Agricultural Production Economics: The Art of Production Theory

Transcription

1 University of Kentucky UKnowledge Agricultural Economics Textbook Gallery Agricultural Economics -1 Agricultural Production Economics: The Art of Production Theory David L. Debertin University of Kentucky, Click here to let us know how access to this document benefits you. Follow this and additional works at: Part of the Agricultural Economics Commons Recommended Citation Debertin, David L., "Agricultural Production Economics: The Art of Production Theory" (1). Agricultural Economics Textbook Gallery.. This Book is brought to you for free and open access by the Agricultural Economics at UKnowledge. It has been accepted for inclusion in Agricultural Economics Textbook Gallery by an authorized administrator of UKnowledge. For more information, please contact

2 Agricultural Production Economics The Art of Production Theory David L. Debertin

3 Agricultural Production Economics The Art of Production Theory Agricultural Production Economics (The Art of Production Theory) is a companion book of color illustrations to Agricultural Production Economics (Second Edition, Amazon Createspace 1) and is a free download. A bound print copy is also available on amazon.com at a nominal cost under the following ISBN numbers: ISBN- 13: ISBN- 1: 1719 This is a book of full-color illustrations intended for use as a companion to Agricultural Production Economics, Second Edition. Each of the 9 pages of illustrations is a large, full-color version of the corresponding numbered figure in the book Agricultural Production Economics. The illustrations are each a labor of love by the author representing a combination of science and art. They combine modern computer graphics technologies with the author s skills as both as a production economist and as a graphics artist. Technologies used in making the illustrations trace the evolution of computer graphics over the past 3 years. Many of the hand-drawn illustrations were initially drawn using the Draw Partner routines from Harvard Graphics. Wire-grid 3-D illustrations were created using SAS Graph. Some illustrations combine hand-drawn lines using Draw Partner and the draw features of Microsoft PowerPoint with computer-generated graphics from SAS. As a companion text to Agricultural Production Economics, Second Edition, these color figures display the full vibrancy of the modern production theory of economics. This is one of three agricultural economics textbooks by David L. Debertin. Agricultural Production Economics (Second Edition, Amazon Createspace 1) is a revised edition of the Textbook Agricultural Production Economics published by Macmillan in 19 (ISBN --3-3). and a free pdf download of the entire book. As the author, I own the copyright. Amazon markets bound print copies of the book at amazon.com at a nominal price for classroom use. Bound paper copies of the book can also be ordered through college bookstores using the following ISBN numbers: ISBN or ISBN The third book is aimed at upper-division undergraduate students of microeconomics in agricultural economics and economics. It is a -page book titled Applied Microeconomics (Consumption, Production and Markets) and is a free download. Bound print copies are also available at amazon.com and through college bookstores at a nominal cost under the following ISBN numbers: ISBN 13: ISBN-1: This book Applied Microeconomics is much newer than Agricultural Production Economics, having been completed in 1. As the author, I would suggest downloading and studying this Applied Microeconomics book before diving into Agricultural Production Economics. This book uses spreadsheets to calculate numbers and draw graphs. Many of the examples and numbers are the same ones used in Agricultural Production Economics, so the two books are tied to each other.

4 If you have difficulty accessing or downloading any of these books, or have other questions, contact me at the address, below. David L. Debertin Professor Emeritus University of Kentucky Department of Agricultural Economics Lexington, Kentucky,

5 David L. Debertin is Professor Emeritus of Agricultural Economics at the University of Kentucky, Lexington, Kentucky and has been on the University of Kentucky Agricultural Economics faculty since 197 with a specialization in agricultural production and community resource economics. He received a B.S. and an M.S. degree from North Dakota State University, and completed a Ph.D. in Agricultural Economics at Purdue University in He has taught the introductory graduate-level course in agricultural production economics in each year he has been at the University of Kentucky. The first edition of Agricultural Production economics was published in hardback by Macmillan in 19. He began work on the second edition of the book after the Macmillan edition went out of print in 199, taking advantage of emerging two-and three-dimensional computer graphics technologies by linking these to the calculus of the modern theory of production economics. This is a book of full-color illustrations intended for use as a companion to Agricultural Production Economics, Second Edition. Each of the 9 pages of illustrations is a large, full-color version of the corresponding numbered figure in the book Agricultural Production Economics.

6 Agricultural Production Economics THE ART OFPRODUCTION THEORY DAVID L. DEBERTIN University of Kentucky This is a book of full-color illustrations intended for use as a companion to -page Agricultural Production Economics, Second Edition. Each of the 9 pages of illustrations is a large, full-color version of the corresponding numbered figure in the book kagricultural l Production Economics, Second Edition. The illustrations are each a labor of love by the author representing a combination of science and art. They combine modern computer graphics technologies with the author s skills as both as a production economist and as a technical graphics artist. Technologies used in making the illustrations ti trace the evolution of computer graphics over the past 3 years. Many of the handdrawn illustrations were initially drawn using the Draw Partner routines from Harvard Graphics. Wire-grid 3-D illustrations were created using SAS Graph. Some illustrations combine hand-drawn lines using Draw Partner and the draw features of Microsoft PowerPoint P with computer-generated graphics from SAS. As a companion text to Agricultural Production Economics, Second Edition, these color figures display the full vibrancy of the modern production theory of economics.

7 1 David L. Debertin Second Printing, December, 1 David L. Debertin University of Kentucky, Department of Agricultural Economics C.E.B. Bldg. Lexington, KY 5-77 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, without permission from the author. Debertin, David L. Agricultural Production Economics The Art of Production Theory 1. Agricultural production economics. Agriculture Economic aspects Econometric models ISBN- 13: ISBN- 1: 1719 BISAC: Business and Economics/Economics/Microeconomics

8 Price Supply p 1 p Demand (New Income) Demand (Old Income) q q 1 Quantity Figure 1.1 Supply and Demand y y = x y y=x y y=x.5 A x B x C x Figure.1 Three Production Functions 1

9 y C y = f(x) D y x B A x Figure. Approximate and Exact MPP

10 y or TPP Slope Equals MPP Equals Maximum APP Slope Equals Zero Maximum TPP Maximum APP TPP y = f(x 1 ) Slope Equals APP Inflection Point x x o * 1 1 MPP or APP Maximum MPP A Maximum APP B x 1 MPP APP MPP x 1 Figure.3 A Neoclassical Production Function 3

11 TPP 1 1 y = 13.9 TPP Maximum 1 y = 5.9 TPP y = 5.3 MPP Maximum Inflection Point APP Maximum MPP APP MPP = APP MPP Figure. TPP, MPP and APP for Corn (y) Response to Nitrogen (x) Based on Table.5 Data APP MPP x x

12 + MPP MPP (a) MPP (b) MPP (c) (d) f > f1 > MPP f MPP f1 MPP f 1 1 > > = f > f > f > f > 3 f = f3 < 3 MPP MPP (e) f1 > + f + (f) 1 > (g) f1 > f < f < f < f MPP > f = f3 < 3 3 MPP MPP MPP MPP MPP f1 f f + (h) < (i) 1 < (j) 1 < (k) f < MPP f < MPP f < MPP f < f < f = f3 > = 3 3 f MPP - MPP - MPP MPP - (l) + f1 < + (m) f1 < (n) f1 < f > MPP f > MPP f > f > f = f < 3 3 MPP MPP MPP MPP Figure.5 MPP s for the Production Function y = f(x) 5

13 y, MPP or APP E p >1 E p >1 < E p <1 E p < B A E p =1 APP C x - MPP Figure. MPP, APP and the Elasticity of Production

14 TVP $ py or ptpp TVP Inflection Point $ VMP = pmpp AVP = papp MFC VMP x MFC AVP x Figure 3.1 The Relationship Between TVP, VMP, AVP, and MFC 7

15 $ TVP TFC Maximum AVP Maximum Profit Parallel Zero Profit TFC Zero Slope Maximum TVP TVP Zero Profit Parallel Maximum VMP Inflection Point Minimum Profit Maximum Profit VMP AVP MFC $ Profit $ v o Minimum Profit VMP = MFC Maximum VMP x* VMP = MFC Maximum Profit Zero VMP x MFC =v o AVP = o p APP x VMP Minimum Profit Zero Profit x* Zero Profit x Profit Figure 3. TVP, TFC, VMP, MFC and Profit

16 $ TVP Profit 3 1 $ x TFC TVP 3 Profit 1 TFC Figure 3.3 TVP, TFC and Profit (Top and Second Panel) x 9

17 $ x Figure 3.3 TVP, TFC and Profit (Third Panel) AVP MFC.9 MFC.5.5 MFC VMP $ Figure 3.3 Profit Maximization under Varying Assumptions with Respect to Input Prices (Bottom Panel) x

18 y TPP Stage I Stage II Stage III A B C y x x APP MPP Figure 3. Stages of Production and the Neoclassical Production Function 11

19 $ D E Loss C B MFC Revenue Per Unit Cost Per Unit AVP A x* x VMP Figure 3.5 If VMP is Greater than AVP, the Farmer Will Not Operate $ VMP MFC MFC x VMP Figure 3. The Relationship Between VMP and MFC Illustrating the 1 Imputed Value of an Input

20 $ SRMC1 SRAC SRAC1 SRMC SRAC SRAC3 SRMC3 SRMC SRMC5 SRAC5 LRAC y Figure.1 Short and Long Run Average and Marginal Cost with Envelope Long Run Average Cost 13

21 $ TC VC or TVC Minimum slope of TC Inflection Point Minimum slope of TVC FC $ AC* y AVC* B MC AC AVC A 1 FC = k AFC* Figure. Cost Functions on the Output Side AFC y

22 $ AFC AC AC + AVC AFC AVC AFC MC Stage II Stage III AFC AFC AFC y* y MC - - Figure.3 Behavior of Cost Curves as Output Approaches a Technical Maximum y* 15

23 TC TR $ TVC p Parallel y Parallel FC $ y MC MR =p AC AVC Maximum Profit AFC y $ + Zero Profit Profit y - Minimum Profit 1 Figure. Cost Functions and Profit Functions

24 $ 5 TR TC VC 3 1 Maximum Profit Profit FC Zero Profit y = ~ y 7 $ MC 5 3 MR AC AVC 1 AFC y Figure.5 The Profit-Maximizing Output Level Based on Data Contained in Table.1 17

25 Y Maximum APP Maximum TPP Y 5 o TPP Maximum MPP (Inflection Point) $ X TC = vx $ TVC Y Minimum AVC X V v =priceofx Minimum MC (Inflection Point) X Y Figure. A Cost Function as an Inverse Production Function 1

26 MC = Supply $ AVC p 3 p p 1 y Figure.7 Aggregate Supply When the Ratio MC/AC = 1/b and b is less than 1 19

27 Corn Yield Y X 11 9 X 1 Figure 5.1 Production Response Surface Based on Data Contained in Table 5.1 X X Potash 1 Figure 5. Isoquants for the Production Surface in Figure 5.1 Based on Data Contained in Table 5.1

28 x x x 1 x x 1 x x 1 y x 1 Figure 5.3 Illustration of Diminishing MRS x 1 x 1

29 Figure 5. Isoquants and a Production Surface (Panel A) Figure 5. Isoquants and a Production Surface (Panel B)

30 Figure 5. Isoquants and a Production Surface (Panel C) Figure 5. Isoquants and a Production Surface (Panel D) 3

31 Figure 5. Isoquants and a Production Surface (Panel E) Y X Figure 5. Isoquants and a Production Surface (Panel F)

32 X Figure 5.5 Some Possible Production Surfaces and Isoquant Map A.The Production Surface 5 X Figure 5.5 Some Possible Production Surfaces and Isoquant Map B. The Isoquant Map 5

33 Y X 1 Figure 5.5 Some Possible Production Surfaces and Isoquant Map C. The Production Surface 1 X 1 Figure 5.5 Some Possible Production Surfaces and Isoquant Map D. The Isoquants

34 Y X Figure 5.5 Some Possible Production Surfaces and Isoquant Maps E. The Production Surface 1 1 X 1 Figure 5.5 Some Possible Production Surfaces and Isoquant Maps F. The Isoquants 7

35 Y X.3. Figure 5.5 Some Possible Production Surfaces and Isoquant Maps K. The Production Surface X Figure 5.5 Some Possible Production Surfaces and Isoquant Maps L. The Isoquants

36 Y X 1 Figure 5.5 Some Possible Production Surfaces and Isoquant Maps G. The Production Surface 1 X 1 Figure 5.5 Some Possible Production Surfaces and Isoquant Maps H. The Isoquants 9

37 Y X Figure 5.5 Some Possible Production Surfaces and Isoquant Maps I. The Production Surface 1. X Figure 5.5 Some Possible Production Surfaces and Isoquant Maps J. The Isoquants

38 3. x. Ridge Line for x x * 1 1. Ridge Line for x 1. x **. x *** x 1 y y = f (x 1 x *) y = f (x 1 x ** ) y = f ( x 1 x*** ) x Figure 5. Ridge Lines and a Family of Production Functions For Input x 1 31

39 Y Maximum A. The Surface X Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 1 1 X Maximum B. The Contour Lines 1 Figure.1 Alternative Surfaces and Contours Illustrating 3 Second Order Conditions

40 Y X Minimum C. The Surface Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 1 1 X Minimum D. The Contour Lines 1 Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 33

41 Y Saddle E. The Surface X 1 Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 1 X Saddle 3 1 F. The Contour Lines Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions

42 Y Saddle G. The Surface X Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 1 1 X Saddle H. The Contour Lines 1 Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 35

43 Y 7-17 Saddle I. The Surface X Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 5 X Saddle -1-3 J. The Contour Lines Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions

44 Y Saddle K. The Surface 1 X Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions X 3 1 Saddle I. The Contour Lines Figure.1 Alternative Surfaces and Contours Illustrating Second Order Conditions 37

45 Global Maximum Y Local Max Saddle Saddle Local Max 1 Surface 1 1 X Saddle Local Minimum Local Max Saddle Figure. Critical Values for the Polynomial y = x 1 1 x x 13.35x 1 + x 1 x + 1. x 3.35x 1 1 Contour Lines Figure. Critical Values for the Polynomial y = x 1 1 x x 1. x 3 35x +x +1x 3 35x 1.35x 1 x 1 x 1. x.35x

46 X 3. o C /v. Expansion Path v1 v o C /v Figure 7.1 Iso-outlay Lines and the Isoquant Map X 1 $ Global Profit Maximum (Pseudo Scale Lines Intersect) Global Output Maximum (Ridge Lines Intersect) Constrained Output Maxima (Bundle Allocated According to Expansion Path Conditions) Price of the Input Bundle Top Panel The Input Bundle X VMP of X Figure 7. Global Output and Profit Maximization for the Bundle 39

47 Global Output Maximum (Ridge Lines Intersect) Y 5 Global Profit Maximum (Pseudo Scale Lines Intersect) 17 Sample Isoquant (Constrained Maximum Below Global Output or Profit Maximum) Bottom Panel X Figure 7. Global Output and Profit Maximization for the Bundle

48 X Point on Pseudo Scale Line Point on Ridge Line x * $ Profit Maximum for x Holding 1 x constant at x * Output Maximum for x 1 Holding x constant at x * py = f (x 1 x * ) = TVP MFC = v VMP x x * 1 Figure 7.3 Deriving a Point on a Pseudo Scale Line 1

49 X Global 1 Profit Maximum 1 Global Output Maximum Isocost Lines X X Figure 7. The Complete Factor-Factor Model

50 Y Global Output Maximum 5 Global Profit Maximum 17 Constrained Output Maximum X Figure 7.5 Constrained and Global Profit and Output Maxima along the Expansion Path 3

51 Revenue, Profit Global Revenue Maximization $ 5 Global Profit Maximization Ridge Line Ridge Line 1 Pseudo Scale Line 153 Pseudo Scale Line X Total Revenue Surface 1 1 Profit Surface Figure.1 TVP- and Profit-Maximizing Surfaces 1 1 1

52 X 1 Global Output Max 1 1 Global Profit Max X X 1 Isorevenue Lines Isoprofit Lines Figure. Isorevenue and Isoproduct Contours 5

53 x Solution Isoquant y' Budget Constraint x 1 Figure.3 A Corner Solution

54 Y A 1 X B C Figure. A. Point B Less than A and C Y A B C X Figure. B. Point B Equal to A and C 7

55 Y 5 17 B 3 A C X Y Figure. C. Point B Greater than A and C 5 17 B 3 A C X Figure. D. Point B Greater than A and C 1

56 Y Y A B C A B C X X Y Y B 17 3 A B C 3 A C X X Figure. Constrained Maximization under Alternative Isoquant Convexity or Concavity Conditions 9

57 Land 1 Global Profit Maximum = 1 Global Output Maximum 1 = A B C L* L* R X X X (a bundle of all inputs but land) Figure.5 The Acreage Allotment Problem 5

58 x x A B C D A>AB>BC>CD AB > BC > CD x A B C D A<AB<BC<CD AB < BC < CD 3 1 x 1 x C D B 3 A 1 A = AB = BC = CD x 1 Figure 9.1 Economies, Diseconomies and Constant Returns to Scale For a Production Function with Two Inputs 51

59 1 X 1 Figure 1.1 Isoquants for the Cobb-Douglas Production Function 5

60 A. Surface y = x 1. x. 1 X 1 B. Isoquants y = x 1. x. Figure 1. Surfaces and Isoquants for the Cobb-Douglas Type Production Function 53

61 C. Surface y = x 1.1 x. 1 X 1 D. Isoquants y = x 1.1 x. Figure 1. Surfaces and Isoquants for the Cobb-Douglas 5 Type Production Function

62 E. Surface y = x 1. x. 1 X 1 F. Isoquants y = x 1. x. Figure 1. Surfaces and Isoquants for the Cobb-Douglas Type Production Function 55

63 G. Surface y = x x X 1 H. Isoquants y = x 1. x 1.5 Figure 1. Surfaces and Isoquants for the Cobb-Douglas Type Production Function 5

64 I. Surface y = x x X 1 J. Isoquants y = x x 1.5 Figure 1. Surfaces and Isoquants for a Cobb-Douglas Type Production Function 57

65 A. Surface 1 X B. Isoquants 1 5 Figure 11.1 The Spillman Production Function

66 3 - X Ridge Line Maximum Output Figure 11. Isoquants and Ridge Lines for the Transcendental, 1 = -; 1 = 3 = 59

67 X A. Surface B. Isoquants Figure 11.3 The Transcendental Production Function Under Varying Parameter Assumptions

68 C. Surface 3.9 X D. Isoquants Figure 11.3 The Transcendental Production Function Under Varying Parameter Assumptions 1

69 E. Surface X F. Isoquants Figure 11.3 The Transcendental Production Function Under Varying Parameter Assumptions

70 G. Surface.5 X H. Isoquants Figure 11.3 The Transcendental Production Function Under Varying Parameter Assumptions 3

71 I. Surface 1. X J. Isoquants Figure 11.3 The Transcendental Production Function Under Varying Parameter Assumptions

72 A. Surface X B. Isoquants Figure 11. The Polynomial y = x 1 + x 1.5 x 13 + x + x.5 x 3 +. x 1 x 5

73 F x M H D K B P Midpoint P 1 y* C J A E L G X 1 Figure 1.1 The Arc Elasticity of Substitution

74 A. Case 1 Surface 1 X B. Case 1 Isoquants 1 Figure 1. Production Surfaces and Isoquants for the CES Production Function under Varying Assumptions about 7

75 C. Case Surface 1 X x = -1/ (k/ D. Case Isoquants 1 x 1 = -1/ (k/ Figure 1. Production Surfaces and Isoquants for the CES Production Function under Varying Assumptions about

76 E. Case 3 Surface 1 X 1 F. Case 3 Isoquants Figure 1. Production Surfaces and Isoquants for the CES Production Function under Varying Assumptions about 9

77 G. Case Surface 1 X 1 J Case Isoquants Figure 1. Production Surfaces and Isoquants for the CES Production 7 Function under Varying Assumptions about

78 I. Case 5 Surface approaches -1 1 X 1 J. Case 5 Isoquants approaches -1 Figure 1. Production Surfaces and Isoquants for the CES Production Function under Varying Assumptions about 71

79 $ MFC1 MFC AVP Input (x) Demand MFC3 MFC x VMP Figure 13.1 The Demand Function for Input x (No Other Inputs) 7

80 x x x y" y' y" y' x x 1 1 A B C y' x y" 1 Figure 13. Possible Impacts of an Increase in the Price of x 1 on the use of x 73

81 $ Input (x) Demand AVP1 MFC1 AVP MFC MFC3 AVP3 VMP1 VMP x VMP3 1 Figure Demand for Input x 1 when a Decrease in the Price of x 1 Increases the Use of x 7

82 Maximum TR p Total Revenue TR = ay by Ep > 1 Ep = 1 Demand p = a - by Ep < 1 Ep = - Ep M T y Marginal Revenue MR = a - by Figure 1.1 Total Revenue, Marginal Revenue, and the Elasticity of Demand 75

83 $ $ o p TPP o p TPP TVP n p TPP TVP n p TPP A x o x n x x B x o x n $ o o p = p (y ) n n p = p (y ) o o y = y (x ) n n y = y(x ) TVP n o p TPP p TPP C x o x n x Figure 1. Possible TVP Functions Under Variable Product Prices 7

84 Guns Production Possibilities Curve for a Resource Bundle X o Butter Figure 15.1 A Classic Production Possibilities Curve 77

85 Corn (bu. per acre) 13 TPP 111 x (other inputs) Panel A Figure 15. Deriving i a Product Transformation Function from Two Production Functions 7

86 Soybeans (bu. per acre) 55 TPP x (other inputs) Panel B Figure 15. Deriving a Product Transformation Function from Two Production Functions 79

87 Soybeans (bu. per acre) x = Corn (bu. per acre) Panel C Figure 15. Deriving a Product Transformation Function from Two Production Functions

88 y y Supplementary Range Competitive y 1 Supplementary y 1 y Complementary Range y Complementary y 1 Joint y 1 Figure 15.3 Competitive, Supplementary, Complementary and Joint Products 1

89 X Y Y1 A. Surface ν approaches -1 1 Y 1 Y1 B. Isoproduct Contours ν approaches -1 Figure 15. Isoproduct Surfaces and Isoproduct Contours for a CES Type of Function, ν <-1

90 X Y C. Surface ν = - Y1 1 1 Y 1 Y1 D. Isoproduct Contours ν = - Figure 15. Isoproduct Surfaces and Isoproduct Contours for a CES Type of Function, ν <-1 3

91 X Y E. Surface ν = -5 Y1 1 1 Y 1 Y1 F. Isoproduct Contours ν = -5 Figure 15. Isoproduct Surfaces and Isoproduct Contours for a CES Type of Function, ν <-1

92 X Y G. Surface ν = - Y1 1 1 Y 1 Y1 H. Isoproduct Contours ν = - Figure 15. Isoproduct Surfaces and Isoproduct Contours for a CES Type of Function, ν <-1 5

93 Figure 1.1 A Family of Product Transformation Functions

94 1 Product Transformation Functions Y R o p Output Expansion Path Isorevenue Lines Y1 R o 1 p p 1 p 1 Figure 1. Product Transformation Functions, Isorevenue Lines and the Output Expansion Path 7

95 Tobacco Output Pseudo Scale Line for Tobacco Global Profit Maximum 1 Output Expansion Path A Output Pseudo Scale Line For Other Crops (Y) T* B C 1 1 Y Figure 1.3 An Output Quota

96 Forage (z ) Isoquants for Beef Production MRS x1 x = RPT z 1 z Product Transformation Function for Grain and Forage Grain (z ) 1 Forage (z ) Sell Produce p Isocost or Isorevenue z 1 p Line z Produce Purchase Grain (z ) 1 Figure 17.1 An Intermediate Product Model 9

97 $ per bu. B C M C AC AVC MR = Price of Corn A Output of Corn Figure 19.1 Output of Corn and Per Bushel Cost of Production 9

98 Probabilities and Outcomes are Known Probabilities And Outcomes Are not known Risky Events Uncertain Events Figure.1 A Risk and Uncertainty Continuum 91

99 Utility Utility Risk-Averse Utility Income Risk-Neutral Income Risk-Preferrer Income Figure. Three Possible Functions Linking Utility to Income 9

100 Expected Income Expected Income Risk-Averse Income Variance Risk-Neutral Income Variance Expected Income Risk Preferrer Income Variance Figure.3 Indifference Curves Linking the Variance of Expected Income with Expected Income y Curve B Curve A Curve C Figure. Long Run Planning: Specialized and Non-Specialized Facilities 93 y 1

101 y 1 Constraint 1 (Amount of x 1 Available) 1 /3 y Feasible Region Constraint (Amount of x Available) 5 Product Transformation Function Objective Function Feasible Region /3 y Figure.1 Linear Programming Solution in Product Space 9

102 x 3 Constraint Isoquant Isoquant Feasible Region Feasible Constraint 1 Objective Function x Figure. Linear Programming Solution in Factor Space 95

103 x x Diagram A x x 1 x 1 Diagram B Diagram C x 1 9 Figure 3.1 Some Possible Impacts of Technological Change

104 X X Assumption 1 Holds Assumption 1 Fails X 1 X 1 X X Assumption Fails X 1 Assumption Holds X 1 Figure.1 Assumptions (1) and () and the Isoquant Map 97

105 X X P 1 P X X 1 X 1 X 1 Figure. A Graphical Representation of the Elasticity of Substitution 9