Maximizing Profits in Agricultural Production: Marginal Analysis and Economic Principles

1. Farm Management Chapter 7 Economic Principles Choosing Production Levels

2. Chapter Outline • The Production Function • Marginal Analysis • Law of Diminishing Marginal Returns • How Much Input to Use • Using Marginal Concepts • Marginal Value Product and Marginal Input Cost • Equal Marginal Principle

3. Chapter Objectives • Explain the concept of marginalism • Show the relation between a variable input and output by use of a production function • Describe the concepts of average and marginal physical products • Illustrate the law of diminishing returns • Find the profit-maximizing point using marginal concepts • Explain the use of the equal marginal principal

4. The Production Function The production function is a systematic way of showing the relation between different amounts of a resource or input that can be used to produce a product and the corresponding output.

5. Figure 7-1Example of the production process in agriculture Insert figure 7-1 here, no title

6. Table 7-1 Production Function in Tabular Form Note that TPP is the portion of yield attributed to nitrogen use.

7. Total Physical Product Total physical product (TPP) is the amount of production expected from using each input level. Output or yield is often called total physical product.

8. Average Physical Product Average physical product (APP) is the average amount of output produced per unit of input used. APP = TPP input level

9. Marginal Analysis The term marginal refers to incremental changes, either increases or decreases, that occur at the edge or at the “margin.” It may help to mentally substitute “extra” or “additional” whenever the word marginally is used. But keep in mind that the “extra” can be negative.

10. Marginal Physical Product Marginal physical product (MPP) is the additional TPP produced by using an additional unit of input. MPP = TPP input level

11. Law of Diminishing Marginal Returns As additional units of a variable input are used in combination with one or more fixed inputs, marginal physical product will eventually begin to decline. Diminishing returns may start with the first unit of input used, or may start later after a period of increasing returns.

12. Figure 7-2 Graphical illustration of a production function

13. Stages of Production • Stage I: APP increasing, MPP>APP, TPP increasing • Stage II: APP decreasing, MPP<APP, TPP increasing • Stage III: TPP decreasing, MPP<0

14. How Much Input to Use • Do not produce in Stage III, because more output can be produced with less input. • Do not normally produce in Stage I because the average productivity of the inputs continues to rise in this stage. • Stage II is the “rational stage” of production.

15. Total Cost and Total Revenue • Multiply the amount of a variable input by its price per unit to get the variable cost for that input. • Add the variable cost(s) for the input(s) to the fixed costs to get Total Cost (TC). • To find Total Revenue (TR), multiply the output level by the output price per unit. • The accounting profit is the difference between TR and TC.

16. Table 7-2 Total Cost, Total Revenue, and Profit nitrogen price = $.25; corn price = $2.50

17. Using Marginal Concepts • Profit-maximizing level of input can be found by examining marginal changes in costs and revenues • Marginal revenue is the change in total revenue from selling one more unit of output • Marginal cost is the additional cost of producing that additional unit of output

18. Marginal Revenue  total revenue MR =  total physical product If output price is constant: MR = output selling price

19. Marginal Cost  total cost MC =  total physical product

20. The Decision Rule MR=MC The decision rule, MR=MC, leads to the profit-maximizing point. If data in a table is such that this point can’t be found exactly, use the closest point, without letting MR fall below MC.

21. Table 7-3 Marginal Revenue, Marginal Cost and the Optimum Output nitrogen price = $.25; corn price = $2.50

22. Table 7-4 Marginal Revenue and Marginal Cost Under Varying Prices

23. If output and input prices are constant, then the rule MR=MC is equivalent to MPP = where Pi is the input price and Po is the output price Pi ____ Po Price Ratios and Profit Maximization

24. Marginal Value Product and Marginal Input Cost • Marginal Value Product (MVP) is the change in revenue associated with increasing input use by one unit • Marginal Input Cost is the cost of buying one more unit of input (which will equal the input price if it doesn’t change as additional input is purchased) • The decision rule is MVP=MIC

25. Equal Marginal Principal In some situations an input may be limited so that the profit-maximizing point cannot be reached for all possible uses. A limited input should be allocated among competing uses in such a way that the marginal value products of the last unit used on each alternative are equal.

26. 4th 2nd 1st 5th 3rd 6th Table 7-5 Application of the Equal Marginal Principle to the Allocation of Irrigation Water Each application of 4 acre-inches is a total use of 400 acre inches.

27. Figure 7-3 Illustration of the equal marginal system

28. Figure 7-4 Optimal selling weight for beef cattle Insert figure 7-4 here, no title

29. Summary Economic principles using the concept of marginality provide useful guidelines for decision making. MVP and MIC are equated to find the profit-maximizing input level. MR and MC are equated to find the profit-maximizing output level. The equal marginal principle is used when a limited input must be allocated among competing uses.