1. Producer Decision Making
Two - Variable Inputs and
Enterprise Selection
Chapter 5

2. Three Types of Relationships Producers Must Understand
1 Factor - Product relationship deals with choosing the level of an input, in order to be efficient.
2 Factor - Factor relationship deals with choosing between competing factors.
3 Product - Product relationship deals with choosing between competing products.

3. Factor - Factor Choosing the optimal proportion of the
inputs in order to efficiently produce
output.

4. Two-Variable Input Functions
A two - variable input production function can take on
the following form:
amounts
Y = f (X1, X2) where X1 and X2 can vary in

5. Two-Variable Input Functions
A two - variable input production function can also
take on another form:
Y = f (X1, X2 X3, X4) where X1 and X2 can vary
in amounts and X3, X4 are
fixed.

6. Isoproduct Contours X2 . A . B . C
(Isoquants) . D . E Y X1

7. Isoproduct Contours X2
Perfect Substitutes Y X1

8. Isoproduct Contours Perfect Substitutes
Perfect substitutes are able to replace one another
without affecting output.
For every unit decrease in one input a constant unit
increase in the other input will hold output at the
same level.
Example : Water From Well 1 and Water
from Well 2

9. Isoproduct Contours X2
Perfect Complements Y X1

10. Isoproduct Contours Perfect Complements
Perfect Complements must be used in a constant
proportion to be efficient.
Therefore, an additional amount of one resource will do
nothing for output. There is no decision for the
determining the ratio of use.
Example: Tractor and Plow.

11. Isoproduct Contours X2
Imperfect Substitutes Y X1

12. Imperfect Substitutes
The most common problem faced by producers. Factors
will substitute for one another, but not at a
constant rate.
Successive equal incremental reductions in one
input, must be matched by increasingly larger
increases in the other input in order to hold output
constant.
This is what gives the curved shape to the isoquant.

13. Imperfect Substitutes
Example: Land and Fertilizer
As we decrease available land, we must use
increasingly more fertilizer to make up for the
lost land.

14. Imperfect Substitutes
Land
Fertilizer 10
100 9
220 8
360 7
520 6
700

15. Marginal Rate of Substitution
Is the rate at which resources substitute for
one another.

16. Marginal Rate of Substitution
Is the rate at which resources substitute for
one another. ∆ ∆
MRTS X1,X2 = X2 / X1
This ignores the sign

17. Marginal Rate of Substitution
Diminishing Marginal Rate of Substitution - as one input is increased one unit at a time, the units of the other inputs needed to produce the same level of output become fewer.

18. Diminishing Marginal Rate of SubstitutionX2 ∆ X2 Y X1 ∆ X1

19. Diminishing Marginal Rate of SubstitutionX2 ∆ X2 Y X1 ∆ X1

20. Diminishing Marginal Rate of SubstitutionX2 ∆ Y X2 X1 ∆ X1

21. Diminishing Marginal Rate of SubstitutionX2 ∆ X2
Y=50
Y=25 X1

22. What is the Optimum or Least Cost Combination of inputs to use?
Water
100 lbs. Cotton
Fertilizer

23. Least Cost Combination
Water
Fertilizer $ .50 lb
125
Water $ .10 Gallon
$ 10 spent on inputs
100 75 50 25
100 lbs. Cotton
Fertilizer

24. Least Cost Combination
Water
Fertilizer $ .50 lb
125
Water $ .10 Gallon
$ 10 spent on inputs
100 75 50 . 25
100 lbs. Cotton
Fertilizer

25. Least Cost Combination
Water
Fertilizer $ .50 lb .
Water $ .10 Gallon
125
$ 10 spent on inputs
100 75 50 25 .
100 lbs. Cotton
Fertilizer

26. Least Cost Combination
Water
Fertilizer $ .50 lb .
125
Water $ .10 Gallon
$ 10 spent on inputs
100 75 50 25 .
100 lbs. Cotton
Fertilizer

27. Least Cost Combination
Water
Fertilizer $ .50 lb .
125
Water $ .10 Gallon
100
$ 10 spent on inputs 75
Optimal input level .
12 lbs. Fertilizer 50
40 Gal. Water . 25
100 lbs. Cotton
Fertilizer

28. . . . Change in Price of input Water Fertilizer $ .50 lb 125
Water $ .20 Gallon
100
$ 10 spent on inputs 75 .
Optimal input level
16 lbs. Fertilizer 50
10 Gal. Water . 25 .
100 lbs. Cotton
Fertilizer

29. . . . Change in Price of input Water Fertilizer $ .50 lb 125
80 lbs. Cotton
Water $ .20 Gallon
100
$ 10 spent on inputs 75 .
Optimal input level
16 lbs. Fertilizer 50
10 Gal. Water . 25 .
100 lbs. Cotton
Fertilizer

30. Product - Product
Choosing the optimal combination of products to produce given fixed amounts of land, labor, capital and management.

31. Product - Product
Production Possibilities - The full range of products a farm can produce given the set of resources in the farm's control.

32. Product - Product Soybeans 1000 Bushels 7 6 5 4 3 2 1 2 4 6 8 10 12
Grain Sorghum 1000 bushels

33. Product - Product Marginal Rate of Product Substitution
Measures the differing rates at which either of
the products will replace (substitute for) the
other along the production possibilities curve.

34. Product - Product MRPS Y1 Y2 = Y2 / Y1
Marginal Rate of Product Substitution
Measures the differing rates at which either of
the products will replace (substitute for) the
other along the production possibilities curve.
MRPS Y1 Y2 = Y2 / Y1

35. Product - Product Y2 Y2 7 Y1 6 5 4 3 2 1 Y1

36. . Product - Product Soybeans 1000 Bushels 7 6 A 5 4 3 2 1
Grain Sorghum 1000 bushels

37. . Product - Product Soybeans 1000 Bushels 7 6 5 4 3 B 2 1
Grain Sorghum 1000 bushels

38. Product - Product Isorevenue Line— Finding the optimum combination
Soybeans 1000 Bushels
Isorevenue Line— Finding the optimum combination 7 6 5
Price Grain Sorghum $2.50 4
Price Soybeans $3.75 3 2 1
Grain Sorghum 1000 bushels

39. . Isorevenue Line Soybeans 1000 Bushels 7 Price Grain Sorghum $2.50 6
Price Soybeans $3.75 5
Isorevenue Line $22,500 4
$22,500
= 6,000 SB 3
$3.75 2 1
Grain Sorghum 1000 bushels

40. . . Isorevenue Line Soybeans 1000 Bushels Price Grain Sorghum $2.50 7
Price Soybeans $3.75 6
Isorevenue Line $22,500 5
$22,500
= 9,000 GS 4
$2.50 3 2 . 1
Grain Sorghum 1000 bushels

41. . . Isorevenue Line Soybeans 1000 Bushels 7 Price Grain Sorghum $2.506
Price Soybeans $3.75 5
Isorevenue Line $22,500 4
Slope = PY1 3
PY2 2 . 1
Grain Sorghum 1000 bushels

42. Isorevenue Line Soybeans 1000 Bushels 7 Price Grain Sorghum $2.50 6
Price Soybeans $3.75 5 4 3 2 1
Grain Sorghum 1000 bushels

43. Isorevenue Line Soybeans 1000 Bushels Price Grain Sorghum $2.50 7
Price Soybeans $3.75 6 5 4 3 2 1
Grain Sorghum 1000 bushels

44. Point of Revenue Maximization
Y2 / Y1 = PY1 / PY2 Y2 Y2 Y1
PY1 / PY2 Y1

45. . Isorevenue Line - Optimum Soybeans 1000 Bushels
Price Grain Sorghum $2.50 7
Price Soybeans $3.75 6
Farmer would produce 5
9,000 bushels GS .
4,000 bushels SB 4
Revenue = ? 3 2 1
Grain Sorghum 1000 bushels

46. . Isorevenue Line - Optimum Soybeans 1000 Bushels
Price Grain Sorghum $2.50 7
Price Soybeans $3.75 6
Farmer would produce 5
9,000 bushels GS .
4,000 bushels SB 4
Revenue = $37,500 3 2 1
Grain Sorghum 1000 bushels