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s

Chapter 7

Keep Your Eye On The Marginals!As you must by now suspect correctly, the concept of the “marginal” is applied throughout Economics. Reliable understanding and use of the principles of economics requires familiarity with a persistent focusing on the marginals, rather than the averages. To ensure your familiarity with “marginals”, this chapter explains marginals and uses them to illustrate the maximizing of a total by equalizing the marginals. Exactly what that preceding sentence means will become apparent before you finish this chapter. Here, initially, we note simply that it's almost a "truism", yet it's extremely powerful for analysis. While this chapter and the examples may seem to be digressions into simple arithmetic – and they are very simple – they certainly are not digressions. Knowing the meaning of the "marginal", and forces toward "equalizing the marginals", will ease as well as strengthen your understanding of the operation of the economy. In fact the principle is used in all sciences and characterizes virtually all your own every-day decisions! Learning the meaning and developing an ease in using marginals is like learning to ride a bicycle or to swim. At first it's rather unfamiliar and unusual, but we confidently assure you it will very quickly become second nature to always think of the marginals instead of the averages. . So bear with us initially, because it really quite simple, and furthermore. without a familiarity with and concentration on "marginals", you won't understand economic analysis and events.

Totals, Marginals and AveragesTest ScoresSuppose you have taken two tests in a class, receiving scores of 80 and 86, for a current total of 166 (=80+86), as listed in Table 1. Your average score of those two tests is 83 (=166/2). You now take a third test and score 89, raising your total score to 255 (=166+89). That additional test score is your marginal score Because that marginal score of 89 on the third test is higher than your preceding average (83) of the first two scores, your new average, of the three test scores, rises from 83 to 85 (=255/3). The total score is 255, the average score over all three tests is 85, and the addition to your total points – the score on the most recent test, 89 – is called the "marginal" test score. The average is more like a historical measure of the past, whereas the “marginal” is more identifiable with the future or the present. It’s the present or future that is the basis of a current decision. This suggests it’s the marginal, not the average, that should guide decisions, as the following examples also will demonstrate.

Table 1: Marginal, Total and Average Test Scores

Tests Marginals Total Averages

1 80 80 80

2 86 166 83

3 89 255 85

CostTake another example that is more pertinent to economics, and summarized in Table 2. A firm producing chairs can make one chair a day, at a total daily cost of $100. If it makes two chairs a day, the total daily cost rises to $180. The increase (=$180-$100) in costs to make two rather than just one chair daily is $80. The $80 increase in the total cost when making one more unit is called the "marginal” cost.

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Table 2: Marginal, Total and Average Costs of Chairs

Chairs Marginal Cost

Total Cost

Average Cost

1 100 100 100

2 80 180 90

3 105 285 95

Producing three chairs daily raises the total cost to $285. That increase of $105 ($285-$180) is the marginal cost at three units daily. The average cost at three units is now $95 (=$285/3) instead of $90. Adding a cost, the marginal cost of ($105), that exceeds the former average cost ($90) will pull up the average, as it does here from $90 to $95. Looking back at the change from one chair to two chairs daily, the average cost fell from $100 to $90, because the $80 marginal cost at two chairs was less than the preceding ($100) at one chair. (We continue to indicate the average, just to ensure you don’t confuse it with the marginal.) The concepts -- total, average and marginal -- are so simple, it may seem hardly worth all this explanation. But let's extend this exposition to a more realistic situation in which the “marginal” is not so immediately obvious, and is therefore sometimes ignored by the observer.

Revenue

Suppose you are selling chairs. The revenue data are in Table 3. Note that the “Revenue” to the seller is the amount paid by the buyer – and which we called “Market Value” in the previous chapter. “Market Value” and “Revenue” are generally the same amounts, just viewed from different perspectives depending on whether you are a buyer or a seller. Often, rather than calling these by different names, the convention is to call it “Revenue”, but you are then cautioned to make sure you understand whether it is an amount paid by buyers (demanders) or received by sellers (suppliers).

Table 3: Prices, Total, Marginal and Average Revenues

Chairs Daily

Price Total Revenue

Marginal Revenue

Average Revenue

1 110 110 110 110

2 100 200 90 100

3 90 270 70 90

Suppose you set your price at $150. The demand from buyers – shown as the first two columns in Table 3 – indicates that you won't sell any at that high a price. So what's the sense of calling that a price? None whatever, except ego-satisfaction. But, egos are expensive to maintain, so you cut your price to $110, and "lo and behold” you sell one chair a day. Your total revenue, or total sales value, is $110 a day. To sell more chairs each day, you cut the price to $100 and succeed in selling two chairs daily. Your total daily revenue rises to $200. Now, we look at the "marginal revenue" – the increase in total daily revenue consequent to selling one more chair each day. The marginal is $90 –the increase from $110 to $200 from selling two chairs rather than one. Notice that the marginal revenue, $90, the increase in total revenue, is less than the $100 price received for that second chair. It’s less because, to sell two chairs per day, you had to cut the price from $110 down to $100 on both units now sold. You give-up $10 on the one chair you could have sold if the price hadn’t been cut to sell more chairs. The marginal revenue is $90. This is the increase in total revenue when selling two chairs at $100 each, rather than one chair for $110. And if you look at the average revenue per chair at 2 chairs daily, it’s the $100 price of the two chairs, $100 (=$200/2).

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You could sell three chairs daily if you cut the price to $90. Your total daily sales revenue would be $270 (=3X$90). The marginal revenue, i.e., the increase in total revenue, would be only $70 (=$270-$200), though the price of chairs is now $90. The marginal revenue is the change in the total revenue consequent to cutting the price on all units enough to sell one more per day. In this example, the price was cut on all chairs sold that day. The $10 cut in price means the two chairs that would otherwise have been sold at $100 each are sold at $90. That $20 reduction ($10 on each of the two chairs) offsets part of the $90 price received on the third chair, bringing the increase to $70 -- the marginal revenue at 3 chairs. Though the price of a chairs $90, the marginal revenue associated with the third chair is only $70. You have to be careful to keep in mind always that the marginal is the change in the total , not just the amount obtained on the additional marginal unit sold .

Who Did It?

One last example reveals another potential misunderstanding of what the marginal measures. In a retail store, more retail clerks enable better service and more sales revenue as illustrated in Table 4.

Table 4: Total, Marginal and Average Sales by Clerks

Clerks Total Sales Marginal Sales Average Sales

1 $1,000 $1,000 $1,000

2 $1,800 $ 800 $ 900

One clerk alone generates sales revenue of $1,000. With a second clerk, the revenue rises to $1,800. The marginal is $800. The average with only one clerk is $1,000, with two clerks and the average is $900 (=$1,800/2). But the point of this example is revealed by the question, "What's the sales revenue of the second clerk?” That is, “What’s the marginal revenue with two clerks?” Suppose that clerk registered zero sales, while the first one's sales leaped to $1,800, because the second clerk assisted customers and the first clerk recorded the sales. The marginal revenue is $800 with a second clerk . That doesn’t mean that the second clerk had to make those added $800 of sales. It means only that the two sales clerks as a team generated sales of $1,800, an increase of $800. The marginal sales "of", "by, "with" or "at" two clerks is $800. Always, the marginal is the change in the total consequent to including one more. A good way to keep the semantics of this straight is to refer to the marginal as being “associated with” the additional unit.

We'll continually be referring to “marginal.” Knowing the marginal concept well is necessary for understanding a very wide range of otherwise mysterious economic events. That's why we ran the risk of being overly detailed and elementary at this stage of the text. It's not the mathematics that is hard. It's that the concepts and relationships must be carefully identified, remembered, and used.

Use the Marginal, Or the Average?

As an example of the importance of “marginals”, suppose you were told that the average cost per life saved from expenditures on automobile airbags was $1,000,000 while the average cost of a life saved with seat belts was only $500,000. Seat belts were twice as effective per dollar. If still greater safety were to be sought, should it be obtained by spending more for airbags or for seat belts? You shouldn't answer without knowing what the marginal cost is for saving more lives by airbags and what the marginal cost is for saving lives by seat belts. That might be $2,000,000 if seat belts are used to save an extra life, while it's only $1,100,000 with airbags. Given these numbers, the marginal cost is lower for airbags than seat belts. That comparison of the marginal costs reverses the ranking by the average costs. The average does not tell what the additional effects or additional costs will be. It only summarizes the past – the accumulated – effects, not the next or additional effects. Always when considering where to put more resources or time, or whatever the "input" is, the marginal effect is pertinent, not the average per unit of input to date. This is so important that it’s one of the reasons for starting this text by explaining the meaning and measure of the “marginal”. If you avoid thinking about the “average” when you should be thinking of the “marginal”, you’ll find economic analysis is surprisingly simple, powerful, and valuable. But if you fail to distinguish between “ average ” and “ marginal ”, you are doomed to failure!

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Relations among Totals, Marginals and AveragesNow that you know what is meant by the marginal and the average values, it’s easy to see how the total, the marginal and the average are related to each other. In Table 5, the first column lists the number of inputs of labor in some productive act. The second column lists the marginal products – the increases in products as additional units of labor are applied. The third column lists the total product at each amount of input of labor. The following relationships are noticeable in this table. (1) The total products increase by the amounts of the successive marginal products. That’s always true by definition, because the marginal product is defined to be the change in the "total product” with each added input. (2) In this table, a special feature is that successive positive marginal products get larger at first, but then later begin to decrease in size (meaning the successive totals are increased, though later by the increases being to diminish). The amount of inputs at which the total product begins to increase by diminishing amounts (where the marginals start to be smaller) is called the “point of diminishing marginal returns from that kind of input.” (3) The “total” will always decrease, when the “marginal” is negative. That’s always true because, a “negative marginal” is just another way to say the total decreases. (4) If the marginal is less than the prior average, the new average is lowered. Saying the same thing, from the reversed point of view, when an added input lowers the average product per unit of that kind of input, the marginal product must be less than the average product.

Table 5: Production and Inputs

(1) (2) (3) (4) Labor Marginal Product Total Product Average Product Per Unit of Labor

First 6 6 6 (=6/1)

Second 10 16 8 (=16/2)

Third 8 24 8 (=24/3)

Fourth 6 30 7.5 (=30/4).

Fifth 4 34 6.8 (=34/5)

Sixth 2 36 6 (=36/6)

Seventh 0 36 5.14 (=36/7)

Eighth -1 35 4.375 (=35/8)

A graph of the three measures, marginal, total and average, is in Figure 1. It shows the marginals rise to a maximum and then start to decrease. The total rises, and where it rises the marginal must be positive -- because the marginal is --by definition-- the change in the total. Where the total is maximized (and then starts to fall), the marginal must be zero (or change from positive to negative.) When the total falls, the marginal must be negative, because the marginal is, by definition, the change in the total.

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Figure 1: The relationships between Marginals, Totals, and Averages

A General Task: The Assignment of A Limited Supply Among Alternative Uses

We have explained the marginal in such detail because it’s critical for the valid applications of economic analysis. We’ll start with a simple example of the basic nature of many situations we’ll be analyzing. You have 24 HOURS per day. You assign some of the 24 hours to work, some to eating, some to recreation, some to studying, some to sleep; and some to each of the other things you do. Look at another similar “assignment of a limited resource.” You have $100 of income daily. How much of the $100 do you spend for food, for pleasure, for education, for transportation, and for each of the goods you buy, as well as some for saving for future expenditures. Both these assignment problems are merely special examples of a more general problem. “With a limited total of productive resources to be assigned among various uses, “What “principle”, or “rule” determines the assignments among the possible uses of the limited amount of your resource so as to maximize the achieved worth? With that objective, the maximization of the aggregated benefits, the answer is, “Assign available units to the highest valued of the remaining alternative uses.” Or, “Add a unit to the activity with the highest available marginal product.” Or, “Never add a unit to a use that has lower marginal product than available elsewhere.” In short, “Keep the marginal returns equalized.” To illustrate that, we’ll use a simple ‘toy” example, stripped of all extraneous detail.

How Much to Each Opportunity?

Imagine you have ten coin-like tokens, which you can insert in two “money machines”, A and B, from which dollars will be obtained. You goal is to maximize the number of dollars you get from the two machines. The amounts that can be obtained from each of Machine A and Machine B are listed in Table 6. We can call the amounts obtained – the “returns”, “payoffs”, “products” or whatever is appropriate for the situation. You could even think of this problem as the daily one in which you are spending your dollars of income to buy various consumption goods, or where to invest your savings. But let’s not get ahead of

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the exposition of the basics Right now, the problem is posed as “the best use of tokens so as to maximize the aggregated returns from the two machines.”

Table 6

Marginal and Average Dollar Returns From Machine A

Marginal, Total and Average Returns from Machine B

Tokens Marginal Total Average Tokens Marginal Total Averages

1 20 20 20 1 15 15 15

2 18 38 19 2 14.5 29.5 14.75

3 16 54 18 3 14 43.5 14.5

4 14 68 17 4 13.5 57 14.25

5 12 80 16 5 13 70 14

6 10 90 15 6 12.5 82.5 13.75

7 8 98 14 7 12 94.5 13.5

8 6 104 13 8 11.5 106 13.25

9 4 108 12 9 11 117 13

10 2 110 11 10 10.5 127.5 12.75

11 0 110 10 11 10 137.5 12.5

Successively decreasing marginal returns from each machine are indicated by the decreasing values in the “Marginals” column. The marginals are the increases in the total dollar outputs from a machine with the added tokens. The average per token is the sum of the marginals (which equals the “totals”) divided by the associated number of inserted tokens.

Figures 2 and 3 are graphs of the marginal and average returns from machine A and from machine B. As can be seen from Table 6, the marginal outputs from Machine B start at a lower value, $15, than for machine A, but the marginals of Machine B decrease less rapidly. As a result, in this particular example, beginning with the fifth token in B, the marginal returns will be higher than after a fifth token in A. . You can see that the total output for any machine is the sum of the successive marginal outputs over the range of tokens used in a machine.

Figure 2: Machine A Figure 3: Machine B

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Maximize The Aggregate Return

Since the purpose of putting tokens in the machines is to get as much money as possible with the ten available tokens, you might put all ten tokens into machine B and you’d get $127.50. Machine B's total payoff with ten tokens is greater than machine A's payoff with all ten tokens (=$110). But, if you can allocate the tokens between the two machines, rather than putting all in just one, you could get even more. You'd allocate the tokens so as to "equalize the marginals" of the two machines. You’ll ignore the averages! We'll now explain in detail that will probably take longer to explain than for you to understand the idea. Because the principle is so important and used so often, we'll take the risk of being excessively detailed. Table 7 shows the allocation of the tokens that maximizes the total return from the two machines.

Table 7: Aggregated Marginal and Average Returns from Two MachinesTokens Machines and

Tokens Used In Machine.

Marginal Returns

Total Returns

Average Returns

1 1st in A 20 20 201 1st in A 20 20 20

2 2nd in A 18 38 19

3 3rd in A 16 54 18

4 4th is 1st in B 15 69 17.25

5 5th is 2nd in B 14.5 83.5 16.7

6 5th is 3rd in B 14 97.5 16.25

7 7th is 4th in A 14 111.5 15.93

8 8th is 4th in B 13.5 125 15.63

9 9th is 5th in B 13 138 15.33

10 10th is 6th in B 12.5 150.5 15.05

11 11th is 5th in A 12 162.5 14.77

12 12th is 7th in B 12 174.5 14.54

13 13th is 8th in B 11.5 186 14.31

14 14th is 9th in B 11 197 14.07

15 15th is 10th in B 10.5 207.5 13.83

16 16th is 11th in B 10 217.5 13.63

17 17th is 6th in A 10 218.5 13.41

You would put the first token in the machine that yielded the highest marginal return. That's machine A, which pays $20. The second token would also go into machine A, because its marginal return is $18, which is more than the $15 return for the first token in machine B. Continuing, you'd put the third token in machine A getting $16, its marginal return at three tokens. The fourth token in machine A has a marginal yield of $14, but that's less than the $15 marginal return for the first token in machine B. So, the fourth token becomes the first one in machine B.

Stop for a moment and look at how the averages can mislead. The average return with a fourth token in machine A would be $17. And the average with one token in machine B is $15. The average with 4 tokens in A is greater than the average with one token in B. Nevertheless, we put that fourth token in B, because the marginals, not the averages, are pertinent for determining where to add tokens. Notice that if we mistakenly used the average to direct where we put the fourth token, and so put that token in the Machine A, our total return would be lower, 68, rather than the 69 we’d get by using the marginals to direct our tokens. This is a crucially important point, and is worth repeating.

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Consider the next token, the fifth. It would get $14.5 from machine B, compared to the marginal return of only $14 as a fourth token in machine A. That fifth token does not go into the machine with the highest available average, which would be machine A. We put the fifth token in B rather than in A because the marginal return from A is only $14, whereas it’s $14.5 from machine B. Always compare marginals, not averages, for allocating inputs.

To assure complete familiarity with the principle, let’s go beyond the five tokens (three in machine A and two in B). A sixth token would, as the fourth in machine A, have a marginal return of 14, and as the third in machine B, would have also $14 as the marginal return. The marginal return is the same from each machine, so the sixth would go to either, and the seventh to the other -- yielding four in A and three in B. The eighth token would be put in machine B, as its fourth token, for a marginal return of $13.50. That token would have had a marginal return of only $12 in machine A. Continuing, the ninth token would go in machine B, with a marginal return of $13 (at its fifth token). This marginal return is $1 larger than the $12 marginal return from machine A (as the 5th token in it). The tenth token would also go into machine B, as its sixth, with a marginal return of $12.50. That's more than the $12 marginal return it would get as the fifth token in machine A.

Observing the rule of never neglecting a higher available marginal, the ten tokens would go four in A and six in B. The four tokens in machine A obtained $20+$18+$16+$14 = $68. The six tokens in B obtained $15 + $14.50 +$14+$13.50+$13+$12.50 = $82.50, the aggregate total is $150.50 (=$68+$82.50) from the ten tokens. No allocation other than four in A and six in B will get as much. Try to get more. You won't succeed.

If we mistakenly but stubbornly persisted in looking at the averages as a clue about where to put the next token, we’d have put six in A and four in B. (Do you see why?) The total return from A would be $90 (=6x$15) and from B, $57 (=4x$14.25) for a grand total of $147. That's less than the $150.50 we got by correctly treating the marginals as the indicator of where to put tokens while ignoring the averages.

A Few More Tokens, as a (Hopefully!) Redundant Exercise:

If, in our example, there were 15 tokens, instead of only 10 tokens, the total return would be $207.5(=$80 from the 5 tokens in machine A plus $127.5 with the 10 tokens in machine B.) The value-maximizing action would be to put nine tokens in A and 6 in B. Thus, the eleventh token could be inserted in either machine A or B, because the marginal product is $12, the same marginal product as the fifth in machine A or the seventh in B. The twelfth would go to whichever the eleventh didn't. The marginals in each are $12, but the average in A is $16 and only $13.50 in B. Averages are irrelevant for allocating inputs: only marginals matter.

The thirteenth should go into machine B, as the eighth in machine B, with a marginal payoff of $11.50. That's larger than the marginal return of $10, the 6th token in machine A. The average with eight in B is $13.25 and the average with five in A is $16. (Just in case you missed it before, the averages are irrelevant for determining how to maximize the payoff.) The fourteenth token should go in machine B as the ninth in that machine with a $11 marginal payoff, which is $1 larger than the $10 marginal payoff it would get as the sixth in machine A. Finally, the 15th would be the 10th in machine B, with a marginal yield of $10.5, instead of being the sixth token in machine A.

Graphic RepresentationYou might want to look at Figure 4, which shows the marginals listed in Table 6. It shows the allocations of inputs that equalizes the marginal yields from inputs from several “machines”).

(1) The Marginal Product Curves of Each MachineThe marginal payoffs from each of the machines are shown by two sets of successive bars, one set for each machine. In this example, the marginal bars for machine A start higher than for machine B. But they decrease more rapidly. The total return from a machine can be measured as the combined area of the marginal bars. For three tokens in machine A, the total area of the first three marginal return bars represents the total return. For ten tokens, four in A and six in B, the total return is indicated by the total area of the first four marginal bars for A and the first six marginal bars for B.

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Figure 4: Allocating Successive Tokens Between Two Machines To Maximize Total PayoffIn general, don’t put a token where the marginal return is less than the marginal return available elsewhere. Here, marginal products from machine A start higher but decline faster than from machine B. With ten tokens, the largest reward (output) can be obtained with four tokens in machine A and six in B --even though the average in B is lower than the average in A. The horizontal dark gray line cuts through the two marginal “curves” at the same values (heights) at the 4A, 6B allocation. The light gray line shows the return maximizing allocation if there were 15 tokens. In that case, one would put 5 tokens in machine A and 10 in machine B.

If we think of the inputs as perfectly divisible and continuous (like hours of labor input, instead of tokens), the heights of the bars would be smoothed into lines representing the marginal returns from continuous measures of inputs. This is represented in Figure 4. The amount of inputs to each machine should be adjusted so as to equate their achieved marginal returns.

In the graph the total return of a machine is represented graphically by the area under the marginal return line out to the amount of the input. With two machines, the total return of the two is the total of the areas under each marginal return line, for the amount of each input.

And with it we can identify a principle that pervades much of economics and everything else in your life. Even if no one understands it, you can be sure the test of competitive survival will result in people doing what the principle says – as you’ll understand later.

We will use it to understand how competition and market prices help coordinate production and consumption for millions of people. It’s the basis of the explanation of why people trade with each other, personally, geographically and internationally. It explains many pricing tactics that you experience every day. It shows why profits reflect increases in total output, rather than being merely gains by one person at the expense of another. It’s the reason investors in stocks buy a cross-section of the whole stock market. It’s the basis for international trade, and it implies that restrictions on trade reduce the total national products. In brief, it’s crucial to all economics. So, what IS the principle? We can guess that you might have deduced it, but will keep you hanging while we demonstrate one more important analytical tool and application (or viewpoint) that will prove helpful in future analytics.

Aggregated Marginal Product CurvePresented next, in Figure 5, is a very useful though initially complicated looking graph of the marginal returns from both machines. It may initially appear forbidding, but it’s just more detailed, not more difficult. It shows the principle of maximizing by equalizing the marginal returns. [Unsolicited Advice! It probably takes more time to explain than to learn and become familiar

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with the graph. Most of the graphs used later will be simpler. They are an important method of guiding the economic analysis. Some time spent now becoming familiar with this one will have large (marginal and total) returns later.]

Figure 5: Marginal Products From Machines A and B

With two machines the inputs are allocated so as to obtain highest marginal product currently available, thereby maximizing total product. In general, with a given amount of inputs and several alternative uses, allocate the inputs to alternatives with the highest available marginal products. Never put an input to a use with a lower marginal product than available elsewhere. In this graph the alternatives machines are A and B. The dark and light gray lines show the same allocations as those from Figure 4, only now they also show the total number of tokens along the line Sab.

In the left side of Figure 5, the two marginal returns lines are shown, -- one for each machine. They are added horizontally to get, on the extreme right side, the line Sab. That aggregate line represents the marginal returns from the machines when inputs are applied so as to maintain equal marginal returns from each machine. Adding tokens in this way is represented by sliding down each marginal returns curve at equal heights on each. To make that explicit on the graph, a horizontal line extends across both marginal returns curves and cuts the two marginal returns lines at the same height -- indicating by the horizontal distances the number of tokens in each machine that equalizes the marginal returns. The total number of tokens allocated between the machines is where the horizontal line cuts the aggregate marginal returns line. The aggregate marginal returns line slopes down, but less steeply than the component lines.

From the point on the “aggregate marginal returns line” directly above the total amount of inputs available. (measured along the horizontal axis), a horizontal line is drawn back to the left edge of the diagram. The dark gray horizontal line intersects the two individual marginal returns lines, at four and six, respectively, indicating that four tokens should be used in machine A and six in machine B. At that combination, the total return (payoff, reward, or whatever it’s called) is maximized. No other distribution (allocation) of the ten tokens will result in a larger amount of money. You can readily see that the greater the number of tokens available, the lower will the resulting marginal returns.

In general, for any specified total number of tokens, all you have to do is draw a vertical line at the total number on the horizontal scale. From its intersection with the aggregate marginal returns line, a horizontal line intersects the marginal returns curves, indicating the appropriate amounts of the input in each respective machine to equalize the individual marginal returns – and to maximize the total return.

A Basic Principle In Economic Analysis: The Equalization of Marginals at the Maximum Aggregated Return."At last, we explicitly recognize it! This extremely useful principle is by now, we hope, obvious. The trick – which is easy – is to interpret situations in terms of equalizing the marginals. You’ll get a lot of practice doing that, beginning in the next chapter on gains from trade by, yes, equalizing the marginals. More briefly, “Allocate resources so as to keep their marginal returns equal — or as near as possible.” Or, “If marginal products aren’t equal, there’s a gain to be had by equalizing them by reallocating the productive resources.”

We’ve explained, probably in more detail than necessary for some readers, the meaning of marginals and how they enter into our decisions. We did so, because your progress in learning economic principles and understanding economic events requires

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(a) familiarity with the difference between averages and marginals. In the next chapter, we’ll return to economics to explore some more features of the demand concept and principle. We’ll see how the concept of marginal worths helps us understand what the demand curve means.

Another Note on Names and Labels: Sometimes we (and other economists) will say “marginal product.” Sometimes we’ll say “marginal returns.” And sometimes we’ll say “marginal yield.” We don’t do this to annoy or confuse you; we do it because it is commonplace in the real world for people to use the terms “product,” returns,” and yield” interchangeably in this context—and thus, so shall we.

At last, after the next chapter, which completes the exposition and explanation of the principles of "demand", you'll be adequately equipped to apply economic principles to separate the valid from the mass of invalid conceptions and assertions about economic affairs. As a bonus, you’ll be able to more reliably protect your future hard-earned wealth.

Brief Appendix: Check and Broaden Your Understanding.

Measurement of Marginals with Multiple Inputs.

The examples in this chapter have concentrated on the results from changing one input factor. We wrote, for example, about how the cost of production changes due to making an additional chair, how the revenue changes due to selling an additional chair, and how the payout changes from inserting additional tokens into either machine A or machine B. But, often the realized output result depends on several input factors, all of which can change. What does “Marginal” mean under those conditions? In economics – as in virtually every other discipline that studies cause and effect relationships – we analyze the effect of a single contributing factor on the outcome by (1) noting the amounts of ALL contributing input factors and their collective effect on the resulting output, and then (2) marginally increasing ONLY ONE of the input factors (say X) WHILE KEEPING ALL OTHER CONTRIBUTING INPUT FACTORS AT AN UNCHANGED LEVEL. The change in the resulting output level will be due to the change in X in combination with the other unchanged input factors. That will be the marginal return (or marginal yield, or marginal product, etc.) of X.

Notice there are two important concepts here: (1) In marginal analysis, we only allow one input factor to change at a time since if we allowed several inputs to change, it would be impossible to attribute the change in the resulting output to any single input that changed. Hence, it would be meaningless to talk about the “Marginal Return from X” if other inputs changing also contributed to the resulting changed output level. (2) The constant level of the other inputs affects the “Marginal Return from X” even though they are not changing. A simple example will suffice. It is easy to imagine a production process that depends on the total work space available as well as the number of workers. So the productive inputs are (A) workspace, and (B) workers. If we ask what the marginal product of a second worker is, we are assuming that the workspace is set and unchanging while we measure the additional output associated with adding the second worker. Within this example, consider two different scenarios: (1) The unchanging workspace is expansive, and (2) the unchanging workspace is adequate for one worker, but very cramped for two. If the workspace is expansive the addition of the second worker will certainly have a different effect on the associated additional output as compared to when the unchanged workspace becomes cramped when a second worker is added to the process.

Economics does have analytical capabilities to measure the effect when all inputs increase (or decrease) by the same proportion. These are called “scale” changes and will be explained in more detail in a later chapter.

Diminishing Marginal Returns and Diminishing Total Returns .

There’s another factual feature about the behavior of the marginal product as more inputs are applied for production. The fact is that the marginal products will, beyond some amount of the input, begin to decrease as more than that critical amount of the input is applied to fixed amounts of other productive inputs. For example, as more labor is put to work with a given amount of other goods and materials, beyond some amount of the labor, the marginal products of successive increases in the amount of labor will decrease. Consider an example, to make this point clear.

Table 8 is a schedule of marginal products as more inputs are put to work. Think of the inputs as the number of employees in a factory. In general, the greater the number of employees, the larger the total output. The totals, listed in column 3, increase as more workers are added, but (at least after the second worker) by diminishing increments. The marginal product—that is, the

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change in the total product-- is at a maximum with the second worker. For more workers the marginal products decrease. The decrease in marginal product is called “diminishing marginal productivity”. It can be more generally expressed as follows: “Beyond some amount of one kind of input that is being applied to fixed amounts of other productive resources, the marginal product of that input will begin to decrease. That’s called the point of diminishing marginal returns to that input. In this example, the point at which the marginal product diminishes is at the second laborer -- 2 units of labor. For larger amounts of labor, the marginal products diminish from 10, down through 8, 7, 5, etc. The total product increase up to 36 units with 6 workers, beyond which the total decreases – when labor over-congests the productive facility. With more than 6 people the total product begins to fall from its maximum of 36 units. Its marginal products are negative. The point at which total product begins to fall with more labor is called the point of diminishing total returns.

Table 8:

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Number of Workers

Marginal Product

Produced

Total Product

Produced1 10 102 8 183 7 254 5 305 4 346 2 367 -4 32