Chapter three:  Marginalism

Author:  Lori Alden

Deciding how much to consume  

            The concept of opportunity cost helps you decide whether to do something, such as whether to go to college or to a movie.  Lots of decisions, though, are not about whether to do something, but about how much to do something.  To deal with these kinds of decisions, economists use another powerful technique, called marginalism. 

            To see how the technique works, let's use it to solve a very simple "how much" problem:  how many hamburgers to eat for lunch.  We're not recommending, of course, that you whip out a calculator and go through this analysis the next time you order hamburgers.  After all, even household pets (except for goldfish) can figure out when to stop eating.  We just want to work through a simple problem so that we can come up with a method for handling more difficult ones.  

            Suppose that you're at a fast food restaurant and that you’re about to order some hamburgers.  Their price is $1 each.  Table 1 shows the total benefit and opportunity cost to you of buying and eating different quantities of these hamburgers.  The opportunity cost of each quantity is equal to the price of a hamburger ($1) times the number of hamburgers.  (Since you're already at the front of the line at the restaurant, we can ignore the cost to you of driving there or standing in line -- those are now sunk costs.)   

            Notice what happens in the total benefit column as you buy more hamburgers.  The first one would give you a benefit of $2.50.  But you wouldn't be as hungry after eating that one, so consuming a second one would increase your total benefit by a smaller amount, $1.50.  A third hamburger would increase your benefit by even less, $.50.  And after three hamburgers, consuming a fourth would be so unappealing that it would actually reduce your total benefit by $.10.  

                                                                 Table 1  

          Quantity of       Total       Opportunity
    Hamburgers       Benefit         Cost  

         0            $   0          $   0
         1             2.50           1.00 
         2             4.00           2.00
         3             4.50           3.00
         4             4.40           4.00

 

            You can see this more clearly in Table 2.  The new columns show the marginal benefit and price of consuming each of the four hamburgers.  Economists use the word marginal to mean "extra" or "additional."  The marginal benefit of each hamburger is simply the additional benefit you would get if you consumed it.  The opportunity cost of consuming each additional hamburger is given by its price.

 

                                                                 Table 2  

 

             How many hamburgers should you buy?  Clearly, you should buy at least one.  The marginal benefit of the first hamburger is $2.50, but its price is only $1.00.  By consuming it, you can make yourself better off by $1.50.  This $1.50 is your marginal gain, the amount you gain from increasing what you're doing by one unit.  Here's how to calculate the marginal gain you get from consuming more of something:

 

            The marginal gain from consuming one more unit of something is equal to the difference between its marginal benefit and price.

 

            You should also buy a second hamburger, since doing so will give you a marginal gain of $.50.  But you shouldn’t buy a third one. Since its price exceeds its marginal benefit, consuming a third hamburger would make you worse off by $.50.  Nor should you buy a fourth hamburger -- doing so would make you worse off by $1.10.  

            The method that we used to solve the hamburger problem was to compare the marginal benefit and price of each hamburger, taking them one at a time.  This technique, called marginalism, involves comparing the benefits and costs of making small changes in whatever you're doing.  Marginalism tackles the problem of how many hamburgers to get by breaking it down into many small problems:  Should you buy the first hamburger?  Should you buy the second hamburger?  Should you buy the third hamburger?  

            Once you've done that, you simply compare the marginal benefit and price of each hamburger in turn.  If the marginal benefit of another hamburger is greater than its price, then you should buy it.  If its price exceeds its marginal benefit, then you shouldn't buy it.  And this rule applies not only to hamburgers, but to almost everything you consume.   

            This rule also can be expressed in terms of marginal gains.  Remember that the marginal gain tells you how much better off you'll be if you consume one more unit of a good or service.  As long as it's positive -- that is, as long as marginal benefit exceeds price -- consuming an additional unit of something will make you better off.  Only when the marginal gain becomes negative -- when marginal benefit falls below price -- will further consumption make you worse off.  This suggests the following rule for deciding how much to do anything:  

            Continue doing something as long as the marginal gain is positive.  

            Again, marginalism is a good way to decide how much to do something --how many hamburgers to buy, how much milk to drink, or how many times to jog around a track.  Not all decisions are like this though.  Some, like whether to buy a car or travel to Greece , are all-or-nothing decisions -- you either do them or you don't.  These kinds of decisions deal with whether to do something, not how much to do something.  Since those problems can't be broken down easily into smaller parts, marginalism isn't the appropriate tool for solving them.

 

The Law of Diminishing Marginal Benefits  

            We've seen that the marginal benefit of each additional hamburger goes down as you consume more and more of them.  This is true of almost anything you do.  Your first glass of milk is more satisfying than your third.  Your first trip on a Ferris wheel is more thrilling than your twenty-fifth.   

            This phenomenon of diminishing marginal benefits is so common that economists have dubbed it, aptly enough, the Law of Diminishing Marginal Benefits. The Law explains why we don't normally eat 21 hamburgers at a sitting.  After just a few hamburgers, the marginal benefit from eating another one tends to fall below its price, telling us to stop.  

            Many business firms have devised ingenious ways of exploiting the Law of Diminishing Marginal Benefits.  Since the Law states that people value the first unit of anything they consume more than the second or third, many firms have found it profitable to charge their customers more for the first unit than for later units.  

            Take hamburgers, for example.  We saw that when the price of a hamburger is $1, you'll buy two hamburgers.  But the hamburger stand can squeeze more money out of you if it offers "one hamburger for $2, or two for $3."  Now the price of the first hamburger is $2, but the price of the second is only $1.  

            Table 3 shows the hamburger problem with these new prices.  As before, it's worthwhile for you to buy two hamburgers, but this time your marginal gain from the first hamburger is only $.50, instead of $1.50.  The hamburger stand was able to squeeze $1 from you by charging more for the first hamburger.  

 

                                                                 Table 3  

                          Marginal                   Marginal
   Hamburger           Benefit       Price          Gain  

      1st               $2.50        $2.00         $ .50
      2nd                1.50         1.00           .50

 

The Law of Diminishing Returns

            On Saturday morning, Rhonda drove to Carla Masuda's shop for her third day of work.  Lisa and Frank were already busy, making cornhusk dolls and packing them in huge boxes to be shipped to the Cornucopia Company.  Cornucopia plans to advertise the dolls in its fall catalogue.  

            "The boss wants to see you," said Frank, as he quickly fashioned a damp cornhusk into a bonnet and tied it under the doll's chin.  "She sounds kind of grumpy."  

            Rhonda found Carla in her office.  Papers, cancelled checks, and peanut shells were strewn all over her desk.  

            "Did you want to see me, Carla?"  

            Carla glowered at Rhonda.  "Yeah, there's something I want to show you."  She picked up a piece of paper from the table and handed it to Rhonda.  It showed last Saturday’s hourly doll production.  

            "I don't know what's wrong with you kids nowadays," said Carla as Rhonda studied the paper.  "Lisa was the first one I hired and she's always been a good worker.  Then I hired Frank . . . He tries hard, but look at the numbers.  I don't get nearly the work out of him that I do out of Lisa."

      

            Rhonda looked at the paper again.  Sure enough, as a result of hiring Frank, the number of dolls made per hour increased from 12 to 22 per hour, or by 10.  That was two dolls less than what Lisa made working alone.  Rhonda was puzzled.  Frank always seemed to work just as hard as Lisa.  

            Carla leaned back and rubbed her temples.  "Jane's even worse--I get only 8 extra dolls per hour out of her.  And then I go and hire you.  We're making only 6 extra dolls an hour more since you came.  I can't afford to employ goof-offs."  

            "I don't understand this, Carla.  I work just as hard as everyone else."  

            "Well, it's not hard enough!  I'm giving you one more chance to clean up your act."             

 

The Law of Diminishing Returns  

            Lisa produced 12 dolls an hour when she was the only worker.  With four workers, Carla expected to get four times as many dolls, or 48 an hour.  But her workers produce only 36 dolls an hour.  What can explain this?  

            Contrary to what Carla believes, the problem isn't that the other workers are lazier than Lisa.  It's that they all have to share a small space and a limited amount of equipment, like the work table and the sink.  When Lisa was the only worker, she had the whole place to herself and could get a lot done.  As more workers were hired, they had less space to work in, and they often wasted time waiting to use the equipment.  This meant that everyone, including Lisa, produced fewer dolls.

 

 

           Let's explain this using economic terms.   Inputs are the resources used by a firm to produce the goods or services, or output, that it sells.  There are two kinds of inputs:  fixed and variable.  Fixed inputs can't be changed in the short run.  In Carla's garage, for example, the garage space and the sink are fixed inputs because Carla can't easily change them.  On the other hand, it's relatively easy for her to vary the number of workers she uses, perhaps by hiring or firing them.  Inputs -- like workers -- that can be used in varying amounts in the short run are called variable inputs.   

            As Carla hired more workers, each worker became less productive.  The productivity of these workers is measured by dividing the total output by the number of workers.  When Carla hired only two workers, for example, they each produced 22 dolls/2 workers = 11 dolls/worker.  But when three workers were crowded into the small garage, productivity dropped to 30 dolls/3 workers = 10 dolls/worker.  With four workers, productivity dropped even more, to 36 dolls/4 workers = 9 dolls/worker.  

            This drop in productivity is implied by the Law of Diminishing Returns.  The Law states that adding more of a variable input to the fixed inputs in a production activity eventually results in smaller and smaller increases in output.  

            The Law applies at some point to any production activity that you do.  After Thanksgiving Dinner, for example, your relatives probably troop into the kitchen to do the dishes.  Two or three relatives working as a team can finish off the dishes rather quickly.  If more relatives come in to help, the dishes probably will get done a bit quicker, but not by much.  Since there's only one sink and dish drainer, the extra relatives often just stand around with dish towels waiting for dishes to dry.  

            The Law also applies to inputs other than labor.  Adding a little fertilizer to your garden will often give you a big increase in vegetables.  As you add more and more fertilizer, your crop increases, but by smaller and smaller amounts.  At some point, adding more fertilizer might even burn the crops and actually reduce the amount of vegetables you produce.

 

Deciding how many workers to hire  

            Firms can use the technique of marginalism to help them decide how many workers to hire, how much fertilizer to use, how many machines to buy -- how much of any variable input to use.  Again, the trick is to break the problem down into many small problems.  When deciding how many workers to hire, for example, a firm might decide whether to hire the first worker, then whether to hire a second, then whether to hire a third, and so on. 

            As before, the basic rule is that one should continue doing something as long as the marginal gain is positive.  Table 4 shows the marginal gain Carla would get from hiring different workers.   It’s equal to the amount of extra money per hour that Carla makes as a result of hiring a worker ($2 per doll times the number of extra dolls that are produced) less $6, the hourly wage Carla pays each worker.  

            Should Carla continue to employ Rhonda?   If she does, then 6 additional dolls will be produced each hour.  This will enable Carla to earn an extra $12 per hour from selling the dolls.  Yet Rhonda's wage is only $6 a hour.  Since the value of the extra output produced as a result of hiring her ($12) exceeds her wage ($6), Carla should keep her.  

            Should Carla hire yet another worker?  Hiring a fifth worker would result in 4 additional dolls per hour, which Carla can sell for $8.  Since she'd only have to pay the worker $6 an hour in order to make that $8, hiring the worker would give her a marginal gain of $2 an hour.  So yes, she should hire a fifth worker.  How about a sixth?  If a sixth worker produced an additional 2 dolls an hour, then hiring that worker would bring in only $4 an hour.  At a wage of $6 an hour, hiring this worker means that Carla would lose $2 an hour.  Clearly, she shouldn't hire a sixth worker.

 

                                                                 Table 4

 

  

Deciding how much to produce  

            Notice that when Carla decides how many workers to hire, she's also deciding how many dolls to produce.  As Table 4 shows, 5 workers will produce a total of 12 + 10 + 8 + 6 + 4 = 40 dolls per hour.  If she hires only 4 workers, they will produce 12 + 10 + 8 + 6 = 36 dolls per hour.  If she hires 6 workers, they will produce 12 + 10 + 8 + 6 + 4 + 2 = 42 dolls per hour.  

            There's a way to rearrange the information in Table 4 so that it expresses the problem directly as one of how much to produce rather than one of how many workers to hire.  As with other marginal problems, the basic rule is simple.  The firm should keep producing output as long as there's a marginal gain from doing so.  Here's how to determine a firm's marginal gain from production:

 

            The marginal gain from producing one more unit of output is equal to the difference between the price the firm receives for that unit and the marginal cost of producing it. 

 

The marginal cost of an additional unit of output is equal to the increase in the firm's opportunity cost that results from producing that unit.  

            Let's use this rule to decide how many cornhusk dolls Carla should produce each hour.  Should Carla's firm produce the first 12 dolls?  To produce that many in an hour, Carla would need to hire one worker, say Lisa, and pay her $6.  This means that producing each of those dolls adds $6/12 dolls or $.50/doll to the firm's costs.  Since the price of each doll is $2, Carla makes a marginal gain of $1.50 on each of the first 12 dolls produced.  Clearly, she should produce them.

 

                                                                 Table 5

   

            Carla would have to hire another worker (say, Frank) to produce the next 10 dolls -- and pay him $6 an hour.  This means that each of those dolls would cost her $6 /10 dolls, or $.60/doll.  She can get $2 for them, though, so she should produce these as well.  

            As Table 5 shows, she also should produce the next 8, then the next 6, and then the next 4 dolls -- each of these will yield a marginal gain.  But she shouldn't produce the next 2 dolls -- she'd lose $1 on each of them.  

            Marginalism tells us that Carla should produce 12 + 10 + 8 + 6 + 4 = 40 dolls.  To do so, of course, she'll have to hire 5 workers.  Notice that 5 workers is the answer we came up with in the previous section when we asked how many workers she should hire.  In problems like this, deciding how much to produce is just another way of deciding how many workers to hire.  

            And notice something else.  As additional dolls are produced, their marginal cost goes up.   This is perfectly normal.  It follows from the Law of Diminishing Returns, which tells us that hiring more workers results in less and less additional output.  This, in turn, implies that additional units of output require more and more additional time -- and therefore money -- to produce.   

            For example, here's how much time it takes to produce each of the first 12 dolls when Lisa works alone:  

                                         60 minutes/12 dolls = 5 minutes/doll  

Carla pays her $6 an hour, or 10¢ an minute, so each of the first 12 dolls costs 5 minutes X 10¢/minute = $.50 to produce.  But when Carla hires Rhonda, she gets only 6 additional dolls.  Here's how much additional time is required to produce each of these dolls:  

                                         60 minutes/6 dolls = 10 minutes/doll  

More money is required, too.  Each of these 6 dolls costs 10 minutes X 10¢/minute = $1.00 to produce.  

            The Law of Diminishing Returns, then, implies that the marginal cost of producing additional output eventually rises.  And this phenomenon occurs with other variable inputs as well:  

            Because of the Law of Diminishing Returns, the marginal cost of producing any good eventually rises.

 

Deciding how much to produce for your own consumption  

            When deciding how much to consume, you should compare marginal benefit to price.  When deciding how much to produce, you should compare price to marginal cost.  But what should you do if you're producing something for your own consumption?  

            Problems like that are priceless -- literally.  Consider what happens when you iron a shirt, or clean your room, or write in your diary.  In each case, you're producing and consuming a service, yet you don't charge yourself -- or pay yourself -- anything.  But without a price to guide you, how can you decide how much to produce and how much to consume?  

            Don't worry.  There's a way to decide how much to produce for your own consumption that works without a price.  As usual, the decision rule is to continue producing and consuming something as long as there's a marginal gain.  Marginal gain, though, is measured this way:  

            The marginal gain from producing an additional unit of something for your own consumption is the difference between its marginal benefit and marginal cost.  

            Suppose, for example, that you're in a blackberry patch.  How many berries should you pick (or produce) and eat (or consume)?  Clearly, the longer you work, the more blackberries you'll get.  But as you pick, the marginal cost of getting the blackberries is likely to rise higher and higher.  This is because you're going to pick the easy ones first, like the waist-level clumps on the outside of the blackberry patch.  After those are gone, you'll have to bend over or wade through thorns to get more.  

            As you consume more and more, the marginal benefit you’ll get from additional blackberries goes down.   This follows from the Law of Diminishing Marginal Benefits described earlier in this chapter.  Table 6 shows the marginal benefit, the marginal cost, and marginal gain that you would get from picking different amounts of blackberries.  

                                                                 Table 6

 

Berries (cups)	Marginal Benefit	Marginal Cost	Marginal Gain
First	$2.00	$ .50	$1.50
Second	1.50	1.00	.50
Third	1.00	1.50	- .50
Fourth	.50	2.00	-1.50

 

            The first and second cups of blackberries will each give you a positive marginal gain, so you should pick these.  But after two cups, the marginal gain from picking blackberries becomes negative.  Eating extra blackberries is now less appealing, and picking them is now harder (remember, you’ve already picked the easiest blackberries).  Don’t waste your time picking more than two cups.  

            Table 7 summarizes the decision rules for consumers, producers, and producer-consumers.  Notice that the basic rule stays the same:  Keep doing something as long as the marginal gain is positive.  The only difference is in how marginal gain is defined.

  Table 7

Decision rules  

Basic rule:  Continue doing something as long as the marginal gain is positive.

 

  Type of Decision                                              Marginal Gain

 

How much to consume?                               Marginal Benefit - Price
How many workers to hire?                         Value of additional output - wage
How much to produce?                                Price - marginal cost
How much to produce and consume?        Marginal benefit - marginal cost     

 

 

Water is a far more valuable resource than diamonds -- yet the price of diamonds is much higher.  This so-called Paradox of Value puzzled economists until the late 19th century, when the concept of marginalism was developed.  The solution to the paradox is that the value of a resource is measured by its total benefit, but its price reflects its marginal benefit.  The total benefit of water to people is much larger than that of diamonds.  But since water is relatively plentiful, the marginal benefit (and price) of another glass is much lower than the marginal benefit of another diamond.

 

  Ne quid nimis

 

A researcher once polled a number of economists to see if they agreed or disagreed with this maxim:  "Anything worth doing is worth doing well."  The response?  Seventy-four percent disagreed.

The researcher wasn't surprised, because marginalism teaches that some things worth doing aren't worth doing well.  Take cooking, for example.  Gourmet Magazine offers the following recipe for Guacamole Dip:

 

                                           Gourmet Magazine Guacamole

2 ripe avocados (preferably California )
1 small onion, minced
1 garlic clove, minced and mashed to a paste with ½ teaspoon salt
4 teaspoons fresh lime juice, or to taste
½ teaspoon ground cumin
1 fresh or pickled jalapeño chili if desired, seeded and minced (wear rubber gloves)
3 tablespoons chopped fresh coriander if desired

Halve and pit the avocados and scoop the flesh into a bowl.  Mash the avocados coarse with a fork and stir in the onion, the garlic paste, the lime juice, the cumin, the chili, and the coriander.  The guacamole may be made 2 hours in advance, its surface covered with plastic wrap, and chilled.  Makes about 2 cups.

If you follow Gourmet's directions, you'll create a truly exquisite guacamole dip.  But if you want to make a good--but not great--guacamole dip, you might try this recipe:

 

                                                 The Author's Guacamole

2 avocados (preferably ripe)
1 squirt of lemon or lime juice
1 dash tabasco sauce (optional)

  Remove the avocado peels and pits.  Mash everything else together with a fork.  Chill if made ahead.

Suppose you've invited some friends over to watch the World Series on television and you want to serve them guacamole dip with nacho-flavored tortilla chips.  Which recipe would you use?   The author's guacamole recipe takes about 5 minutes.  Gourmet's takes about 20 minutes, and requires extra ingredients.  Is it worth the extra trouble to turn a good guacamole into a great one? 

Maybe not.  If you suspect that your guests are going to wolf down your dip after dulling their palates with sodas and tortilla chips, then the nuances of a gourmet dip might be lost on them.  The marginal benefit from the extra effort might not cover the marginal cost.  While guacamole dip may be worth doing, it's not necessarily worth doing well.

Besides, you've got a lot of other things to do if you have guests coming.  You'll need to clean the house -- put things away, wipe off the counters, vacuum the carpet.  Should you also clean under the sofa or behind the bookshelf?  Probably not.  Nobody will see the dirt there.  The marginal cost of cleaning those places doesn't cover the marginal benefit.

Marginalism, then, suggests that we don't overdo things.  This isn't a new idea -- the Roman playwright Terence said much the same thing over 2,000 years ago with these words:

 

                                                           Ne quid nimis.

 

That's Latin for "Moderation in all things." 

Now stop for a moment and ask yourself some questions.  When you ironed your shirt this morning, did you remove every single wrinkle?  Did you brush your teeth for 20 minutes?  Did you triple-check every answer on every homework assignment?  If you answered no to these questions, then congratulations.  You're already applying the idea of marginalism and Ne quid nimis to your personal decisions. 

Consider too these social decisions:  Should automakers be required to build perfectly safe cars?  Should absolutely all pollution be eliminated?  Should every bit of waste and fraud be abolished from government?

Marginalism suggests not.  Consider, for example, what it would take to have a perfectly safe car.  The car would probably look like a tank, go about 5 miles per hour, cost a fortune, and get poor gas mileage to boot.  We've already taken advantage of the most inexpensive ways of making cars safer -- seat belts, radial tires, safety glass, headrests, airbags, and so forth.  Each of these innovations have saved many lives.  Additional innovations, like heavier car bodies and ejection seats, would be much more costly and yet save fewer lives.  At some point, the marginal cost of adding another safety feature will exceed the marginal benefit. 

 

            Photo idea:  Picture of child on tricycle (with roll bar) wearing helmet, knee pads, and elbow pads.  Caption:  How much safety is appropriate?  This child could be made even safer if the sidewalk was padded with foam rubber.  Would such a precaution be worth it?

 

Don't overdo moderation

Even maxims like Ne quid nimis need to be used with moderation.  Arnold Schwartzenegger certainly wasn't moderate about working out and his hard work was rewarded with a very successful acting career.  Athletes like Kristi Yamaguchi, Jackie Joyner-Kersee, and Carl Lewis practiced hard for years before winning medals in the Olympics.  Yo-Yo Ma spent years studying the cello before becoming an accomplished musician.

In the next chapter, we'll see that it makes economic sense for people to specialize in one or more skills by devoting lots of time to them.  In developing these skills, moderation doesn't make sense─you may want to become the best you can be. 

Nor is moderation always appropriate for love, passions, and principles.  Consider the words of William Lloyd Garrison, who argued passionately against slavery in the 19th century:  

            On this subject I do not wish to think, or speak, or write, with moderation.  No!  No!  Tell a man whose house is on fire to give a moderate alarm; tell him to moderately rescue his wife from the hands of the ravisher; tell the mother to gradually extricate her babe from the fire into which it has fallen; but urge me not to use moderation.

Perhaps the Roman playwright Terence should have written, "Moderation in most (but not all) things."  Our heroes must, after all, practice moderation in most of what they do just to be able to find the time to develop their talents or pursue their causes.  It's partly because they're content with second-rate guacamole, dirt under their bookcases, and wrinkles in their shirts that they're able to excel in the areas that matter most to them.

           

          

 

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