Agricultural Production Economics – eBook

Spread the knowledge

Author: Devid L Debertin

Download (PDF, Unknown)

Table of Contents
Chapter 1. Introduction …………………………………………………………………………………………..1
1.1 Economics Defined……………………………………………………………………………………. 2
1.2 The Logic of Economic Theory…………………………………………………………………… 2
1.3 Economic Theory as Abstraction…………………………………………………………………. 3
1.4 Economic Theory Versus Economic Model………………………………………………….. 3
1.5 Representing Economic Relationships …………………………………………………………. 4
1.6 Consumption Versus Production Economics ………………………………………………… 4
1.7 Microeconomics Versus Macroeconomics……………………………………………………. 5
1.8 Statics Versus Dynamics ……………………………………………………………………………. 6
1.9 Economics Versus Agricultural Economics ………………………………………………….. 7
1.10 Agricultural Production Economics …………………………………………………………….. 7
1.11 The Assumptions of Pure Competition…………………………………………………………. 8
1.12 Why Retain the Purely Competitive Model…………………………………………………. 10
1.13 Concluding Comments …………………………………………………………………………….. 10
Questions for Thought and Class Discussion ………………………………………………. 12
References……………………………………………………………………………………………….12
Chapter 2. Production With One Variable Input…………………………………………………….13
2.1 What Is a Production Function ………………………………………………………………….. 14
2.2 Fixed Versus Variable Inputs and the Length of Run …………………………………… 17
2.3 The Law of Diminishing Returns ………………………………………………………………. 19
2.4 Marginal and Average Physical Product …………………………………………………….. 21
2.5 MPP and the Marginal Product Function ……………………………………………………. 22
2.6 A Neoclassical Production Function …………………………………………………………..26
2.7 MPP and APP for the Neoclassical Function ………………………………………………. 28
2.8 Sign, Slope and Curvature ………………………………………………………………………… 29
2.9 A Single-Input Production Elasticity………………………………………………………….. 33
2.10 Elasticities of Production for a Neoclassical Production Function………………….. 35
2.11 Further Topics on the Elasticity of Production…………………………………………….. 36
2.12 Concluding Comments …………………………………………………………………………….. 37
Problems and Exercises ……………………………………………………………………………. 37

Chapter 3. Profit Maximization with One Input and One Output……………………………39
3.1 Total Physical Product Versus Total Value of the Product ……………………………. 40
3.2 Total Factor or Resource Cost …………………………………………………………………… 41
3.3 Value of the Marginal Product and Marginal Factor Cost……………………………… 41
3.4 Equating VMP and MFC …………………………………………………………………………. 43
3.5 Calculating the Exact Level of Input Use to Maximize Output or Profits ……….. 45
3.6 General Conditions for Profit Maximization……………………………………………….. 51
3.7 Necessary and Sufficient Conditions………………………………………………………….. 52
3.8 The Three Stages of the Neoclassical Production Functiom ………………………….. 52
3.9 Further Topics on States of Production ………………………………………………………. 56
3.10 The Imputed Value of an Additional Unit of an Input ………………………………….. 56
ii
3.11 Concluding Comments………………………………………………………………………………59
Problems and Exercises……………………………………………………………………………..59
Chapter 4. Costs, Returns and Profits on the Output Side ……………………………………….61
4.1 Some Basic Definitions……………………………………………………………………………..62
4.2 Simple Profit Maximization from the Output Side ………………………………………..68
4.3 The Duality of Cost and Production…………………………………………………………….71
4.4 The Inverse of a Production Function………………………………………………………….74
4.5 Linkages between Cost and Production Functions ………………………………………..76
4.6 The Supply Function for the Firm……………………………………………………………….77
4.7 Concluding Comments………………………………………………………………………………79
Problems and Exercises……………………………………………………………………………..79
Chapter 5. Production with Two Inputs…………………………………………………………………..81
5.1 Introduction ……………………………………………………………………………………………..82
5.2 An Isoquant and the Marginal Rate of Substitution……………………………………….86
5.3 Isoquants and Ridge Lines …………………………………………………………………………93
5.4 MRS and the Marginal Product…………………………………………………………………..95
5.5 Partial and Total Derivatives and the Marginal Rate of Substitution………………..97
5.6 Concluding Comments………………………………………………………………………………99
Notes …………………………………………………………………………………………………….100
Problems and Exercises……………………………………………………………………………100

Chapter 6. Maximization in the Two-Input Case …………………………………………………..102
6.1 Introduction to Maximization……………………………………………………………………103
6.2 The Maximum of a Function…………………………………………………………………….104
6.3 Some Illustrative Examples………………………………………………………………………105
6.4 Some Matrix Algebra Principles……………………………………………………………….110
6.5 A Further Illustration……………………………………………………………………………….111
6.6 Maximizing a Profit Function with Two Inputs…………………………………………..112
6.7 A Comparison with Output- or Yield-Maximization Criteria………………………..115
6.8 Concluding Comments…………………………………………………………………………….116
Notes …………………………………………………………………………………………………….117
Problems and Exercises……………………………………………………………………………117

Chapter 7. Maximization Subject to Budget Constraints……………………………………….118
7.1 Introduction ……………………………………………………………………………………………119
7.2 The Budget Constraint …………………………………………………………………………….119
7.3 The Budget Constraint and the Isoquant Map……………………………………………..121
7.4 Isoclines and the Expansion Path………………………………………………………………123
7.5 General Expansion Path Conditions…………………………………………………………..124
7.6 The Production Function for the Bundle…………………………………………………….126
7.7 Pseudo-Scale Lines …………………………………………………………………………………128
7.8 Summary of Marginal Conditions and Concluding Comments ……………………..131
Problems and Exercises……………………………………………………………………………134
Chapter 8. Further Topics in Constrained Maximization and Minimization…………..135
8.1 Simple Mathematics of Global Profit Maximization ……………………………………136
8.2 Constrained Revue Maximization……………………………………………………………..138
iii
8.3 Second Order Conditions………………………………………………………………………… 142
8.4 Interpretation of the Lagrangean Multiplier ………………………………………………. 143
8.5 Constrained Output Maximization …………………………………………………………… 145
8.6 Cost-Minimization Subject to a Revenue Constraint ………………………………….. 147
8.7 Application in the Design of a Lease………………………………………………………… 148
8.7.1 Cash Rent ………………………………………………………………………………….. 148
8.7.2 Shared Rental Arrangements………………………………………………………… 149
8.8 An Application to an Acreage Allotment Problem……………………………………… 151
8.9 Concluding Comments …………………………………………………………………………… 154
Problems and Exercises ………………………………………………………………………….. 155
Reference ………………………………………………………………………………………………156

Chapter 9. Returns to Scale, Homogeneous Functions, and Euler’s Theorem…………157
9.1 Economies and Diseconomies of Size………………………………………………………. 158
9.2 Economies and Diseconomies of Scale …………………………………………………….. 159
9.3 Homogeneous Production Functions………………………………………………………… 161
9.4 Returns to Scale and Individual Production Elasticities………………………………. 162
9.5 Duality of Production and Cost for the Input Bundle………………………………….. 164
9.6 Euler’s Theorem ……………………………………………………………………………………. 167
9.7 Concluding Comments …………………………………………………………………………… 168
Problems and Exercises ………………………………………………………………………….. 169
Chapter 10. The Cobb-Douglas Production Function …………………………………………….171
10.1 Introduction…………………………………………………………………………………………… 172
10.2 The Original Cobb-Douglas Function ………………………………………………………. 172
10.3 Early Generalizations……………………………………………………………………………… 173
10.4 Some Characteristics of the Cobb-Douglas Type of Function ……………………… 174
10.5 Isoquants for the Cobb-Douglas Type of Function …………………………………….. 175
10.6 The Production Surface for the Cobb-Douglas Production Function…………….. 177
10.7 Profit Maximization with the Cobb-Douglas Production Function……………….. 180
10.8 Duality and the Cobb-Douglas Production Function…………………………………… 181
10.9 Constrained Output or Revenue Maximization ………………………………………….. 184
10.10 Concluding Comments …………………………………………………………………………… 185
Problems and Exercises ………………………………………………………………………….. 185
Reference ……………………………………………………………………………………………… 186
Chapter 11. Other Agricultural Production Functions …………………………………………..187
11.1 Introduction…………………………………………………………………………………………… 188
11.2 The Spillman…………………………………………………………………………………………. 188
11.3 The Transcendental Production Function………………………………………………….. 189
11.4 The Two-Input Transcendental………………………………………………………………… 190
11.5 Illustrations and Applications of the Transcendental ………………………………….. 193
11.6 Cobb-Douglas with Variable Input Elasticities ………………………………………….. 196
11.7 de Janvry Modifications …………………………………………………………………………. 196
11.8 Polynomial Forms………………………………………………………………………………….. 197
11.9 Concluding Comments …………………………………………………………………………… 198
Problems and Exercises ………………………………………………………………………….. 198
References…………………………………………………………………………………………….. 199

iv
Chapter 12. The Elasticity of Substitution……………………………………………………………….200
12.1 An Introduction to the Concept…………………………………………………………………201
12.2 Elasticities of Substitution and the Cobb Douglas Function………………………….204
12.3 Policy Applications of the Elasticity of Substitution ……………………………………205
12.4 The CES Production Function…………………………………………………………………..207
12.5 Elasticities of Substitution and the Translog Production Function …………………210
12.6 Concluding Comments…………………………………………………………………………….213
Notes …………………………………………………………………………………………………….213
Problems and Exercises……………………………………………………………………………213
References ……………………………………………………………………………………………..214

Chapter 13. The Demand for Inputs to the Production Process ………………………………215
13.1 Introduction ……………………………………………………………………………………………216
13.2 A Single-Input Setting……………………………………………………………………………..216
13.3 The Elasticity of Input Demand ………………………………………………………………..218
13.4 Technical Complements, Competitiveness and Independence ………………………221
13.5 Input Demand Functions in a Two-Input Setting…………………………………………222
13.6 Input Demand Functions Under Constrained Maximization …………………………225
13.7 Comparative Statics and Input Demand Elasticities …………………………………….227
13.8 Concluding Comments…………………………………………………………………………….230
Notes …………………………………………………………………………………………………….230
Problems and Exercises……………………………………………………………………………231
Reference……………………………………………………………………………………………….231

Chapter 14. Variable Product and Input Prices …………………………………………………….232
14.1 Relaxing the Assumptions of Pure Competition ………………………………………….233
14.2 Variation in Output Prices from the Output Side…………………………………………233
14.3 Variation in Output Prices from the Input Side……………………………………………236
14.4 Variable Input Prices……………………………………………………………………………….239
14.5 A General Profit Maximization Statement………………………………………………….239
14.6 Concluding Comments…………………………………………………………………………….241
Problems and Exercises……………………………………………………………………………242

Chapter 15. Production of More Than One Product……………………………………………….243
15.1 Production Possibilities for a Society…………………………………………………………244
15.2 Production Possibilities at the Farm Level………………………………………………….245
15.3 General Relationships ……………………………………………………………………………..247
15.4 Competitive, Supplementary, Complementary and Joint Products…………………249
15.5 Product Transformations from Single-Input Production Functions………………..250
15.6 Product Transformation and the Output Elasticity of Substitution …………………254
15.7 Concluding Comments…………………………………………………………………………….257
Problems and Exercises……………………………………………………………………………258
References ……………………………………………………………………………………………..258
Chapter 16. Maximization in a Two-Output Setting……………………………………………….259
16.1 The Family of Product Transformation Functions……………………………………….260
16.2 Maximization of Output…………………………………………………………………………..260
16.3 The Isorevenue Line………………………………………………………………………………..261
16.4 Constrained Revenue Maximization ………………………………………………………….262
v
16.5 Simple Mathematics of Constrained Revenue Maximization ………………………. 265
16.6 Second-Order Conditions ……………………………………………………………………….. 268
16.7 An Additional Example ………………………………………………………………………….. 270
16.8 Minimization Subject to a Revenue Constraint ………………………………………….. 273
16.9 An Output Restriction Application…………………………………………………………… 275
16.10 Concluding Comments …………………………………………………………………………… 277
Problems and Exercises ………………………………………………………………………….. 277

Chapter 17. Two Outputs and Two Inputs…………………………………………………………….279
17.1 Introduction…………………………………………………………………………………………… 280
17.2 Two Inputs and Two Outputs: A Basic Presentation…………………………………… 280
17.3 Some General Principles…………………………………………………………………………. 282
17.4 The Constrained Maximization Problem…………………………………………………… 284
17.5 An Intermediate Product Model ………………………………………………………………. 285
17.6 Concluding Comments …………………………………………………………………………… 289
Problems and Exercises ………………………………………………………………………….. 290

Chapter 18. General Multiple-Product and Multiple-Input Conditions…………………..291
18.1 Introduction…………………………………………………………………………………………… 292
18.2 Multiple Inputs and a Single Output…………………………………………………………. 292
18.3 Many Outputs and a Single Input …………………………………………………………….. 295
18.4 Many Inputs and Many Outputs ………………………………………………………………. 296
18.5 Concluding Comments …………………………………………………………………………… 299
Notes……………………………………………………………………………………………………. 300
Problems and Exercises ………………………………………………………………………….. 300

Chapter 19. Enterprise Budgeting and Marginal Analysis ……………………………………..301
19.1 The Development of an Enterprise Budget………………………………………………… 302
19.2 The Level of Output to be Produced…………………………………………………………. 304
19.3 The Variable Input Levels ………………………………………………………………………. 305
19.4 The Fixed Input Allocation……………………………………………………………………… 306
19.5 The Economies of Size and Farm Budgets………………………………………………… 307
19.6 Price and Output Uncertainty ………………………………………………………………….. 307
19.7 Concluding Comments …………………………………………………………………………… 308
Problems and Exercises ………………………………………………………………………….. 308
Chapter 20. Decision Making in an Environment of Risk And Uncertainty …………….309
20.1 Risk and Uncertainty Defined …………………………………………………………………. 310
20.2 Farmer Attitudes Toward Risk and Uncertainty…………………………………………. 310
20.3 Actions, States of Nature, Probabilities and Consequences …………………………. 312
20.4 Risk Preference and Utility……………………………………………………………………… 314
20.5 Risk, Uncertainty and Marginal Analysis………………………………………………….. 316
20.6 Strategies for Dealing with Risk and Uncertainty ………………………………………. 318
20.6.1 Insure Against Risk……………………………………………………………………… 318
20.6.2 Contracts……………………………………………………………………………………. 319
20.6.3 Flexible Facilities and Equipment ………………………………………………… 319
20.6.4 Diversification …………………………………………………………………………… 320
20.6.5 Government Programs ………………………………………………………………… 321
20.7 Concluding Comments …………………………………………………………………………… 322
vi
Problems and Exercises……………………………………………………………………………322
Reference……………………………………………………………………………………………….323
Chapter 21.1 Time and Agricultural Production Processes ……………………………………..324
21.1 Introduction ……………………………………………………………………………………………325
21.2 Alternative Goals of a Farm Manager over Many Seasons……………………………325
21.2.1 Long-Run Profit Maximization ……………………………………………………..325
21.2.2 Accumulation of Wealth……………………………………………………………….326
21.2.3 Other Goals…………………………………………………………………………………326
21.3 Time as an Input to the Production Process ………………………………………………..327
21.4 Time, Inflation, Interest Rates and Net Worth …………………………………………….328
21.5 Discounting Future Revenues and Costs…………………………………………………….329
21.5.1 The Present Value of a Dollar ……………………………………………………….329
21.5.2 Discounting Revenues with the Present Value Formula ……………………330
21.5.3 Compounding Revenues and Costs ………………………………………………..331
21.6 Polyperiod Production and Marginal Analysis ……………………………………………332
21.7 Concluding Comments…………………………………………………………………………….335
Problems and Exercises……………………………………………………………………………336

Chapter 22. Linear Programming and Marginal Analysis………………………………………337
22.1 Introduction ……………………………………………………………………………………………338
22.2 Classical Optimization and Linear Programming ………………………………………..338
22.3 Assumptions of Linear Programming ………………………………………………………..339
22.4 Technical Requirements and Fixed-Proportion Production Functions ……………340
22.5 A Simple Constrained Maximization Problem ……………………………………………340
22.6 Other Approaches for Solving Linear Programming Models ………………………..343
22.7 The Simplex Method……………………………………………………………………………….344
22.8 Duality…………………………………………………………………………………………………..348
22.9 An Application ……………………………………………………………………………………….350
22.10 Concluding Comments…………………………………………………………………………….353
Problems and Exercises……………………………………………………………………………354
Chapter 23. Frontiers in Agricultural Production Economics Research ………………….355
23.1 Management and Agricultural Production Functions …………………………………..356
23.1.1 Alternative Approaches to Management …………………………………………356
23.1.2 Management and Profit Maximization ……………………………………………357
23.2 New Technology and the Agricultural Production Function …………………………358
23.2.1 Some Examples …………………………………………………………………………..360
23.2.2 Time and Technology …………………………………………………………………..361
23.3 Conceptual Issues in Estimating Agricultural Production Functions………………362
23.4 Concluding Comments…………………………………………………………………………….364
Problems and Exercises……………………………………………………………………………364
Reference……………………………………………………………………………………………….365
Chapter 24. Contemporary Production Theory: The Factor Side……………………………366
24.1 Introduction ……………………………………………………………………………………………367
24.2 Fundamentals of Duality ………………………………………………………………………….367
24.3 Duality Theorems……………………………………………………………………………………373
24.4 The Envelope Theorem ……………………………………………………………………………374
vii
24.5 Shephard’s Lemma ………………………………………………………………………………… 374
24.6 Hotelling’s Lemma ………………………………………………………………………………… 376
24.7 Alternative Elasticity of Substitution Measures …………………………………………. 378
24.8 Elasticities of Substitution and the Cobb-Douglas Specification ………………….. 383
24.9 The CES, or Constant Elasticity of Substitution Specification …………………….. 384
24.10 The Transcendental Production Function and Sigma………………………………….. 385
24.11 Linear in the Parameters Functional Forms
And the Translog Production Function……………………………………………………… 386
24.12 Restrictions and Other Estimation Problems……………………………………………… 389
24.13 Elasticities of Substitution for U.S. Agriculture…………………………………………. 389
24.14 An Empirical Illustration ………………………………………………………………………… 390
24.15 Theoretical Derivation……………………………………………………………………………. 390
24.16 Empirical Results…………………………………………………………………………………… 392
24.17 Concluding Comments …………………………………………………………………………… 395
References……………………………………………………………………………………………..395
Chapter 25. Contemporary Production Theory: The Product Side …………………………398
25.1 Introduction…………………………………………………………………………………………… 399
25.2 Duality in Product Space …………………………………………………………………………399
25.3 Cobb-Douglas-Like Product Space ………………………………………………………….. 401
25.4 CES-Like Functions in Product Space ……………………………………………………… 402
25.5 Alternative Elasticity of Substitution Measures in Product Space ………………… 403
25.6 Translog-Like Functions in Product Space………………………………………………… 408
25.7 Translog Revenue Functions …………………………………………………………………… 408
25.8 Empirical Applications …………………………………………………………………………… 410
Note …………………………………………………………………………………………………….. 411
References……………………………………………………………………………………………..411

Leave a Reply

Your email address will not be published. Required fields are marked *