ISBN: 3790814237
TITLE: Contributions to Economics
AUTHOR: Coto-Millan
TOC:

Introduction 1
PART I: UTILITY AND CONSUMER DEMAND ANALYSIS 5
1 Theory of Utility and Consumer Behaviour: A Comprehensive Review of Concepts, Properties and the Most Significant Theorems 7
1.1 Theory of Utility 7
1.2 Preference, Choice and Indifference Concept and Utility Function Existence 8
1.3 Properties of the Utility Function 10
1.3.1 Additivity 10
1.3.2 Homogeneity 10
1.3.3 Homotheticity 10
1.3.4 Weak and Strong Separability 11
1.4 Basic Theory (Primal): Marshallian (or Walrasian) Demand Functions 11
1.4.1 Properties of the Marshallian (or Walrasian) Demand Functions 12
1.5 Consumer Equilibrium (Dual): Hicksian (or Compensated) Demand Functions 12
1.5.1 Properties of the Hicksian (or Compensated) Demand Functions 13
1.6 Indirect Utility Function 13
1.7 Expenditure Function 14
1.8 Restrictions of the Demand Systems 14
1.8.1 Engel Aggregation Condition 14
1.8.2 Cournot Aggregation Condition 15
1.8.3 Homogeneity Condition 16
1.8.4 Symmetry or Integrability Condition 16
1.8.5 Negativity Condition 16
1.9 Roy's Identity 17
1.10 Hotelling's Theorem (or Shephard's Lemma for Consumers) 19
1.11 Relationships between the UMP and the EMP 19
1.12 The Slutsky Equation 20
1.13 Complementary and Substitutive Relationships 21
Basic References 23
References and Further Reading 23
2 Alternative Theories of Consumer Behaviour 25
2.1 Introduction 25
2.2 Discrete Choice Models 25
2.3 Time Allocation Models 27
2.3.1 Hicks Model 27
2.3.2 Yield-Leisure Model 28
2.3.3 Extended Yield-Leisure Model 30
2.3.4 Goods-Leisure Model with Time Allocation to Goods Consumption 32
2.3.4.1 Becker's Model 32
2.4 Train-McFadden Synthesis Model 33
2.5 Lancaster's Consumption Technology Model 35
2.6 Jara-Daz Model 37
2.6.1 Jara-Daz and Farah Model (1987) 37
2.6.2 Jara-Daz Model (1998) 39
2.7 Models of Consumer Behaviour with Incomplete Information 42
2.8 Revealed Preference Theory 44
References 46
3 Main Forms of Utility Functions 49
3.1 The Cobb-Douglas Utility Function 49
3.1.1 Properties 49
3.1.2 Marshallian or Ordinary Demands (Primal) 51
3.1.3 The Indirect Utility Function 52
3.1.4 Hicksian or Compensated Demands (Dual) 53
3.1.5 The Expenditure Function 54
3.1.6 Elasticities, Engel Curves and Expenditure Share Functions 55
3.2 The Utility Function of the Constant Elasticity of Substitution (CES) 57
3.2.1 Marshallian Demands 57
3.2.2 The Indirect Utility Function 59
3.2.3 Hicksian Demands 60
3.2.4 The Expenditure Function 60
3.2.5 Application to the Particular CES Utility Function 61
3.2.5.1 The Indirect Utility Function 61
3.2.5.2 The Expenditure Function 61
3.2.5.3 Hicksian Demands 61
3.2.5.4 The Own, Cross and Income Elasticity of the CES Demand System 61
3.2.5.5 Restrictions of CES Demand Systems 62
3.3 The Quasi-linear Utility Functions 64
3.3.1 Marshallian Demands 64
3.3.2 The Indirect Utility Function 65
3.3.3 The Expenditure Function 66
3.3.4 Roy's Identity 66
3.3.5 Hotelling's Theorem: Hicksian Demand Functions 66
3.3.6 Application to the Particular Quasi-linear Utility Function 67
3.3.6.1 The Marshallian Demand 67
3.3.6.2 Restrictions of the Quasi-linear Demand System 67
Recommended Reading 69
4 Study of the Econometric Applications: Demand Functions and Systems 71
4.1 Demand Functions 71
4.2 Application I for Demand Functions: Walrasian (or Marshallian) Demand Functions for Interurban Passenger Transport 72
4.2.1 Model 73
4.2.2 Data 74
4.2.3 Walrasian (or Marshallian) Demands for Interurban Passenger Transport: Air and Road Transport 75
4.2.3.1 Air Transport Demand 75
4.2.3.2 Road Transport Demand 76
4.2.4 Results of the Empirical Research 78
4.3 Complete Demand Systems 78
4.3.1 Linear Expenditure System (LES) 79
4.3.2 Almost Ideal Demand System 80
4.3.3 Diewert Demand Model 81
4.3.4 Translog Demand Model 82
4.4 Application II for Demand Systems: Estimation of an Almost Ideal Demand System (AIDS): Particular Disaggregation for the Main Transport Services 83
4.4.1 Model: Almost Ideal Demand System 83
4.4.2 Data 85
4.4.3 Estimation of the Model 85
4.4.4 Conclusions 87
Basic References 88
References and Further Reading 88
PART II: Production and Firm Supply Analysis 91
5 Theory of Production, Cost and Behaviour of the Firm: A Comprehensive Reformulation 93
5.1 Theory of the Firm 94
5.2 Production Possibility Set and Existence of Production Function 96
5.3 Properties of Production Function 97
5.3.1 Efficiency 98
5.3.2 Differentiability and Continuity 98
5.3.3 Strict Quasi-concavity 98
5.4 The Firm's Equilibrium: Classic Demand, Profit and Direct Supply Functions 98
5.4.1 Profit Maximisation 98
5.4.2 Properties of Input Classic Demand and Output Direct Supply Functions 99
5.4.2.1 Decreasing 100
5.4.2.2 Existence 100
5.4.2.3 Homogeneity 100
5.4.2.4 Symmetry 100
5.4.2.5 Negativity 100
5.4.2.6 Negative Semi-definite 100
5.4.3 Profit Function 100
5.4.4 Properties of the Profit Function: Hotelling's Theorem 101
5.4.4.1 Non-decreasing 101
5.4.4.2 Homogeneity 101
5.4.4.3 Convexity 101
5.4.4.4 Continuity 101
5.4.4.5 Hotelling's Theorem 101
5.5 The Firm's Equilibrium (Primal A) 102
5.6 The Firm's Equilibrium (Primal B): Marshallian Demand and Indirect Supply Functions 103
5.6.1 Output Maximisation 103
5.6.2 Properties of the Input Marshallian Demand and Indirect Supply Functions 104
5.6.2.1 Decreasing 104
5.6.2.2 Existence 104
5.6.2.3 The Lagrange Coefficient (lambda) 104
5.6.2.4 Homogeneity 105
5.6.2.5 Negativity 105
5.6.2.6 Symmetry 105
5.6.2.7 Negative Semi-definite 105
5.6.2.8 Roy's Identity 105
5.7 The Firm's Equilibrium: Input Classic Demand and Output Direct Supply Functions 105
5.7.1 Loss Minimisation 106
5.7.2 Properties of Input Classic Demand and Output Direct Supply Functions 106
5.7.3 Loss and Input Classic Demand Functions: Hotelling's Theorem 106
5.8 The Firm's Equilibrium (Dual A) 107
5.9 The Firm's Equilibrium (Dual B): Input Conditioned Demand and Cost Functions 107
5.9.1 Cost Minimisation 108
5.9.2 Properties of the Input Conditioned Demand 108
5.9.2.1 Non-decreasing 108
5.9.2.2 Existence 108
5.9.2.3 Homogeneity 109
5.9.2.4 The Lagrange Coefficient (mu) 109
5.9.2.5 Negativity 109
5.9.2.6 Symmetry 109
5.9.2.7 Negative Semi-definite 109
5.9.3 Properties of Cost Function: Shephard's Lemma 109
5.9.3.1 Increase 109
5.9.3.2 Homogeneity 110
5.9.3.3 Concavity 110
5.9.3.4 Continuity 110
5.9.3.5 Shephard's Lemma 110
5.10 Diagrammatic Representation of the Main Relationships 111
5.11 Joint Production 115
5.11.1 Income Maximisation 118
5.11.2 Input Minimisation 119
5.12 Short-Run 120
5.12.1 Short-Run and Single Production 122
5.12.2 Short-Run and Joint Production 124
5.13 Reflections on the Main Relationships Designed 125
5.14 The Elasticity of Substitution 126
Basic References 128
References and Further Reading 129
6 Alternative Theories on Companies 131
6.1 Baumol's Sales Income Maximisation Model 131
6.2 Marri's Production Volume Maximisation Model 134
6.3 Cooperative Company Model 136
6.4 Behavioural Models of the Company 140
6.5 Company Models Based on Transaction Cost Economy 140
References 143
7 Main Forms of Production and Cost Functions 145
7.1 The Cobb-Douglas Production Function 145
7.1.1 Characterisation 145
7.1.2 The Marginal Rate of Technical Substitution (MRTS) 146
7.1.3 The Elasticity of Substitution 146
7.1.4 Returns to Scale 147
7.1.5 The Profit Function and Input Demand Functions 147
7.1.6 Hotelling's Theorem 150
7.1.7 The Cost Function and Input Conditioned Demand Functions 151
7.1.8 Shephard's Lemma 153
7.1.9 LRYC and LRMC Curves 154
7.1.10 Applying the Duality 155
7.2 The CES Production Function 157
7.2.1 The Marginal Rate of Technical Substitution (MRTS) 157
7.2.2 Returns to Scale 158
7.2.3 The Elasticity of Substitution 158
7.2.4 The Output Supply Function and Input Demand Functions 159
7.2.5 The Cost Function and Input Conditioned Demand Functions 162
7.2.6 The LRAC and LRMC 164
7.2.7 Applying the Duality 165
Recommended Reading 168
8 Study on Econometric Applications: Production and Cost Functions 169
8.1 Production Functions 170
8.2 Application III for Production Functions: Analysis of the Returns to Scale, Elasticities of Substitution and Behaviour of Shipping Production 171
8.2.1 The Model 171
8.2.2 Data 173
8.2.3 Empirical Results 173
8.3 Cost Function 175
8.4 Other Empirical Functions 176
8.5 Application IV for Cost Functions: Elasticities of Substitution and Behaviour of Shipping Costs 178
8.5.1 Model 178
8.5.2 Data 181
8.5.3 Empirical Results 181
8.5.4 Summary and Conclusions 184
Basic References 185
References and Further Reading 185
PART III: UNCERTAINTY 189
9 Utility, Production and Uncertainty 191
9.1 Introduction 191
9.2 First Stage in the Development of Utility Theory Under Conditions of Uncertainty: the Principle of Expected Value 191
9.3 Second Stage in the Development of Utility Theory Under Conditions of Uncertainty: the Principle of Expected Utility 192
9.4 Third Stage in the Development of Utility Theory Under Conditions of Uncertainty: Von Neumann-Morgenstern Utility Function 193
9.5 Individuals' Attitudes to Risk 195
9.6 Production and Uncertainty 196
9.7 Critiques of the Theory of Expected Utility and the Theory of Limited Rationality 197
9.7.1 Violation of the Axiom of Independence 197
9.7.2 Violation of the Transitivity Axiom 201
References 202
END
