Preference, Production and Capital: Selected Papers of Hirofumi Uzawa

Cover......Page 1
Frontmatter......Page 2
Contents......Page 6
Foreword......Page 12
Preface......Page 14
I - Preference and demand......Page 18
1. Introduction......Page 20
2. Demand functions......Page 23
3. Preference relations......Page 26
4. Preference relations generated by demand functions......Page 27
5. Equivalence of the Weak Axiom and the Strong Axiom......Page 35
6. Demand functions derived from preference relations......Page 37
7. The Slutsky equations and demand functions......Page 39
1. Introduction......Page 44
2. Notation and assumptions......Page 46
3. Necessary conditions for utility maximization......Page 48
4. Sufficient conditions for utility maximization......Page 53
5. An invariance property of the utility functions......Page 61
6. Monotonicity and convexity......Page 62
7. Upper semicontinuity of the utility function Up*(·)......Page 63
8. Lower semicontinuity of the utility function Up*(·)......Page 64
9. An example......Page 69
Appendix......Page 73
1. Introduction......Page 82
2. Time preference......Page 83
3. Optimum savings and consumption schedule......Page 86
4. Solution of the optimum problem......Page 87
5. The long-run consumption function c*(r)......Page 91
6. The short-run consumption function c(y, r)......Page 93
7. Demand for money and other assets......Page 95
II - Duality and production......Page 102
2. The structure of cost functions......Page 104
3. The structure of production......Page 106
1. The Arrow-Chenery-Minhas-Solow production function......Page 109
2. Allen's elasticities of substitution......Page 110
3. A generalization of the Arrow-Chenery-Minhas-Solow production function......Page 112
4. Characterization of production functions with constant elasticities of substitution......Page 115
1. Introduction......Page 119
2. Neutral inventions in Harrod's sense......Page 120
3. Joan Robinson's theorem on neutral inventions......Page 121
4. Stability of the neoclassical growth equilibrium......Page 124
1. A model of endogenous technical change......Page 129
2. Optimum technical change......Page 131
3. Solving the optimum problem......Page 132
III - Concave programming......Page 144
1. Introduction......Page 146
2. Maximum problem and saddle-point problem......Page 147
4. The Kuhn-Tucker Theorem......Page 148
5. A modification of the Kuhn-Tucker Theorem......Page 150
2. Concave programming and saddle-point problem......Page 152
3. The Arrow-Hurwicz gradient method......Page 153
4. A modified Arrow-Hurwicz gradient method......Page 156
5. Concave programming with linear restrictions......Page 159
6. Linear programming......Page 163
1. Introduction......Page 166
2. A model of general equilibrium: one country......Page 169
3. Imputation to the factors of production......Page 172
4. A model of general equilibrium: many countries......Page 177
5. Welfare criteria for factor price equalization......Page 180
6. Partial equalization (linear excess demand)......Page 185
IV - Equilibrium and stability......Page 190
2. Walras's Existence Theorem......Page 192
4. Equivalence theorem......Page 193
1. Introduction......Page 196
2. Transaction rules......Page 197
3. Edgeworth's barter process......Page 201
4. A continuous barter process......Page 204
V - Theory of economic growth......Page 212
1. Introduction......Page 214
3. A two-sector model......Page 215
4. Growth process in the two-sector model......Page 217
5. Capital-intensity hypothesis and the stability of growth equilibrium......Page 218
6. Concluding remarks......Page 220
1. Introduction......Page 223
2. A neoclassical model of economic growth......Page 224
3. The determination of short-run equilibrium......Page 226
4. The determination of long-run equilibrium......Page 230
5. The propensity to save and the inducement to invest......Page 233
6. Inflexibility of factor prices and "involuntary" unemployment......Page 236
1. Introduction......Page 240
2. Intertemporal utility and the rate of time preference......Page 242
3. Time preference and the optimum propensity to save......Page 246
4. Concept of real capital, the production function, and the Penrose curve......Page 250
5. Investment function and marginal efficiency of investment......Page 254
6. An aggregate model of economic growth......Page 257
7. Analysis of the growth equilibrium......Page 260
8. Concluding remarks......Page 265
2. Basic assumptions of the neoclassical growth theory......Page 266
3. Dynamic equilibrium of the neoclassical model......Page 271
4. The neoclassical theory of monetary growth......Page 272
5. A Keynesian theory of economic growth......Page 280
6. Keynesian growth under full employment......Page 291
7. Concluding remarks......Page 295
VI - Optimum growth......Page 298
1. Introduction......Page 300
2. A two-sector model of capital accumulation......Page 301
3. Optimal growth in the two-sector model......Page 304
4. Reduction of optimality conditions......Page 307
5. The case when consumption goods are always more capital-intensive than capital goods......Page 309
6. The case when capital goods are always more capital-intensive than consumption goods......Page 318
8. Summary......Page 324
1. Introduction......Page 330
2. The model......Page 332
3. Analysis of the short-run equilibrium......Page 337
4. Constant average propensity to consume and the quantity theory of money......Page 344
5. Optimum fiscal policies......Page 345
6. Optimum economic growth......Page 346
1. Introduction......Page 357
2. The description of a national economy......Page 358
3. Social overhead capital as a factor of production......Page 359
4. Market allocation......Page 361
5. Pricing of social overhead capital......Page 363
6. Optimum allocation......Page 366
7. The presence of consumers......Page 367
8. Optimum conditions from a dynamic point of view......Page 370
9. Optimum investment in private and social capital -- the simplest case......Page 375
10. Concluding remarks......Page 378
Index......Page 380