Marginal Analysis in Agricultural Production

Marginal Analysis Marginal analysis is used to assist people in allocating their scarce resources to maximize the benefit of the output produced. Simply getting the most value for the resources used.

(Marginal = the next unit) Marginal Analysis Marginal analysis: The analysis of the benefits and costs of the marginal unit of a good or input. (Marginal = the next unit)

Marginal Analysis A technique widely used in business decision-making and ties together much of economic thought. In any situation, people want to maximize net benefits: Net Benefits = Total Benefits - Total Costs

The Control Variable To do marginal analysis, we can change a variable, such as the: the quantity of a good you buy, the quantity of output you produce, or the quantity of an input you use. This variable is called the control variable .

The Control Variable Marginal analysis focuses upon whether the control variable should be increased by one more unit or not.

Key Procedure for Using Marginal Analysis 1.Identify the control variable (cv). 2. Determine what the increase in total benefits would be if one more unit of the control variable were added. This is the marginal benefit of the added unit.

Key Procedure for Using Marginal Analysis 3. Determine what the increase in total cost would be if one more unit of the control variable were added. This is the marginal cost of the added unit.

Key Procedure for Using Marginal Analysis 4. If the unit's marginal benefit exceeds (or equals) its marginal cost, it should be added.

Key Procedure for Using Marginal Analysis Remember to look only at the changes in total benefits and total costs. If a particular cost or benefit does not change, IGNORE IT !

Why Does This Work? Because: Marginal Benefit = Increase in Total Benefits per unit of control variable TR / Qcv = MR where cv = control variable

Why Does This Work? Marginal Cost = Increase in Total Costs per unit of control variable TC / Qcv = MC

Why Does This Work? So: Change in Net Benefits = Marginal Benefit - Marginal Cost

Why Does This Work? When marginal benefits exceed marginal cost, net benefits go up. So the marginal unit of the control variable should be added.

Example: Should a firm produce more ? A firm's net benefit of being in business is PROFIT. The following equation calculates profit: PROFIT = TOTAL REVENUE - TOTAL COST

Example: Should a firm produce more ? Where: TR = (Poutput X Qoutput) n TC =  (Pinputi X Qinputi) i=1 Assume the firm's control variable is the output it produces.

Problem: International Widget is producing fifty widgets at a total cost of $50,000 and is selling them for $1,200 each for a total revenue of $60,000. If it produces a fifty-first widget, its total revenue will be $61,200 and its total cost will be $51,500.

Problem: Should the firm produce the fifty-first widget?

Answer: NO The fifty-first widget's marginal benefit is $1,200 ($61,200 - $60,000) / 1 This is the change in total revenue from producing one additional widget and is called marginal revenue.

Answer: The firm's marginal cost is $1,500 ($51,500 - $50,000) / 1 This is the change in total cost from producing one additional widget. This extra widget should NOT be produced because it does not add to profit:

Marginal Revenue - Marginal Cost Answer: Change in Net Revenue (Benefit) = Marginal Revenue - Marginal Cost - $300 = $1,200 - $1,500

Qcv Qwidgets TR TR TC TC 50 60,000 50,000 1 1,200 1,500 50 60,000 50,000 1 1,200 1,500 51 61,200 51,500 MR = TR / Qcv = $1,200 / 1 = $1,200 MC = TC / Qcv = $1,500 / 1 = $1,500

Summary Marginal analysis forms the basis of economic reasoning. To aid in decision-making, marginal analysis looks at the effects of a small change in the control variable.

Summary Each small change produces some good (its marginal benefit) and some bad (its marginal cost). As long as there is more "good" than "bad", the control variable should be increased (since net benefits will then be increased).

Example : For another year, results were reported from applying six different rates of nitrogen to corn at a 22 000 planting rate. The approximate results were as follows: Pounds of nitrogen Yield of corn(bushell) Additional corn from additional N 10 84 -- 60 117 33 (50 lb.) 110 133 16 (50 lb.) 135 139 6 (25 lb.) 160 144 5 (25 lb.) 210 146 2 (50 lb.)

Yield increase when increasing the amount of N. But the rate of increasing yield is decreasing At prices of 20 cents, per pound for nitrogen and 3.00 dollar per bushell for corn, you would not recover the cost of the fertilizer by going from 160 to 210 pounds for the conditions represented by these data.

What is marginal product? The total product The average product = Total product / Total control variable The marginal product is the additional product when adding one unit of controlvariable

Input Total product (TP) Average Product (AP) Marginal Product (MP) 1 2 3 4 5 6 7 8 9 10 12 30 44 54 62 68 72 74 15 14.66 13.75

1. Yield increase when increasing the amount of input is called technical efficiency 2. Maximum profit – Economic efficiency For another example of explain the principle of diminishing returns is illustrated in Next Example, with nitrogen being added to 1 ha of wheat. All other inputs are assumed to be at the optimum and are held constant.

Example: The response of wheat to different levels of nitrogen Nitrogen/ha (40kg) Yield (kg) Average yield (kg) Marginal yield (kg) 1 2 3 4 5 6 7 8 9 10 900 2900 5000 7000 8500 9500 10250 10750 10000 1450 1666 1750 1700 1583 1464 1343 1194 1000 2000 2100 1500 750 500 -750 Back to slide

Technical efficiency of nitrogen application Stage 1 Y Total yield Wheat yield Average yield N Nitrogen used

Maximum profit (economic efficiency) Maximum profit is calculated by introducing the costs of input and value of output to the analysis. This can be measured and shown graphically as in figure bellow.

Maximum profit (economic efficiency) Stage 1 Stage 2 Stage 3 Y Total Value of yield Value of yield and cost of nitrogen Cost of nitrogen N Nitrogen used

Maximum profit is achieved at a yield of OY using ON of nitrogen Maximum profit is achieved at a yield of OY using ON of nitrogen. This position is determined by drawing a line parallel to the cost line, and where it becomes tangential to the total value line, maximum profit will be made. This will occur in stage 2, and will normally not be at the same point as technical efficiency.

Maximum profit (using marginal analysis) is measured by equating the cost of extra nitrogen (the marginal cost) to the value of the extra yield (marginal revenue) which it creates. When the extra nitrogen costs less than the value of extra yield, then it is worth using nitrogen. If the extra nitrogen costs more than the value of the increased yield, then it is not worth using it. Maximum profit occurs when the extra value of yield (marginal revenue) is equal to (or just greater than) the extra cost (marginal cost) of nitrogen used to create it. This can be illustrated in graphical form, as in Fig. 6.10.

Marginal analysis to determine the profit-maximizing output Total Value Value of yield and cost of nitrogen Marginal Revenue Marginal cost N

Conclusion Maximum profit will occur in any enterprise where: Marginal revenue is ≥ Marginal cost

Example Unit of labor Total Yield 1 10 2 18 3 24 4 31 If the cost price is 15 $, yield price is 3 $ and cost of other management is 10 $ Identify profitable point & net return.

Example

The response of wheat to different levels of nitrogen Nitrogen/ha (40kg) Yield (kg) Average yield (kg) Marginal yield (kg) 1 2 3 4 5 6 7 8 9 10 900 2900 5000 7000 8500 9500 10250 10750 10000 1450 1666 1750 1700 1583 1464 1343 1194 1000 - 2000 2100 1500 750 500 -750 Back to slide

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