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Chapter 6: Agricultural Production Economics

Chapter 6: Agricultural Production Economics. Production with One Input and One Output. A Production Function:. Transformation of. input into output. A technical relationship. ( not behavioral ). Output:. Corn. Tobacco. Wheat. Beef. Milk. JOHN DEERE. Input:. Seed. FERTILIZER.

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Chapter 6: Agricultural Production Economics

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  1. Chapter 6: Agricultural Production Economics Production with One Input and One Output

  2. A Production Function: Transformation of input into output A technical relationship (not behavioral)

  3. Output: Corn Tobacco Wheat Beef Milk

  4. JOHN DEERE Input: Seed FERTILIZER 11-48-0 Fertilizer P205 N K20 Feed Machinery

  5. Fixed versus Variable Inputs Fixed-- Farmer does not expect ? to vary ? ? Over the planning horizon ? Variable-- Farmer expects to vary ? Over the planning horizon ?

  6. Length of Planning Horizon: in the mind of the farmer 6 months? The Growing Season? 2 years? 10 years (for Christmas trees)? Only the farmer knows for sure 6 months ? 2 years ? 50 years ?

  7. JOHN DEERE Old idea-- Inputs could be categorized Land--fixed Labor--variable Machinery--fixed (sort of!) Not a correct idea

  8. Correct idea: Planning horizon determines whether inputs are fixed or variable Short Run--All inputs fixed Intermediate Run--Some fixed, some variable Long Run--All inputs variable

  9. Inputs: Traditional list Land Labor Capital Management

  10. With capital you can purchase land and labor Is management an input??

  11. A Production Function: Y = f(X) Y = output such as bu. of corn X = input such as fertilizer X into Y f(x) = rule for transforming such as: Y = 3X 0.5 Y = X 2 3 Y = .3X + .05X - .002X Each of these are production functions

  12. Y = f(X | X X X ) 1 2 3 4 The output The Variable input Inputs treated as fixed Y Y or TPP TPP = Total Physical Product X | X X X 3 1 2 3 4

  13. Y Y''' Y'' Y or TPP Y' X | X X X X'' X''' X' 1 2 3 4 1 1 1 Specific amount of output from a specific amount of input

  14. Marginal Product The incremental change in output associated with a 1 unit change in the use of the input

  15. Marginal Product of input x: y = change in y x = change in x y = change in y = Marginal Product x = change in x Also called Marginal Physical Product or MPP for short

  16. Diminishing, Constant and Increasing Marginal Product

  17. Case 1: Constant Marginal Product

  18. Constant Marginal Product (y) Output y Constant slope 8 6 4 2 0 (x) Input 3 2 1 4

  19. Constant Marginal Product (y) Output = 2x y Constant slope 8 2 Triangles all the 6 1 same size and slope 2 4 1 unit across 1 2 2 units up 2 1 2 1 0 (x) Input 3 2 1 4

  20. Constant Marginal Product (y) Output = 2x y Constant slope 8 2 Each additional 6 1 unit of X 2 produces two 4 1 additional units 2 of Y 2 1 2 1 0 (x) Input 3 2 1 4

  21. (y) Output y =bx Constant slope of b b Each additional b unit of x produces b b 1 additional Units b of y b 1 b The Marginal Product of an 1 b additional unit b of x is b 1 0 (x) Input 3 2 1 4 Constant Marginal Product of b

  22. Constant Marginal Product MPP x y/ x x y y

  23. Constant Marginal Product MPP x y / x x y y 0 0 1 2 2 4 3 6 4 8 5 10

  24. Constant Marginal Product MPP x y / x x y y 0 0 1 1 2 1 2 4 1 3 6 1 4 8 1 5 10

  25. Constant Marginal Product MPP x Y / x x y y 0 0 2 1 1 2 2 1 2 4 2 1 3 6 2 1 4 8 1 2 5 10

  26. Constant Marginal Product MPP x Y / x x y y 0 0 2 2/1 1 1 2 2 1 2/1 2 4 2 2/1 1 3 6 2 2/1 1 4 8 2/1 1 2 5 10 MPP = 2 everywhere

  27. Constant MPP b = Marginal y = b Product of an x Additional Unit of x y = bx y b x

  28. Case 2: Increasing Marginal Product

  29. (y) Output 11 Increasing marginal returns 4.5 to the variable 6.5 input 3 1.5 3.5 2 1.3 0.7 0.7 (x) Input 3 5 2 1 4 0 Increasing Marginal Product

  30. Increasing Marginal Product MPP x Y / x x y y 0 0 1 0.7 2 2.0 3 3.5 4 6.5 11.0 5

  31. Increasing Marginal Product MPP x Y / x x y y 0 0 1 1 0.7 1 2 2.0 1 3 3.5 1 4 6.5 1 11.0 5

  32. Increasing Marginal Product MPP increases as x increases MPP x Y / x x y y 0 0 .7 1 1 0.7 1.3 1 2 2.0 1.5 1 3 3.5 3. 1 4 6.5 4.5 1 11.0 5

  33. Increasing Marginal Product MPP increases as x increases MPP x Y / x x y y 0 0 .7 1 .7/1 1 0.7 1.3 1.3/1 1 2 2.0 1.5 1.5/1 1 3 3.5 3. 3.0/1 1 4 6.5 4.5 1 4.5/1 11.0 5

  34. Case 3: Decreasing (Diminishing) Marginal Product

  35. Decreasing (Diminishing) Marginal Product (y) Output y = f(x) 8.8 .3 8.5 1 .5 Slope increases 8 1 1 but at a 7 1 decreasing rate 2 Additional units 5 1 of x produce less and less 5 additional y 1 (x) Input 5 3 2 1 4 0

  36. Decreasing Marginal Product MPP x y / x x y y

  37. Decreasing Marginal Product MPP x y / x x y y 0 0 1 5 2 7 3 8 4 8.5 5 8.8

  38. Decreasing Marginal Product MPP x y / x x y y 0 0 1 1 5 1 2 7 1 3 8 1 4 8.5 1 5 8.8

  39. Decreasing Marginal Product MPP x y / x x y y 0 0 5 1 1 5 2 1 2 7 1 1 3 8 0.5 1 4 8.5 1 0.3 5 8.8

  40. Decreasing Marginal Product As the use of x increases, MPP decreases MPP x y / x x y y 0 0 5 1 5/1 1 5 2 1 2/1 2 7 1 1 1/1 3 8 0.5 1 .5/1 4 8.5 1 0.3 .3/1 5 8.8

  41. X | X X X X A Neoclassical Production Function 1 2 3 4 5

  42. X | X X X X A Neoclassical Production Function Y 1 2 3 4 5

  43. X | X X X X A Neoclassical Production Function Y Increasing MPP (and TPP) 1 2 3 4 5

  44. X | X X X X A Neoclassical Production Function Y Inflection Point Increasing MPP (and TPP) 1 2 3 4 5

  45. X | X X X X A Neoclassical Production Function Y Decreasing MPP Increasing TPP Inflection Point Increasing MPP (and TPP) 1 2 3 4 5

  46. X | X X X X A Neoclassical Production Function Maximum TPP 0 MPP Y Decreasing MPP Increasing TPP Inflection Point Increasing MPP (and TPP) 1 2 3 4 5

  47. X | X X X X A Neoclassical Production Function Maximum TPP 0 MPP Y Decreasing MPP Negative MPP Increasing TPP Declining TPP Inflection Point Increasing MPP (and TPP) 1 2 3 4 5

  48. Law of Diminishing (Marginal) Returns As units of the variable input (X ) 1 are added to units of the fixed inputs ( X , X , X , X ) 2 3 4 5 we eventually reach a point where each ADDITIONAL unit of the variable input (X ) 1 produces Less and Less ADDITIONAL output!

  49. X | X X X X Maximum TPP 0 MPP Y Decreasing MPP Negative MPP Increasing TPP Declining TPP Inflection Point Increasing MPP Law of Diminishing (and TPP) Returns holds Starting Here 1 2 3 4 5

  50. X | X X X X Maximum TPP 0 MPP Y Decreasing MPP Negative MPP Declining TPP Increasing TPP Inflection Increasing MPP Point (and TPP) 1 2 3 4 5

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