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Farm Management

Chapter 7Economic Principles—

Choosing Production Levels

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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

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Chapter Objectives1. Explain the concept of marginalism2. Show the relation between a variable input

and output by use of a production function3. Describe the concepts of average and

marginal physical products4. Illustrate the law of diminishing returns5. Find the profit-maximizing point using

marginal concepts6. Explain the use of the equal marginal

principal

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The Production Function

The production function is a systematicway of showing the relation between different amounts of a resource orinput that can be used to produce aproduct and the corresponding output.

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Table 7-1 Production Function in Tabular Form

Total Average MarginalNitrogen physical physical physical

Input applied Yield product product productlevel (lbs.) (bu.) (TPP) (APP) (MPP)

0 0 130 0 -- --1 25 148 18 18.00 182 50 162 32 16.00 143 75 170 40 13.33 84 100 177 47 11.75 75 125 180 50 10.00 36 150 182 52 8.67 27 175 183 53 7.57 18 200 183 53 6.63 0

Note that TPP is the portion of yield attributed tonitrogen use.

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Total Physical Product

Total physical product (TPP) is theamount of production expected from using each input level. Output oryield is often called total physical product.

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Average Physical Product

Average physical product (APP) is the average amount of output produced per unit of input used.

APP = TPP

input level

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Marginal Analysis

The term marginal refers to incrementalchanges, 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 marginallyis used. But keep in mind that the “extra”can be negative.

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Marginal Physical Product

Marginal physical product (MPP) is the additional TPP produced by using an additional unit of input.

MPP = TPP

input level

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Law of Diminishing Marginal Returns

As additional units of a variable inputare used in combination with one ormore fixed inputs, marginal physicalproduct will eventually begin to decline.

Diminishing returns may start with thefirst unit of input used, or may startlater after a period of increasing returns.

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Figure 7-2 Graphical illustration of a production function

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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

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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.

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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.

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Table 7-2 Total Cost, Total Revenue, and Profit

nitrogen price = $.25; corn price = $2.50

Nitrogen Total Total

Input applied Yield cost revenue Profit ($)level (lbs.) (bu.) (TC) $ (TR) $ (TR-TC)

0 0 130 400.00 325.00 (75.00)1 25 148 406.25 370.00 (36.25)2 50 162 412.50 405.00 (7.50)3 75 170 418.75 425.00 6.254 100 177 425.00 442.50 17.505 125 180 431.25 450.00 18.756 150 182 437.50 455.00 17.507 175 183 443.75 457.50 13.758 200 183 450.00 457.50 7.50

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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

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Marginal Revenue

MR = total revenue

total physical product

If output price is constant:

MR = output selling price

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Marginal Cost

MC = total cost

total physical product

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The Decision Rule

MR=MC

The decision rule, MR=MC, leads to theprofit-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.

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Table 7-3 Marginal Revenue, Marginal Cost

and the Optimum Output

nitrogen price = $.25; corn price = $2.50

Margnal Marginal MarginalNitrogen physical Total Total revenue cost

Input applied Yield product revenue cost (MR) ($) (MC) ($)level (lbs.) (bu.) (MPP) (TR) $ (TC) $ (ΔTR/ΔTPP) (ΔTC/ΔTPP)

0 0 130 -- 325.00 400.00 -- --1 25 148 18 370.00 406.25 2.5 > 0.352 50 162 32 405.00 412.50 2.5 > 0.453 75 170 40 425.00 418.75 2.5 > 0.784 100 177 47 442.50 425.00 2.5 > 0.895 125 180 50 450.00 431.25 2.5 > 2.086 150 182 52 455.00 437.50 2.5 < 3.137 175 183 53 457.50 443.75 2.5 < 6.258 200 183 53 457.50 450.00

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Table 7-4 Marginal Revenue and Marginal Cost

Under Varying Prices

Marginal Marginal Marginal MarginalNitrogen Total Total revenue cost revenue cost

Input applied Yield revenue cost (MR) ($) (MC) ($) (MR) ($) (MC) ($)level (lbs.) (bu.) (TR) $ (TC) $ (corn price =$2.50) (N price = $.50)) (corn price =$3.50) (N price =$.25)

0 0 130 325.00 400.00 -- -- -- --1 25 148 370.00 412.50 2.50 > 0.69 3.50 > 0.352 50 162 405.00 425.00 2.50 > 0.89 3.50 > 0.453 75 170 425.00 437.50 2.50 > 1.56 3.50 > 0.784 100 177 442.50 450.00 2.50 > 1.79 3.50 > 0.895 125 180 450.00 462.50 2.50 < 4.17 3.50 > 2.086 150 182 455.00 475.00 2.50 < 6.25 3.50 > 3.137 175 183 457.50 487.50 2.50 < 12.50 3.50 < 6.258 200 183 457.50 500.00

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Price Ratios and Profit Maximization

If output and input prices are constant,then the rule MR=MC is equivalent to

MPP =

where Pi is the input price and Po isthe output price

Po

Pi____

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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

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Equal Marginal Principal

In some situations an input may belimited so that the profit-maximizingpoint cannot be reached for all possible uses. A limited input shouldbe allocated among competing uses insuch a way that the marginal value products of the last unit used on eachalternative are equal.

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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.

Irrigation Grainwater Wheat Sorghum Cotton

(acre-inch) (100 acres) (100 acres) (100 acres)

04 1,200 1,600 1,8008 800 1,200 1,50012 600 800 1,20016 300 500 80020 50 200 400

Marginal value products ($)

1st2nd

3rd

4th

5th

6th

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Figure 7-3 Illustration of the equal marginal system

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Summary

Economic principles using the conceptof marginality provide useful guidelinesfor decision making. MVP and MIC areequated to find the profit-maximizing inputlevel. MR and MC are equated to findthe profit-maximizing output level. The equal marginal principle is used when alimited input must be allocated amongcompeting uses.