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El. knyga: Disequilibrium Economics: Oligopoly, Trade, and Macrodynamics

  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Apr-2018
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319744155
Kitos knygos pagal šią temą:
Disequilibrium Economics: Oligopoly, Trade, and MacrodynamicsDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Apr-2018
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319744155
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This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author’s over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve “research stubs” – outlined research agendas that have not yet been fully worked on – are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.
Part I Introductory Matter
1 Utility and Demand
3(14)
1.1 The Paradox of Value
3(2)
1.1.1 Indifference
4(1)
1.1.2 Altruism
5(1)
1.2 Utility and Demand Functions
5(5)
1.2.1 Linear Demand
5(2)
1.2.2 Cobb-Douglas Utility
7(2)
1.2.3 Cobb-Douglas Coefficients and Advertising
9(1)
1.3 Lancaster's New Demand Theory
10(7)
1.3.1 Properties and Commodities
10(1)
1.3.2 Optimum
11(1)
1.3.3 "Shadow" Property Prices
12(1)
1.3.4 Demand Functions
13(1)
1.3.5 Product Design
14(1)
1.3.6 Inverse Demand and Revenue
15(1)
References
15(2)
2 Elements of Production
17(24)
2.1 Inputs, Output, and the Production Function
18(14)
2.1.1 Decreasing Returns
18(2)
2.1.2 The CES Function
20(6)
2.1.3 Cost and Capacity Limits
26(6)
2.2 Returns to Scale
32(4)
2.3 Fixed Costs
36(5)
References
37(4)
Part II Models
3 Cournot I: Constant Returns
41(32)
3.1 Introduction
42(5)
3.1.1 Biographical
42(1)
3.1.2 Cournot's Contribution
42(1)
3.1.3 Cournot's Heritage
43(4)
3.2 Formal Model
47(3)
3.2.1 Iso-Elastic Demand
47(3)
3.3 The Iterative Process
50(2)
3.4 Stability of the Cournot Point
52(1)
3.5 Periodic Points and Chaos
53(4)
3.6 Adaptive Expectations
57(1)
3.7 The Neimark Bifurcation
57(7)
3.8 Critical Lines and Absorbing Area
64(2)
3.9 Conclusion
66(1)
3.10 Computer Programs
66(7)
3.10.1 Drawing Periodic Tongues
67(1)
3.10.2 Positive Lyapunov Exponent
68(2)
3.10.3 Drawing Critical Lines and Absorbing Areas
70(1)
References
71(2)
4 Cournot II: Returns to Scale and Stability
73(24)
4.1 Introduction
74(1)
4.1.1 The "Theocharis Problem"
74(1)
4.1.2 Capacity Limits
75(1)
4.2 Duopoly with Capacity Limits
75(6)
4.2.1 Production and Cost
75(1)
4.2.2 Long Run Cost
76(2)
4.2.3 Reaction Functions
78(2)
4.2.4 Numerics
80(1)
4.3 Increasing Competition
81(4)
4.3.1 Production and Cost Functions
83(1)
4.3.2 Reaction Functions
84(1)
4.4 Equilibrium and Its Stability
85(5)
4.4.1 Cournot Equilibrium
85(2)
4.4.2 Cost Structure in Cournot Equilibrium
87(1)
4.4.3 Stability of Cournot Equilibrium
88(2)
4.5 Capital and Investment
90(7)
4.5.1 Equilibrium with Identical Firms
90(1)
4.5.2 Some Numerics
91(2)
4.5.3 Endogenous Investment Decisions
93(3)
4.5.4 The Cournot Agenda
96(1)
References
96(1)
5 Bertrand
97(28)
5.1 Some History
98(1)
5.1.1 Biographical
98(1)
5.1.2 Bertrand's Argument
98(1)
5.2 Introduction
99(2)
5.2.1 Substitutes
100(1)
5.3 A Solution: Lancaster
101(6)
5.3.1 Properties and Commodities
102(1)
5.3.2 Utility
103(1)
5.3.3 Budget Constraint
103(1)
5.3.4 Optimization
104(1)
5.3.5 Demand Functions
105(1)
5.3.6 Inverse Demand
105(2)
5.4 Duopoly
107(1)
5.4.1 Amoroso Formulas
107(1)
5.5 Reaction Functions
108(6)
5.5.1 Approximating the Reaction Functions
110(2)
5.5.2 Fixed Point Destabilization
112(2)
5.6 Numerical Results
114(3)
5.6.1 Computation Model
114(3)
5.7 Product Design
117(1)
5.7.1 Introduction
117(1)
5.8 The Model
118(4)
5.8.1 The Production Possibility Frontier
118(1)
5.8.2 Optimum Design
118(3)
5.8.3 Design Update Rule
121(1)
5.9 The Design Update Map
122(3)
References
123(2)
6 Stackelberg
125(30)
6.1 Some History
126(4)
6.1.1 Biographical
126(1)
6.1.2 Stackelberg Leadership
126(1)
6.1.3 The Stackelberg Model
127(1)
6.1.4 Digression
128(2)
6.2 Unifying Cournot and Stackelberg
130(1)
6.2.1 Agenda
130(1)
6.3 Model Setup
131(5)
6.3.1 Cournot Action
131(2)
6.3.2 Digression on Profits
133(1)
6.3.3 Stackelberg Action
134(2)
6.4 A Proposed Map
136(1)
6.4.1 Profit Considerations
136(1)
6.5 The Map
136(4)
6.5.1 The Parameter Plane
137(3)
6.6 Numerics
140(15)
6.6.1 Parameter Space: Attractors and Bifurcations
140(4)
6.6.2 The Phase Plane: Attractors and Basins
144(8)
6.6.3 Rational Expectations
152(1)
References
153(2)
7 Hotelling Duopoly
155(28)
7.1 Introduction
156(7)
7.1.1 Biographical
156(1)
7.1.2 Some History
157(1)
7.1.3 Digression About Space
158(5)
7.2 The Model
163(7)
7.2.1 Assumptions and Notation
163(2)
7.2.2 Total Demand and Profits
165(1)
7.2.3 Market Area Endpoints
165(1)
7.2.4 Interpretation of the Cases
166(1)
7.2.5 Demand and Optimal Location
167(6)
7.2.6 Profit Maximization and Mill Price
173(3)
7.3 Summary for the Cases
176(7)
7.4 Equilibria
177(4)
7.4.1 Duopoly
178(2)
7.4.2 Monopolies
180(1)
7.5 Further Issues
181(2)
7.5.1 Different Time Scales
182(1)
7.5.2 Different Pricing Policies
182(1)
References
182(1)
8 Disequilibrium Trade and Pricing of Durable Commodities
183(18)
8.1 Introduction
184(2)
8.2 Assumptions
186(5)
8.2.1 Notation
186(1)
8.2.2 Budget Constraints
186(1)
8.2.3 Utility Functions
187(1)
8.2.4 Individual Optima
188(1)
8.2.5 Trade
189(1)
8.2.6 Excess Demand
190(1)
8.2.7 Tatonnement
191(1)
8.3 The Model
191(1)
8.4 Numerical Analysis and Graphics
191(8)
8.4.1 The Phase Plane
191(6)
8.4.2 Bifurcation Diagrams
197(2)
8.5 Summary
199(2)
References
200(1)
9 Macroeconomics and the Trade Cycle
201(42)
9.1 Background
201(7)
9.1.1 Flows
202(2)
9.1.2 The MONIAC
204(1)
9.1.3 Protagonists
205(1)
9.1.4 The Multiplier-Accelerator Model
206(2)
9.2 The Models
208(4)
9.2.1 The Original Samuelson-Hicks Model
209(2)
9.2.2 Digression on Technology
211(1)
9.3 Floor Only
212(14)
9.3.1 The Formal Model
212(5)
9.3.2 Stationary Relative Dynamics
217(4)
9.3.3 Periodicity
221(2)
9.3.4 Absolute and Relative Variables
223(3)
9.4 Ceiling Included
226(17)
9.4.1 Exponential Decay and Half-Life
226(1)
9.4.2 Tying the Ceiling to Capital Stock
226(5)
9.4.3 The Relative System
231(5)
9.4.4 Numerical Results
236(2)
References
238(5)
Part III Model Stubs
10 Introduction to the Stubs
243(2)
11 Caudex Primus
245(6)
11.1 A Formal Model
246(2)
11.1.1 Demand
246(1)
11.1.2 Cost and Profit
247(1)
11.1.3 Reaction Functions
248(1)
11.2 Capacity Limits
248(3)
Reference
249(2)
12 Caudex Secundus
251(4)
12.1 Hotelling in 2D
251(4)
13 Caudex Tertius
255(4)
13.1 The Open Economy
255(3)
13.2 Addendum: Small and Big Economies
258(1)
Reference
258(1)
14 Caudex Quartus
259(4)
14.1 Dynamic Stackelberg
259(4)
Reference
261(2)
15 Caudex Quintus
263(4)
15.1 Product Design
263(4)
16 Caudex Sextus
267(4)
16.1 Migration
267(4)
References
270(1)
17 Caudex Septimus
271(4)
17.1 Advertising
271(4)
18 Caudex Octavus
275(10)
18.1 Interregional Trade
275(1)
18.2 The Static Model
276(2)
18.3 The Dynamic Model
278(1)
18.4 Discretizing
278(2)
18.5 Price Dynamic Alone
280(2)
18.6 Suggested Agenda
282(3)
References
284(1)
19 Caudex Nonus
285(4)
19.1 Business Cycle Diffusion
285(4)
References
287(2)
20 Caudex Decimus
289(4)
20.1 Disequilibrium Trade: Several Agents
289(4)
21 Caudex Undecimus
293(10)
21.1 Disequilibrium Trade: Several Commodities
293(1)
21.2 Some Geometry
294(3)
21.2.1 Digression on the Preparation of Solid Box Picture
295(2)
21.3 Bilateral Deals
297(3)
21.3.1 Bilateral Deal x, y
299(1)
21.3.2 Bilateral Deal x, z
300(1)
21.4 Trade Maps
300(1)
21.5 Arbitrary Numbers of Traders and Commodities
301(2)
22 Caudex Duodecimus
303
22.1 Duopolists with Multiple Plants
303
References
307
Tönu Puu is a Swedish economist of Estonian descent. He worked as acting full professor of economics at Uppsala University from 1963-1970, where he received his Ph.D., and was appointed ordinary professor of economics at Umeå University in 1971. Since 2001, when he became an emeritus professor, he has been working as a senior professor at the Centre for Regional Science (CERUM). In 2014 he was awarded the Doctor Jubilaris of Uppsala University. Puu has published over 20 books and more than 120 scholarly articles on economics, philosophy and mathematics. Topics studied include portfolio selection, investment and production, philosophy of science (in collaboration with Sir Karl Popper), spatial economics, economics of the arts, nonlinear dynamic processes, oligopoly and business cycles.Puu was founder and director of the Nordic Baroque Music Festival from 1987 to 2001 and in this capacity received the Prize for Extraordinary Promotion of Culture, awarded by the county government. Other musical interests include playing the viola da gamba and being a "luthier", making his own instruments.
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