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