Calculus and techniques of optimization with microeconomic applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 368 S. graph. Darst. 26 cm |
| ISBN: | 9789812774934 9812774939 |
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MARC
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| 245 | 1 | 0 | |a Calculus and techniques of optimization with microeconomic applications |c John Hoag |
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Record in the Search Index
| _version_ | 1804137562934083584 |
|---|---|
| adam_text | Contents
Acknowledgments
To The Instructor
To The Student
Introduction
Section I Sets and Functions
Section II What is Mathematics?
Theorems and Proof
Styles of Proof
Section III Matrix Algebra
Adding and Multiplying Matrices
Determinants
Matrix Inverse
Section IV Linear Algebra
Linear Combinations and Dependency
Rank
Solutions to Linear Equations
Lines and Vectors
Linear Functions
Xl
xiii
XV
xvii
9
9
10
13
14
23
30
37
40
50
55
61
66
viii
Calculus and Techniques of Optimization with
Microeconomic
Applications
Section V Calculus of One Variable
69
Metric Spaces
70
Limits
80
Limits at Infinity
87
Continuity
90
Derivatives
95
Differential
104
Maximum
106
Section VI Calculus of Several Variables
115
Derivatives
117
Total Differential
124
Finding the (Total) Differential
125
Maximum
128
Quadratic Forms
140
Inverse Functions
142
Implicit Function Theorem
149
Implicit Function Theorem
—
Linear Equations
153
Implicit Function Theorem
—
General Case
154
Convexity
161
Section
VII
Techniques of Optimization
175
Optimization
175
Unconstrained Maximum Problem
—
One Variable Case
175
Unconstrained Maximum Problem
—
Several Variables
177
Constrained Maximum Problem
179
Employing the Implicit Function Theorem
179
The Method of
Lagrange 182
Summary
—
Unconstrained and Equality Constraints
186
Inequality Constraints
189
Kuhn-Tucker
191
Section
VIII
Odds and Ends
201
Duality
201
Homogeneous Functions
203
Homothetic Functions
206
Linking Homogeneous Functions and Concavity
206
Envelope Theorem
206
Separating
Hyperplanes 209
Contents
Section
IX
Section X
Section XI
Comparative Statics
213
An Example of Comparative Statics
215
Preferences, Utility, and Demand
217
Elements of a Maximum
217
Preferences and Utility
220
Transformations of Quasiconcave Functions
228
Utility Maximization
231
Interpreting the First-Order Necessary Conditions
232
Demand
233
Applying Comparative Statics to the Consumer Problem
234
Indirect Utility
238
Using Duality
238
Revealed Preference
241
Choice Under Uncertainty
246
Allais
Paradox
252
Risk Aversion
253
Supply
257
Obtaining Total Variable Cost
258
Profit Maximization and Supply in Terms of Output
261
Profit Maximization, Several Inputs
263
Profit Maximization, Several Inputs and Several Outputs
265
Monopoly
266
One Input and One Output
268
Game Theory
271
Games in Normal Form
274
Dominant Strategies
276
Mixed Strategies
282
More Finding Nash
293
Finding Nash for Three Players
305
Interval Strategies Sets with Differentiable Payoffs
315
Cournot with Quadratic Costs
317
Cournot with Asymmetric Information
318
Dynamic Games: The Stackelberg Model
320
Extensive Form
321
Why Nash Equilibrium?
324
χ
Calculus and Techniques of Optimization with
Microeconomic
Applications
Section
XII
Welfare and General Equilibrium
327
Pure Trade
327
Arrow s Theorem
332
A Model with Production
334
Competition and the Market System
337
Welfare Theorems
340
Competitive Equilibrium with Production
341
Robinson Crusoe
342
Section
XIII
Applications
347
The Firm Over Time
347
Pollution Problem
351
Duopoly with Advertising
355
The Averich-Johnson Effect
358
References
363
Index
365
|
| adam_txt |
Contents
Acknowledgments
To The Instructor
To The Student
Introduction
Section I Sets and Functions
Section II What is Mathematics?
Theorems and Proof
Styles of Proof
Section III Matrix Algebra
Adding and Multiplying Matrices
Determinants
Matrix Inverse
Section IV Linear Algebra
Linear Combinations and Dependency
Rank
Solutions to Linear Equations
Lines and Vectors
Linear Functions
Xl
xiii
XV
xvii
9
9
10
13
14
23
30
37
40
50
55
61
66
viii
Calculus and Techniques of Optimization with
Microeconomic
Applications
Section V Calculus of One Variable
69
Metric Spaces
70
Limits
80
Limits at Infinity
87
Continuity
90
Derivatives
95
Differential
104
Maximum
106
Section VI Calculus of Several Variables
115
Derivatives
117
Total Differential
124
Finding the (Total) Differential
125
Maximum
128
Quadratic Forms
140
Inverse Functions
142
Implicit Function Theorem
149
Implicit Function Theorem
—
Linear Equations
153
Implicit Function Theorem
—
General Case
154
Convexity
161
Section
VII
Techniques of Optimization
175
Optimization
175
Unconstrained Maximum Problem
—
One Variable Case
175
Unconstrained Maximum Problem
—
Several Variables
177
Constrained Maximum Problem
179
Employing the Implicit Function Theorem
179
The Method of
Lagrange 182
Summary
—
Unconstrained and Equality Constraints
186
Inequality Constraints
189
Kuhn-Tucker
191
Section
VIII
Odds and Ends
201
Duality
201
Homogeneous Functions
203
Homothetic Functions
206
Linking Homogeneous Functions and Concavity
206
Envelope Theorem
206
Separating
Hyperplanes 209
Contents
Section
IX
Section X
Section XI
Comparative Statics
213
An Example of Comparative Statics
215
Preferences, Utility, and Demand
217
Elements of a Maximum
217
Preferences and Utility
220
Transformations of Quasiconcave Functions
228
Utility Maximization
231
Interpreting the First-Order Necessary Conditions
232
Demand
233
Applying Comparative Statics to the Consumer Problem
234
Indirect Utility
238
Using Duality
238
Revealed Preference
241
Choice Under Uncertainty
246
Allais
Paradox
252
Risk Aversion
253
Supply
257
Obtaining Total Variable Cost
258
Profit Maximization and Supply in Terms of Output
261
Profit Maximization, Several Inputs
263
Profit Maximization, Several Inputs and Several Outputs
265
Monopoly
266
One Input and One Output
268
Game Theory
271
Games in Normal Form
274
Dominant Strategies
276
Mixed Strategies
282
More Finding Nash
293
Finding Nash for Three Players
305
Interval Strategies Sets with Differentiable Payoffs
315
Cournot with Quadratic Costs
317
Cournot with Asymmetric Information
318
Dynamic Games: The Stackelberg Model
320
Extensive Form
321
Why Nash Equilibrium?
324
χ
Calculus and Techniques of Optimization with
Microeconomic
Applications
Section
XII
Welfare and General Equilibrium
327
Pure Trade
327
Arrow's Theorem
332
A Model with Production
334
Competition and the Market System
337
Welfare Theorems
340
Competitive Equilibrium with Production
341
Robinson Crusoe
342
Section
XIII
Applications
347
The Firm Over Time
347
Pollution Problem
351
Duopoly with Advertising
355
The Averich-Johnson Effect
358
References
363
Index
365 |
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| spelling | Hoag, John Verfasser aut Calculus and techniques of optimization with microeconomic applications John Hoag New Jersey [u.a.] World Scientific 2008 XX, 368 S. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Economics, Mathematical Mathematical optimization Microeconomics Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Mikroökonomie (DE-588)4039225-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s Mikroökonomie (DE-588)4039225-9 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016442074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoag, John Calculus and techniques of optimization with microeconomic applications Economics, Mathematical Mathematical optimization Microeconomics Wirtschaftsmathematik (DE-588)4066472-7 gnd Mikroökonomie (DE-588)4039225-9 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4039225-9 (DE-588)4123623-3 |
| title | Calculus and techniques of optimization with microeconomic applications |
| title_auth | Calculus and techniques of optimization with microeconomic applications |
| title_exact_search | Calculus and techniques of optimization with microeconomic applications |
| title_exact_search_txtP | Calculus and techniques of optimization with microeconomic applications |
| title_full | Calculus and techniques of optimization with microeconomic applications John Hoag |
| title_fullStr | Calculus and techniques of optimization with microeconomic applications John Hoag |
| title_full_unstemmed | Calculus and techniques of optimization with microeconomic applications John Hoag |
| title_short | Calculus and techniques of optimization with microeconomic applications |
| title_sort | calculus and techniques of optimization with microeconomic applications |
| topic | Economics, Mathematical Mathematical optimization Microeconomics Wirtschaftsmathematik (DE-588)4066472-7 gnd Mikroökonomie (DE-588)4039225-9 gnd |
| topic_facet | Economics, Mathematical Mathematical optimization Microeconomics Wirtschaftsmathematik Mikroökonomie Lehrbuch |
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