Utility and Production

This book is different from the first edition. There are three entirely new chapters: 2,6 and 9. I have also included new sections in chapters 1,4 and 8. Moreover, the remaining chapters, 3, 5 and 7, have been revised and updated. In chapters 2 and 6 I felt it was necessary to include the main alternative theories ofconsumer and company behaviour along with the neo-classical models. The book contains four chapters oftheory - 1, 2, 5 and 6 - and four chapters with theoretical and empirical applications - 3, 4, 7 and 8. Finally, chapter nine looks at choices made under conditions ofuncertainty. September 2002 P. Coto-Millan Preface to the First Edition Grateful acknowledgment is made to CICYT (Comision Interministerial de Ciencia y Tecnologia), National Plan R+D, Projects N-TXT96-2467 and N­ TXT98-1453 for its fmancial support. This text presents the economic theories on Utility and Production. In addition, such theories are used to explain the real problems of consumers and fIrms and several studies carried out by the author are displayed. Some collaboration by other professors of Economics is mentioned in the corresponding footnotes. The responsibility for errors and omissions, however, rests entirely upon the author. In chapters 1 and 4 of the book I try to present the theory of Utility and Production. Chapter 3 presents new functional forms and two empirical applications, on demand functions and systems. In chapters 2 and 5, the main theorems and properties presented in chapters 1 and 4 are applied.

Inhalt

I: Utility and Consumer Demand Analysis.- 1 Theory of Utility and Consumer Behaviour: A Comprehensive Review of Concepts, Properties and the Most Significant Theorems.- 1.1 Theory of Utility.- 1.2 Preference, Choice and Indifference Concept and Utility Function Existence.- 1.3 Properties of the Utility Function.- 1.3.1 Additivity.- 1.3.2 Homogeneity.- 1.3.3 Homotheticity.- 1.3.4 Weak and Strong Separability.- 1.4 Basic Theory (Primal). Marshallian (or Walrasian) Demand Functions.- 1.4.1 Properties of the Marshallian (or Walrasian) Demand Functions.- 1.5 Consumer Equilibrium (Dual): Hicksian (or Compensated) Demand Functions.- 1.5.1 Properties of the Hicksian (or Compensated) Demand Functions.- 1.6 Indirect Utility Function.- 1.7 Expenditure Function.- 1.8 Restrictions of the Demand Systems.- 1.8.1 Engel Aggregation Condition.- 1.8.2 Cournot Aggregation Condition.- 1.8.3 Homogeneity Condition.- 1.8.4 Symmetry or Integrability Condition.- 1.8.5 Negativity Condition.- 1.9 Roy's Identity.- 1.10 Hotelling's Theorem (or Shephard's Lemma for Consumers).- 1.11 Relationships between the UMP and the EMP.- 1.12 The Slutsky Equation.- 1.13 Complementary and Substitutive Relationships.- Basic References.- References and Further Reading.- 2 Alternative Theories of Consumer Behaviour.- 2.1 Introduction.- 2.2 Discrete Choice Models.- 2.3 Time Allocation Models.- 2.3.1 Hicks Model.- 2.3.2 Yield-Leisure Model.- 2.3.3 Extended Yield-Leisure Model.- 2.3.4 Goods-Leisure Model with Time Allocation to Goods Consumption.- 2.3.4.1 Becker's Model.- 2.4 Train-McFadden Synthesis Model.- 2.5 Lancaster's Consumption Technology Model.- 2.6 Jara-Díaz Model.- 2.6.1 Jara-Díaz and Farah Model (1987).- 2.6.2 Jara-Díaz Model (1998).- 2.7 Models of Consumer Behaviour with Incomplete Information.- 2.8 Revealed Preference Theory.- References.- 3 Main Forms of Utility Functions.- 3.1 The Cobb-Douglas Utility Function.- 3.1.1 Properties.- 3.1.2 Marshallian or Ordinary Demands (Primal).- 3.1.3 The Indirect Utility Function.- 3.1.4 Hicksian or Compensated Demands (Dual).- 3.1.5 The Expenditure Function.- 3.1.6 Elasticities, Engel Curves and Expenditure Share Functions.- 3.2 The Utility Function of the Constant Elasticity of Substitution (CES).- 3.2.1 Marshallian Demands.- 3.2.2 The Indirect Utility Function.- 3.2.3 Hicksian Demands.- 3.2.4 The Expenditure Function.- 3.2.5 Application to the Particular CES Utility Function.- 3.2.5.1 The Indirect Utility Function.- 3.2.5.2 The Expenditure Function.- 3.2.5.3 Hicksian Demands.- 3.2.5.4 The Own, Cross and Income Elasticity of the CES Demand System.- 3.2.5.5 Restrictions of CES Demand Systems.- 3.3 The Quasi-linear Utility Functions.- 3.3.1 Marshallian Demands.- 3.3.2 The Indirect Utility Function.- 3.3.3 The Expenditure Function.- 3.3.4 Roy's Identity.- 3.3.5 Hotelling's Theorem: Hicksian Demand Functions.- 3.3.6 Application to the Particular Quasi-linear Utility Function.- 3.3.6.1 The Marshallian Demand.- 3.3.6.2 Restrictions of the Quasi-linear Demand System.- Recommended Reading.- 4 Study of the Econometric Applications: Demand Functions and Systems.- 4.1 Demand Functions.- 4.2 Application I for Demand Functions: Walrasian (or Marshallian) Demand Functions for Interurban Passenger Transport.- 4.2.1 Model.- 4.2.2 Data.- 4.2.3 Walrasian (or Marshallian) Demands for Interurban Passenger Transport: Air and Road Transport.- 4.2.3.1 Air Transport Demand.- 4.2.3.2 Road Transport Demand.- 4.2.4 Results of the Empirical Research.- 4.3 Complete Demand Systems.- 4.3.1 Linear Expenditure System (LES).- 4.3.2 Almost Ideal Demand System.- 4.3.3 Diewert Demand Model.- 4.3.4 Translog Demand Model.- 4.4 Application II for Demand Systems: Estimation of an Almost Ideal Demand System (AIDS): Particular Disaggregation for the Main Transport Services.- 4.4.1 Model: Almost Ideal Demand System.- 4.4.2 Data.- 4.4.3 Estimation of the Model.- 4.4.4 Conclusions.- Basic References.- References and Further Reading.- II: Production and Firm Supply Analysis.- 5 Theory of Production, Cost and Behaviour of the Firm: A Comprehensive Reformulation.- 5.1 Theory of the Firm.- 5.2 Production Possibility Set and Existence of Production Function.- 5.3 Properties of Production Function.- 5.3.1 Efficiency.- 5.3.2 Differentiability and Continuity.- 5.3.3 Strict Quasi-concavity.- 5.4 The Firm's Equilibrium: Classic Demand, Profit and Direct Supply Functions.- 5.4.1 Profit Maximisation.- 5.4.2 Properties of Input Classic Demand and Output Direct Supply Functions.- 5.4.2.1 Decreasing.- 5.4.2.2 Existence.- 5.4.2.3 Homogeneity.- 5.4.2.4 Symmetry.- 5.4.2.5 Negativity.- 5.4.2.6 Negative Semi-definite.- 5.4.3 Profit Function.- 5.4.4 Properties of the Profit Function: Hotelling's Theorem.- 5.4.4.1 Non-decreasing.- 5.4.4.2 Homogeneity.- 5.4.4.3 Convexity.- 5.4.4.4 Continuity.- 5.4.4.5 Hotelling's Theorem.- 5.5 The Firm's Equilibrium (Primal A).- 5.6 The Firm's Equilibrium (Primal B): Marshallian Demand and Indirect Supply Functions.- 5.6.1 Output Maximisation.- 5.6.2 Properties of the Input Marshallian Demand and Indirect Supply Functions.- 5.6.2.1 Decreasing.- 5.6.2.2 Existence.- 5.6.2.3 The Lagrange Coefficient P).- 5.6.2.4 Homogeneity.- 5.6.2.5 Negativity.- 5.6.2.6 Symmetry.- 5.6.2.7 Negative Semi-definite.- 5.6.2.8 Roy's Identity.- 5.7 The Firm's Equilibrium: Input Classic Demand and Output Direct Supply Functions.- 5.7.1 Loss Minimisation.- 5.7.2 Properties of Input Classic Demand and Output Direct Supply Functions.- 5.7.3 Loss and Input Classic Demand Functions: Hotelling's Theorem.- 5.8 The Firm's Equilibrium (Dual A).- 5.9 The Firm's Equilibrium (Dual B): Input Conditioned Demand and Cost Functions.- 5.9.1 Cost Minimisation.- 5.9.2 Properties of the Input Conditioned Demand.- 5.9.2.1 Non-decreasing.- 5.9.2.2 Existence.- 5.9.2.3 Homogeneity.- 5.9.2.4 The Lagrange Coefficient (µ).- 5.9.2.5 Negativity.- 5.9.2.6 Symmetry.- 5.9.2.7 Negative Semi-definite.- 5.9.3 Properties of Cost Function: Shephard's Lemma.- 5.9.3.1 Increase.- 5.9.3.2 Homogeneity.- 5.9.3.3 Concavity.- 5.9.3.4 Continuity.- 5.9.3.5 Shephard's Lemma.- 5.10 Diagrammatic Representation of the Main Relationships.- 5.11 Joint Production.- 5.11.1 Income Maximisation.- 5.11.2 Input Minimisation.- 5.12 Short-Run.- 5.12.1 Short-Run and Single Production.- 5.12.2 Short-Run and Joint Production.- 5.13 Reflections on the Main Relationships Designed.- 5.14 The Elasticity of Substitution.- Basic References.- References and …