Chapter 8: Production with Two Inputs or Outputs

1. Chapter 8: Production with Two Inputs or Outputs Agricultural Production Economics: Two Inputs or Two Outputs

2. Factor-Factor Relationships Two Inputs, One Output

3. Production Function: Y = f(X ,X |X , X , X ) 1 2 3 4 5 Fixed inputs Variable inputs Output (TPP) * *Total Physical Product

4. Isoquant (equal quantity) X 2 All points on isoquant are the same level of output (like an indifference curve) Y* X 1

5. Isoquants are bowed inward because of the law of X diminishing (marginal) returns 2 Inputs are more productive when used with each other Y* X 1

6. Types of Isoquants: Phosphate 33% N Ammonium Nitrate Tractors Ammonia Nitrogen Tractor Drivers 82 % N Imperfect Substitutes Perfect Substitutes Fixed Proportion (the normal case)

7. Marginal Rate of Substitution MRSx1x2 = x2/ x1 The slope of the isoquant X 2 is the rate at which inputs Nitrogen substitute for each other Fert- izer along the isoquant X2 X1 Corn (100 bu.) Y* Phosphate Fertilizer X 1

8. Marginal Rate of Substitution MRSx1x2 = x2 / x1 Not constant, but the slope varies along the isoquant: nitrogen and phosphate fertilizers are not perfect substitutes!

9. Isocost (Budget Line) for Fertilizer X 2 $30 cash outlay Phosphate $0.30/lb Nitrogen Nitrogen $0.15/lb Fert- Could purchase with $30 izer O either 100 lb P 2 5 or 200 lb N or some combination! Phosphate Fertilizer X 1

10. Isocost (Budget Line) for Fertilizer X 2 $30 cash outlay 200 lb Nitrogen Phosphate $0.30/lb 150 lb Nitrogen Nitrogen Nitrogen $0.15/lb 25 lb Phosphate Fert- Could purchase with $30 izer O either 100 lb P 2 5 or 200 lb N or some combination! 75 lb Phosphate 50 lbs Nitrogen 100 lb Phosphate Phosphate Fertilizer X 1

11. Superimposing the Isoquant on the Budget Line: X 2 Nitrogen 200 lb Nitrogen Fert- 150 lb Nitrogen izer 25 lb Phosphate X2 X1 75 lb Phosphate 50 lbs Nitrogen Corn (100 bu.) Y* 100 lb Phosphate Phosphate Fertilizer X 1

12. Superimposing the Isoquant on the Budget Line: Slope of Isocost = Price of Phosphate - Price of Nitrogen X Nitrogen 2 Nitrogen Slope of Isoquant = 200 lb Nitrogen - Phosphate Fert- 150 lb Nitrogen izer 25 lb Phosphate X2 75 lb Phosphate X1 50 lbs Nitrogen Corn (100 bu.) Y* 100 lb Phosphate X1 Phosphate Fertilizer

13. Superimposing the Isoquant on the Budget Line: Slope of Isocost = Price of Phosphate - Price of Nitrogen X Nitrogen 2 Nitrogen Slope of Isoquant = 200 lb Nitrogen - Phosphate Fert- 150 lb Nitrogen where Optimum Combination 25 lb Phosphate izer Nitrogen Price of Phosphate = Phosphate Price of Nitrogen X2 75 lb Phosphate X1 50 lbs Nitrogen Corn (100 bu.) Y* 100 lb Phosphate Phosphate Fertilizer X 1

14. X 2 Nitrogen where Optimum Combination Fert- Nitrogen Price of Phosphate = izer Phosphate Price of Nitrogen Point of Tangency 80 lbs Corn (100 bu.) Y* 60 lbs Phosphate Fertilizer X 1

15. Isoquant Map For various corn yields X 2 Nitrogen Fert- Corn (160 bu.) izer ) Corn ( 140 bu. 80 lbs Corn (120 bu.) Corn (100 bu.) 60 lbs Phosphate Fertilizer X 1

16. Now Superimpose Isocost (budget) lines (same slope-- different outlays) X 2 Nitrogen Fert- Corn (160 bu.) izer ) Corn ( 140 bu. 80 lbs Corn (120 bu.) Corn (100 bu.) 60 lbs Phosphate Fertilizer X 1

17. Points of Tangency X 2 Nitrogen Fert- Corn (160 bu.) izer ) Corn ( 140 bu. 80 lbs Corn (120 bu.) Corn (100 bu.) 60 lbs Phosphate Fertilizer X 1

18. Expansion Path X 2 Nitrogen Fert- Corn (160 bu.) izer ) Corn (140 bu. 80 lbs Corn (120 bu.) Corn (100 bu.) 60 lbs Phosphate Fertilizer X 1

19. Selection of Combinations of Farm Enterprises

20. Product-Product Relationships Two Products One Variable Input

21. Production Function for Corn and Soybeans 150 bu Yield of Yield of Corn Soybeans 45 bu Input X Input X Phosphate Phosphate Corn Yields Higher than Soybean Yields

22. 150 bu Yield of Yield of Corn Soybeans 45 bu 100 lbs 100 lbs Input X Input X Phosphate Phosphate Assume: Farmer has 100 lbs Phosphate total How should it be allocated between corn and soybean production? Depends on prices of corn & soybeans

23. Data from Production Functions Total Phosphate Phosphate Soybean Corn Phosphate on on Yield Yield Used Corn Soybeans bu/Acre bu/Acre

24. Data from Production Functions Total Phosphate Phosphate Soybean Corn Phosphate on on Yield Yield Used Corn Soybeans bu/Acre bu/Acre 0 100 100 135 0 100 80 20 133 20 40 28 125 100 60 60 35 110 100 40 60 41 100 20 80 45 100 0 100 0

26. Pounds phosphate applied to each crop 0,100 20,80 40,60 60,40 80,20 100,0

27. Production Possibilities from 100 lbs. Phosphate 0,100 20,80 40,60 60,40 80,20 100,0

28. Assume: Price of Corn $3.00/bu Price of Soybeans $8.00/bu Isorevenue Line All combinations of Corn and Soybeans that Produce the Same Total Revenue for example, $1000 could be produced from 125 bushels soybeans or 333 1/3 bushels corn Other possibilities????

29. Corn 333 1/3 bu. Isorevenue for $1000 total revenue Soybean Price 8 Corn Price 3 125 bu. Soybeans

30. Now Bring Back Production Possibilities Curve

31. Production Possibilities from 100 lbs. Phosphate

32. Isorevenue line slope 8/3 8 3

33. Keep Pushing Isorevenue Line Outward Isorevenue line slope 8/3 8 3

34. Solution: 60 lbs Phosphate to Soybeans 40 lbs Phosphate to Corn Point of Tangency 60,40 8 3

35. Output Expansion Path

36. Output Expansion Path: Connects points of tangency between the Product Transformation Curve and the isorevenue lines This is a path along which the firm would expand as production of the two outputs is increased.

37. The slope of Product Transformation Curve equals the negative of the Rate of Product Transformation. The slope of the Isorevenue Line equals the negative ratio of the output prices. At the point of tangency between the Product Transformation Curve and the Isorevenue Line, the slope of the Product Transformation Curve and the slope of the Isorevenue Line are equal. The Output Expansion Path connects all of these points.

38. The Rate of Product Transformation (RPT) is the negative of the slope of the Product Transformation Curve. Hence, the Rate of Product Transformation is Corn Soybeans At the point of tangency between the Product Transformation Curve and the Isorevenue Line Price of Soybeans Corn = Soybeans Price of Corn For a specific input, or resource level, this is the optimum amount of corn and soybeans to be produced.