Minimization of Total Industry Costs of Production

Minimization of Total Industry Costs of Production


♪ [music] ♪ – [Alex] In this chapter,
we return to the invisible hand. We’re going to show
some remarkable properties of competitive markets,
properties that are a product of human action
but not of human design. That is, these properties have
neither been designed nor intended, nor perhaps even understood
by market participants. And yet through the process
of the invisible hand, a spontaneous order evolves in which these desirable properties
are an outcome. Let’s take a look. So for context, recall
that in earlier chapters we learned that markets connect and coordinate actions
all over the world. Think about the rose
and the coordination of actions which was necessary
to deliver the fresh rose to your door on Valentine’s Day. We also learned that
a price is a signal wrapped up in an incentive. That is, prices signal in what uses
resources have the highest value and they provide an incentive
to move resources to those high-valued uses. We also learned
that firms maximize profits by doing two things. First, by producing at the quantity where price is equal
to marginal cost. And second, by entering an industry
when there’s profits, when price is greater
than average cost, and by exiting an industry
when there are losses, when price is less
than average cost. What this chapter is all about
is connecting these ideas, bringing these ideas together. We’re going to show
that competitive markets have two remarkable
invisible hand properties. First, competitive markets
balance production across firms in an industry, so that total industry costs
are minimized for any given quantity of production. Second, entry and exit decisions
balance production across different industries so that the total value
of production is maximized. And we’ll explain
each of these in turn. To show how the invisible hand
minimizes total industry cost, we’re going to start with what looks
to be a quite different problem. Suppose that you owned two farms and you want to produce
200 bushels of corn at the lowest possible cost. How do you do it? Well by looking at
these two marginal cost curves, you might reason that since the cost
of producing any quantity of corn is lower on Farm Two
than on Farm One, then maybe the best thing to do is to produce all 200 units
on Farm Two. I’m going to show you
that that’s wrong. Now, let’s remember
that we could read the cost of producing the Nth unit of corn as the height of the marginal
cost curve for that unit. So here’s the cost of producing
the 200th unit of corn. Now imagine that you produced
all 200 units from Farm Two. Let’s now show a lower cost way
of producing 200 units. For example,
suppose you were to produce 25 fewer units on Farm Two. Your cost will then fall by area A. Now of course now
you’re producing 25 units less, so in order to make up
for that decrease in production, you’ve got to produce
25 more units from Farm One. Notice that in order to produce
those 25 units on Farm One, your costs go up by area B. Now here’s the key point — area A is bigger than area B. In other words by switching cost
from the high marginal cost farm to the low marginal cost farm,
you have decreased your costs by more than you have
increased your costs. In fact you’ve created a savings
of area C, the difference. Now if you follow
through this logic, it implies that whenever
the marginal cost on one farm is higher than the marginal cost
on the other farm, you can save money,
you can save resources, by transferring production
from where the marginal cost is high to where the marginal cost is low. Now what does that mean
if you want to minimize the total cost of production? The logic we just gave implies that if you want to minimize
the total cost of production, you should balance your production
across the two farms so that the marginal costs
on the two farms are equal. In this case a 160 units
from Farm Two and 40 units from Farm One. Again, just think about
if that were not the case. If the marginal cost of production
on Farm Two were higher than on Farm One, then you could
always reduce your cost by producing less on Farm Two
and more on Farm One. But of course
the reverse is also true. If the marginal cost on Farm One
were higher than on Farm Two, you would want
to produce less on Farm One and more on Farm Two. So the way to minimize
your total cost of production is to produce such that
the marginal costs of production are equal on your two farms. Now let’s consider
a much more difficult problem. Suppose we have Pat’s farm
located on the West Coast and Alex’s farm
thousands of miles away on the East Coast. And let us suppose
that no one knows the marginal cost
on both of these farms. Now the problem looks
almost impossible. How could we possibly
allocate production across these two farms
to minimize total costs when no one knows the marginal cost
on both of these farms? Clearly a central planner
would not have enough information to solve this problem. And yet, the market does
solve the problem. Because even though
nobody knows the marginal cost on both of these farms, Pat knows the marginal cost
on Pat’s farm. Alex knows the marginal cost
on Alex’s farm. And both of them know
the price of corn. Now consider,
how does Pat profit maximize? Pat profit maximizes by choosing
to produce that quantity such that price is equal
to Pat’s marginal cost. Alex chooses to profit maximize
by producing that quantity such that price is equal
to Alex’s marginal cost. And since the price of corn
is the same for both of them, they automatically choose
to allocate production across their two farms such that
the marginal cost on Pat’s farm is equal to the marginal cost
on Alex’s farm. And production
is automatically allocated so as to minimize total costs. Now notice that neither Pat
nor Alex intend nor perhaps even understand
this result. It’s only through the operation
of the market, through the operation
of the invisible hand, that production is automatically
allocated across these two farms to minimize total cost
of production. Look at what happens
when the price changes. As the price changes so does
the allocation of production across the two farms
in just such a way that total industry costs
are minimized. This is truly a remarkable result and one that people might not
even have suspected prior to the development
of economics and the ability to see
the invisible hand. So let’s summarize invisible hand
property number one. In a competitive market
with N firms, all firms face
the same market price. And to maximize profits,
each firm adjusts its production, adjusts its output, until price is equal
to that firm’s marginal cost. Therefore, the following
is going to be true. Price is equal to
the marginal cost of Firm One which is equal to
the marginal cost of Firm Two which is equal to
the marginal cost of Firm N. Since these marginal costs
are all the same, the total industry costs
of production are minimized — a remarkable result,
and one due to the invisible hand. Next we’ll look at invisible hand
property number two. – [Narrator] If you want
to test yourself, click “Practice Questions.” Or, if you’re ready to move on
just click “Next Video.” ♪ [music] ♪

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