Analytic Economics


            
  Analytic Economics is a revolutionary concept and approach to economics that 
uses mathematical methods to analyze economic phenomena and to derive analytical 
or numerical results. This book is designed for professionals and graduate students 
who have a background in mathematics and/or economics. The book should be useful to 
economics researchers, business analysts, management scientists, as well as specialists 
on Wall Street. The prerequisites for convenient use of this book are relatively modest. 
The prime requirement is some familiarity with basic concepts of economics. Some 
developments-especially the mathematical proofs for most propositions may require some 
knowledge of more advanced concepts of linear programming, set theory, and numerical 
computation. However, all of the complex proofs can be completely skipped as long as you 
faithfully believe in the proposition statements that are intended to be proven. Instead, 
you can easily use the tools in the Analytic Economics Software to do most of the numerical
computations and graph drawings.
        
    The material in this book is organized into three parts, and the contents of each part 
are arranged as follows:
Part I introduces basic concepts and models used in Analytic Economics.
                                                                             
  PART I OVERVIEW .......................................................1   
  Chapter 1 Introduction ................................................3   
  1.1 Geometric Economics vs. Analytic Economics ........................3   
  1.2 An Overview .......................................................7   
  Chapter 2 Basic Models ................................................8   
  2.1 Macro System and Micro System .....................................8   
  2.2 Production Space ..................................................9   
  2.3 System Parameters .................................................11  
  2.4 Supply Vector and Demand Vector ...................................12  
  2.5 Price Vector ......................................................14  
  2.6 Ideal System and Ideal Assumptions ................................14  
  2.7 Properties of Convex Set ..........................................18  
  2.8 Exercises .........................................................21  



  PART II IDEAL ECONOMICS ...............................................25 
  Chapter 3 Production Possibility Frontier  ............................27 
  3.1 Basic Definitions .................................................27 
  3.2 Shaded Region and Spanned Region ..................................29 
  3.3 Production Ability Parameters .....................................30 
  3.4 Resource Convertible Assumption ...................................32 
  3.5 Micro Production Possibility Frontier .............................35 
  3.6 Exercises .........................................................36 
                                                                            
  Chapter 4 Formulating the Macro PPF ...................................39 
  4.1  Decomposing a Surface into Linear Elements .......................39 
  4.2  Problem Formulation ..............................................40 
  4.3  Basic Properties .................................................43 
  4.4  Piecewise Linear Curve Approach ..................................45 
  4.5  Discrete Set Approach ............................................49 
  4.6  Continuous and Smooth Curve Approach .............................51 
  4.7  A Dummy System: The Four-Family System ...........................55 
  4.8  Elliptic Approximation ...........................................56 
  4.9  Bisection Method and Lookup Table Method .........................57 
  4.10 The Minimum Macro PPF ............................................59 
  4.11 Graphs of Production Possibility Curves ..........................62 
  4.12 Error Analysis ...................................................63 
  4.13 An Algorithm for Constructing the Macro PPR.......................68 
  4.14 Bounds of the Macro PPF ..........................................70 
  4.15 Exercises ........................................................73 
                                                                            
  Chapter 5 Supply ......................................................78 
  5.1 Supply Function ...................................................78 
  5.2 Supply Curve ......................................................80 
  5.3 The Law of Supply .................................................83 
  5.4 Supply Elasticity .................................................85 
  5.5 Supply Function Implied by PPF ....................................88 
  5.6 Supply Function with Partial Information ..........................90 
  5.7 The Law of Specialization and Division of Labor ...................93 
  5.8 Limiting Properties of the Supply Function ........................95 
  5.9 Exercises .........................................................97 
                                                                            
  Chapter 6 Demand ......................................................101
  6.1  Consumer Preferences .............................................101
  6.2  Consumer Satisfaction Function ...................................102
  6.3  Indifference Demand Frontier .....................................103
  6.4  Budget Constraint ................................................106
  6.5  Micro Desirable Demand ...........................................108
  6.6  Consumer Preference Quota ........................................110
  6.7  Demand Function ..................................................113
  6.8  Desirable Demand Frontier ........................................115
  6.9  Demand Curve .....................................................116
  6.10 Lower Bound of Demand ............................................118
  6.11 The Law of Demand ................................................119
  6.12 Demand Elasticity ................................................122
  6.13 Limiting Properties of the Demand Function .......................126
  6.14 Exercises ........................................................128
                                                                            
  Chapter 7 Static General Equilibrium ..................................131
  7.1 Base Price and Price-Index-Free Constraint ........................132
  7.2 A Summary of Supply and Demand Functions ..........................136
  7.3 Static General Equilibrium Equation ...............................138
  7.4 Existence of Partial Equilibrium ..................................142
  7.5 Existence of General Equilibrium ..................................143
  7.6 Supply-Demand Diagram for Partial Equilibrium .....................145
  7.7 PPF-DDF Diagram for General Equilibrium ...........................148
  7.8 Proportional Approximation ........................................151
  7.9 First Order Approximation .........................................155
  7.10 Newton's Method ..................................................156
  7.11 Salesman's Method ................................................157
  7.12 General Equilibrium as an Optimization Problem....................161
  7.13 Exercises ........................................................163


Part III explores the trade theories that are ignored by the ideal system.
  Interesting problems related to either domestic trade and international trade.
such as the equilibrium commercial profit rate with which the total commercial profit 
is maximized, the equilibrium tariff rate with which the government can collect the 
maximum tariff revenue, the equilibrium exchange rate with which the foreign trade 
is balanced, the policies for adjusting each of these rates, the equilibrium selling 
price and purchasing price, the equilibrium export or import amount, are all analyzed 
mathematically.Other application theories, such as taxation, investment, interests rate,
as well as dynamic equilibrium, are under development and will be added in future 
editions of this book.

  PART III  TRADE THEORY  ...............................................167
  Chapter 8 Domestic Trade ..............................................169
  8.1  Trade-in Price and Trade-out Price ...............................169
  8.2  Supply-Demand-Trade Equilibrium ..................................171
  8.3  Salesman's Method for S-D-T Equilibrium ..........................176
  8.4  S-D-T Equilibrium for the Four-Family System .....................178
  8.5  Monopoly Trade ...................................................180
  8.6  Monopoly Trade under Proportional Approximation ..................182
  8.7  Trading Cost Bearing .............................................188
  8.8  Exercises ........................................................191
                                                                            
  Chapter 9 Foreign Trade ...............................................196
  9.1  Isolated Equilibrium and Trade Equilibrium .......................196
  9.2  Big-Market .......................................................197
  9.3  Foreign Trade with Big-Market ....................................198
  9.4  Competitive Model and Monopoly Model .............................201
  9.5  Competitive Equilibrium Price ....................................201
  9.6  Export-Import Amount .............................................205
  9.7  Foreign Currency Equilibrium Equation ............................205
  9.8  Equilibrium Exchange Rate ........................................208
  9.9  Exchange Rate Readjusting Equation ...............................210
  9.10 Maximizing the Total Tariff Collection ...........................211
  9.11 Maximizing the Export-Import Net Profit ..........................212
  9.12 Evaluating the Advantage of Foreign Trade ........................214
  9.13 Exercises ........................................................215
                                                                            
  Chapter 10 Near-Free Foreign Trade ....................................218
  10.1  Proportional Approximation ......................................218
  10.2  Free "Trade .....................................................222
  10.3  Near-Free Foreign Trade Conditions ..............................225
  10.4  Competitive Case ................................................226
  10.5  Monopoly Case ...................................................231
  10.6  Compound System and Virtual Big-Market ..........................236
  10.7  Price Proportional Uniform Tariff ...............................240
  10.8  Static Profit Proportional Tariff ...............................247
  10.9  Dynamic Profit Proportional Tariff ..............................254
  10.10 Exercises .......................................................255
                                                                            
  FREQUENTLY USED NOTATIONS .............................................263
  REFERENCES ............................................................271
  INDEX .................................................................275
        



    
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Cataloging-in-Publication Data on file with the Library of Congress

ISBN:  978-0-971-89340-5

Library of Congress Control Number (LCCN): 2002090952

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