK OF THE MODEL 451
a.Private consumption 459
3.EXOGENOUS FINAL DEMANDS 463
b.Government consumption 472
c.Industrial replacements 473
d.Consumers durables and dwellings 474
e.Social capital 475
f.Exports 475
g.Total exogenous final demand and its rate of change 475
4.ENDOGENOUS DEMANDS AND COMMODITY BALANCES 477
5.INDUSTRY BALANCES 482
6.BALANCES FOR INDUSTRIAL FIXED ASSETS 489
7.FOREIGN TRADE BALANCES 495
8.FINANCIAL BALANCES 502
9.THE END OF THE BEGINNING 507
10.THE NEXT STAGE 508
11.CONCLUSION 511
A LIST OF WORKS CITED 512