Monday, September 22, 2008

On the Theoretical Effects of a Minimum Wage: Brushing up on Econ 102: Microeconomics

(This is more retro-blogging of some stuff I wrote up a couple of years ago to try to explain how economists think of minimum wages in fairly simple theoretical terms. I'd say enjoy, but that might not be the first feeling that comes to mind when you read it.)

Supply and Demand

In a market in goods and services, sellers usually come in with some
price that they're willing to sell at, and buyers come in with some
price they're willing to pay. Buyers will happily pay less, and
sellers will willingly accept more, and different buyers and sellers
all probably have different prices in mind. When the sellers price
their goods and services, or the buyers post their bids, some buyers
will find things at prices they think are acceptable, and some that
are too dear; some sellers will find buyers willing to pay their
price, and others won't. When everyone who can find a deal has done
so, then the remaining buyers and sellers can either adjust their
price to find another match, or they can go home. When everyone has
done a deal or gone home, we say that the market has cleared.

When the market is large enough for a single good or service that is
essentially identical from all providers, we call it a
commodity. In this market, there are enough sellers and enough
buyers that a single price will emerge, called the market clearing
price
, at which every willing buyer and every willing seller will
find a match. Sellers who price their product above this price will
find no takers, because the buyers can find it available elsewhere for
less. Likewise, buyers who are looking for a deal will go away empty
handed, because all the sellers can get a better price from other
buyers.

When the market gets an influx of buyers who want more stuff, or
alternatively the number of things for sale drops, the price of the
goods available will be bid up until the number of buyers willing to
pay matches the number of sellers willing to provide. If for some
reason, there are fewer buyers, or the buyers just don't want that
much of the product, or if more sellers appear with more goods, the
sellers will have to drop their prices to find buyers, since all the
buyers at the old, higher price will be gone, having already done a
deal.

Labor as a Commodity

In general, the service provided by a person as labor is not a
commodity, since each person typically brings unique skills and
productivity levels to bear on the work they perform. Considered
broadly over lots of people with similar skill and productivity
levels, a market will form the outlines of a commodity market in some
particular specialty, but this doesn't really apply to the entire
category of "Labor." One area where it comes close, however, is in the
unskilled or minimum training required labor category. On the seller
side, practically every able-bodied adult can supply this kind of
labor, and most will do so if the price is right. Some will do so even
if the price is minimal. At some price, then, the number of hours of
labor people are willing to supply will equal the quantity demanded,
and the market will clear. Once again, an influx of sellers (laborers)
or a drop in the quantity or labor demanded will tend to push the
price (wage) down, and an influx of buyers (employers) or a rise in
the quantity of labor demanded will tend to push the price up.
Photobucket
Markets with Price Controls

The idea that there should be a minimum or maximum amount that any
particular good or service should cost or that should be made
available doesn't seem intuitively obvious to most people, but when
the service is labor, we bring some other opinions to the table.

In the case of commodity labor, we call a minimum price restriction a
minimum wage. When the minimum wage is less than the market
clearing price, it has little effect. All of the sellers can find a
better deal, that is, a higher wage, and all of the buyers, or
employers, must satisfy their labor demands at the higher price or
leave their jobs unfilled. However, if the minimum wage is higher than
the market clearing price, then more people are willing to sell labor
at that price than employers are willing to buy. As shown in this
diagram, the quantity purchased will be less overall at the higher
price. The difference between this quantity and the quantity that
would be purchased at the market clearing price is the lost employment
opportunity, or the employment gap.
Photobucket


Note that at the higher price, sellers are willing to supply more
labor than at the market clearing price, mostly because more sellers
enter the market. The difference between the number of labor hours
made available and the number purchased is the apparent unemployment,
but this value is larger than the employment gap. One way to interpret
this is that raising the minimum wage above the market clearing price
will artificially inflate unemployment numbers, when the actual effect
on the number of people employed is smaller.

Markets with Supply Controls

The other kind of restrictions that are commonly applied to commodity
labor markets affect supply. Any given seller has only so many hours
of labor available to sell in a week. At a high enough price, some
sellers may be willing to place every waking hour in the market. Once
again new sellers may also enter the market at the high price to sell
a few additional hours of labor.

If a restriction is placed on the number of hours any given seller may
put on the market in a week, then the quantity supplied can only be
increased by adding more suppliers to the market. Sellers lose the
opportunity to sell extra hours at the market price, but an increase
in demand for labor hours will tend to push up the price for the hours
a seller does sell by a small amount, and will bring new sellers some
employment, as the market clearing price for labor hours rises with
the increased demand.

An overtime restriction that allows the supply but increases the price
will have a combination effect. To the extent that marginal cost of
additional labor hours supplied in the labor market is low (in
commodity markets, this cost is typically negligible compared to the
cost of goods) then purchasers will tend to hire more labor from the
less expensive unrestricted market. In the labor market however,
legal, contractual, and physical limits that raise costs to employ a
marginal labor hour are common. These may include a head tax, minimum
employment hour requirements, restriction to hiring from a particular
set of suppliers such as a union, and the costs involved in training
or providing a worker with tools or supplies. These costs are the ones
that can push an employer into purchasing expensive overtime instead
of less expensive regular labor hours.

The Big Fish Market

In a market, pricing power comes about when one party, or group
of parties, comes to the market with the bulk of the supply or the
bulk of the demand. This is when the marginal effect of the remaining
suppliers or purchasers isn't enough to change the price of the bulk
of the goods or services sold. If a seller has pricing power, then to
an extent, that seller may charge more than the net market clearing
price, even if other sellers will sell for less, because even when the
entire amount available at a lower price is purchased, there is still
some significant demand for the remaining amount supplied at the
higher price. In this case, the market may not clear at a single
price; the supplier with pricing power may accept the risk of selling
something less than all the available stuff for sale at the set price.
Other suppliers may go along with the higher pricing and also risk not
selling all of their goods; behavior in this case is mostly determined
by what pricing will maximize profit on the net amount sold.

Similarly, when a buyer has pricing power, other buyers may be willing
to pay more, but only a few suppliers are lucky enough to sell to
them, and the remainder must sell at the lowered offering price of the
buyer with pricing power or not at all, leaving some supply that would
have sold at the net market clearing price. The buyer asserting
pricing power accepts the risk of not getting all the quantity they
wish at the price offered; pricing is generally determined to maximize
the value obtained on the amount purchased.

In a commodity market, goods in one location are interchangeable for
goods in another location; the market may state its price "FOB
Chicago" for instance, and the price between other locations for
buyers and sellers may be adjusted relative to the cost of delivering
the goods elsewhere. Commodity labor tends to be a little less mobile
as well as less interchangeable. For any given person, the cost of
supplying labor hours close to home may be small, but providing it in
the next town or city may be prohibitive.

Pricing Power in Action

Let's consider that in Potterville, adult population 1000, there may
be one employer in town with commodity labor needs, Potter's Mill,
Inc. Being the sole commodity labor buyer gives them some pricing
power relative to all of the potential suppliers of labor hours in
Potterville. Lets say someone with a lot of time on their hands did a
survey, and found all thousand potential workers in Potterville will
provide forty hours of labor a week for ten dollars an hour, but only
five hundred will for five dollars an hour; another hundred people
change their minds for each dollar an hour difference. Now let's say
the mill offers five hundred forty-hour week positions at six dollars
an hour. (Apparently no one at the mill read the survey.) Six hundred
Potterville residents apply, and one hundred are turned away. They
were willing to work, some of them for even less than six dollars an
hour, but the mill only needs so much labor, so they must look
elsewhere.

But what if the mill has six hundred positions, and is only willing to
pay five dollars an hour? Five hundred people from Potterville apply
and all are accepted, and one hundred positions go asking. Potter's
Mill Inc. can raise its offered wage, or do without that labor, but
it's up to the mill. The mill offers 100 positions at six dollars an
hour. One hundred people from Potterville take the jobs. Potter's Mill
has filled its employment needs, and saved five hundred dollars an
hour over what it would have had to pay at a market clearing price for
all six hundred positions, using its pricing power. If the mill needs
more workers, it can go back in the market and pick up another hundred
at seven dollars an hour, another hundred at eight dollars an hour,
and so on. And that's assuming some of the people over in Millerville
don't get wind of this and start applying at lower wages than the
remaining Potterville residents will accept.

Competition and Pricing Power

Let's say another business opens in town - Bailey's Pool Cleaning
Service. It's a small outfit that needs only five workers. If they
offer six dollars an hour, they may get over five hundred applicants
who currently work at the mill for less. They pick five people, and
put them to work. Them mill must fill those positions, and finds that
they must offer a higher wage to do so, but they're still the holders
of substantial pricing power, and they still save a lot of money on
labor.

If forced to compete for the Potterville pool of workers against
enough other employers, Potter's Mill would find it didn't have that
kind of pricing power, and would have to pay the higher market
clearing wage when hiring all its workers. Some workers in that market
would benefit by being paid more than they would have been willing to
work for if they had to. A few employers that would have been willing
to pay more if they needed to, find that they can save their money and
fill their labor needs for less at the market clearing price.

The Minimum Wage Comes to Town

In an effort to curb vagrancy, vandalism, and voyeurism, the town
council in Potterville decides to enact a minimum wage. Some of the
townspeople aren't being paid enough at work to keep up with the rent,
so they wander the streets at night, tagging street signs and looking
in other people's windows. To abate the scourge, they declare a
minimum wage of seven dollars an hour. Currently some six hundred five
people are employed at the town's two businesses, at wages of five or
six dollars an hour. The board of directors at Potter's Mill Inc. goes
over the numbers with management, and determines that they can't
afford to run the business with the extra sixteen hundred dollars an
hour it will cost them given their current workforce level. They
decide to relocate the mill to Millerville. Meanwhile, Bailey's Pool
Cleaning Service could have afforded to give their workers a dollar
raise, except suddenly they don't have any business as all the people
with pools in their back yard are out of work. They reluctantly close
their doors.

Leaving the extreme of Potterville behind, in a larger town with a
more competitive labor market, the effect of a higher minimum wage is
unlikely to create a ghost town. There will be some employers at the
margins whose primary cost of business is commodity labor that will be
in trouble. There will be some few people who are pushed out of the
commodity labor market, unable to command the higher wage when the
number of labor hours purchased falls off. A fair number of people
will be slightly better off, given a raise at the expense of a few
employers whose costs have gone up and whose profit margins have
fallen, or at the expense of the consumers who pay higher prices if
the costs have instead been passed along by those employers.

Conclusion

On net, when the commodity labor market is restricted, just like when
restrictions are placed in any commodity market, the total value of
the exchange possible in that market is cut. We are all worse off in
the aggregate, although for many of us there may have been no effect,
costs may have risen for very few of us, and for another few of us
there was a benefit. Sometimes in some non-economic sense, obtaining
the benefit for a few may outweigh the net negative effect on total
value. It's not easy to say that this is clearly the case for a
minimum wage.

No comments: