Marginal Productivity and Income
The basic theory for resource markets is part of the
theory of the
firm. Key concepts are those of marginal
resource cost (MRC) and marginal
revenue product (MRP). A firm maximizes profit when it
sets MRC equal to MRP. Let us briefly review this
result.
Common sense says that a firm will tend to buy a resource
if the added benefit to the firm (the MRP) exceeds the added
cost (MRC). The added benefit is the value to the firm of
the extra output that the resource produces. If increasing
the amount of the resource raises revenues more than it
raises costs, a firm can increase its profits by using more
of the resource. This is the case of MRP exceeding MRC, so
we have shown that the firm can increase profits when MRP is
greater than MRC. If reducing the amount of a resource cuts
costs by more than it cuts revenues, a firm can increase its
profits by using less of the resource. This is the case of
MRC exceeding MRP, so we have shown that the firm can
increase profits when MRP is less than MRC. It follows that
if the firm has maximized profits, MRP must equal MRC. If
the firm should increase resource use when MRP exceeds MRC,
and if it should decrease resource use when MRP is less than
MRC, then it is using just the right amount when MRP equals
MRC. Three-fourths of the difficulty in understanding this
result comes from the terminology--if you have problems
understanding this result, reason it out with no economic
terminology and then translate the reasoning into
terminology.
The amount of the resource that a firm wants to buy
depends in part on the extra revenue it can get from selling
production that the resource adds. A resource is valuable
not because it directly satisfies some goal, but because it
can indirectly satisfy a goal. Economists say that the
demand for a resource is a derived demand. The demand
for the resource is derived, or comes from, the demand for
the goods and services that the resource produces.
To push the analysis further, assume that many firms buy
the resource and that none of these firms can noticeably
influence price in any market. This assumption that firms
are price
takers means that marginal revenue equals price of
output, and that the marginal resource cost equals the price
of the resource. To make the following discussion less
abstract, suppose that the resource in question is hours of
labor, which means that the price in this market will be
wages.
With these assumptions, we get a diagram similar to that
used to explain the technicalities of economic efficiency.
On the left is Peter Milloy, a representative worker who
sells hours of unskilled labor. His supply curve is drawn so
that it slopes upward. But he is only one of a great many
workers selling in this market. To find the market supply
curve, one must add up all the hours of work that will be
offered at each wage.
On the right is Dynamic Enterprises, one of a great many
buyers of unskilled labor. Its demand curve will be the
downward-sloping part of its MRP curve. The MRP curve is the
demand curve for labor because this curve tells how valuable
another unit of the resource is to the firm. Hence, given a
wage, one can tell how much labor a firm demands by looking
at the MRP curve.
Dynamic Enterprises is only one of a great many buyers of
labor. To find the market demand, one must add up at each
wage the number of labor hours demanded by each firm. The
intersection of the market demand and market supply curve
gives the equilibrium wage--it will hire all workers who
contribute more to the firm than they cost.
There are some important results that come from this
simple analysis. First, owners of resources are paid their
marginal contribution to output. An owner of a
resource that adds a more valuable contribution to output is
paid more than an owner of resource that adds a less
valuable contribution. The key words here are "marginal" and
"adds." For example, garbage collectors perform a vital
service in large cities, and when they go on strike, people
are not only tremendously inconvenienced, but their health
may be threatened. The total value of the services of
garbage collectors is very high. But this high total value
does not mean that the value of another garbage collector is
high. If adding or removing one garbage collector changes
the value of garbage collection services little, his
marginal contribution will give a low wage in this market.
This analysis exactly parallels the diamond-water
paradox.
The graphs above can help illustrate changes that will
raise or lower wages or other payments to inputs. There are
two reasons why the demand curve could shift. First, it
could shift because people value the output more. For
example, the high salaries of professional basketball
players are due to the popularity of basketball as a
spectator sport. A century ago, a man with the same
abilities of a Larry Bird or a Michael Jordan would have
earned a normal income because there was no demand for his
special talents.
Second, the demand curve could shift because of increased
productivity, perhaps caused by changes in the amounts of
other resources. A trend in industrialized societies has
been to replace physical work with machines. As a result,
the rewards going to muscle power have fallen as compared to
the rewards going to brain power. Two hundred years, ago a
strong but stupid man would probably have earned more than
his smart but lame brother. Today, the results would
probably be reversed.
The supply curve can also change, and as it does, so will
the income that the resource earns. A new discovery of metal
ore will reduce the value of known deposits. Increased
availability of education increases the numbers of doctors,
lawyers, teachers, and accountants. If demand for their
services does not change, their increased numbers will cause
their incomes to drop. People who want to control the wages
they earn have usually tried
to control the supply curve.
Adding together all buyers and sellers of unskilled labor
or aggregating them, is useful because it gives us insights.
Sometimes, extreme aggregation is useful, such as treating
all labor services in the same market. This sort of extreme
aggregation is basic to macroeconomics. In the case of labor
markets, such aggregation is useful if we slightly alter the
graph above
Equilibrium in the labor market requires that MRC=MRP.
With the assumption that everyone is a price taker, this
condition can be written as
(1) Marginal Product x Price = Wage.
If we divide both sides by price, we get
(2) Marginal Product = Wage/Price = Real Wage.
The real wage, or wages divided by prices, measures the
purchasing power of what workers earn. If, for example,
wages increase by 10% and so do prices, then the amount that
workers can buy has not changed.
The illustration below graphs the marginal product of
labor and the supply of labor as a function of the real
wage. Suppose that the amount of labor declines. The supply
curve will shift to the left, the marginal worker will
become more productive, and the real wage will rise. Labor
will become more scarce relative to land and equipment,
which have not changed. The Black Death in
14th-century Europe reduced population by about
30% in a few years. As the illustration suggests, real wages
rose as a result.
The graph also suggests why economists in the 19th
century so often saw population control as a way to solve
poverty. Fewer people will, other things held equal,
increase wages and more people will reduce them. However,
those other factors have often not remained equal in the
real world. Europe is densely populated and Africa is
sparsely populated, yet Europe has a vastly higher standard
of living than Africa.
Next we look at something called tournament
theory, which tells us we can error by only focusing on
marginal productivity.
Copyright
Robert Schenk
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