[Narrator] Hi.
Today we are going to look at some models which economists use to help understand
product differentiation.
When do firms choose to make their products similar
to their competitors?
And when and why do they choose
to make their products different from their competitors?
These are called
because the analogy is going to be to location.
Let's begin.
Begin with Harol Hotelling's 1929 linear city model.
Hotelling said, "Let's think about Main Street, USA."
Here's one end of Main Street; let's call this zero.
Here's the other end, one.
And let's imagine for the moment
that firms selling similar products locate here
and here at A and B along this, along Main Street.
Now the firms are selling similar products,
so what are customers going to do?
Well, they are going to shop at the firm which is closest to them.
So clearly, customers located to the left of Firm A will shop at A,
customers to the right of Firm B will shop at B,
and they'll split the customers in the middle.
Now, this is a very simple set up,
but notice that location can be understood
in more abstract ways other than literal distance.
As we'll talk about later,
we might interpret this as
or we might interpret this street,
this location, as being in an abstract space
of sweetness where less sweet are located over here
and more sweet are located over here.
So this model of Harold Hotelling is going to be interpreted
in a number of different ways.
Now, I said, "if the firms locate here."
What we really want to understand is:
Where will the firms locate and what prices will they charge?
That turns out to be quite a difficult problem,
but we're going to take it in steps.
Let's begin by assuming that prices are fixed,
so firms only make a location decision.
What will happen?
In this case, we can show that firms A and B
will choose to locate exactly
in the middle of Main Street.
That is, there will be a principle of minimum differentiation.
In this case, A will get half of the market.
Everybody to the left of Firm A will come and shop at A.
B will get half of the market.
Everybody to the right of Firm B will choose
to locate at Firm B, will choose to shop at Firm B.
Now, why is this the case?
The easiest way to show that this is the equilibrium
is to show that any other possibility cannot be an equilibrium.
So, for example, suppose that Firm A were to locate off center.
What would Firm B do in this case?
Well, in this case, by locating next to Firm A,
Firm B can grab up more than 50% of the market.
So, in this situation, Firm A will get everyone to the left,
which is a small portion,
and Firm B will get everyone to the right,
which is a majority, more than the majority, of the market.
So Firm B will get more than half of the market.
Firm A will get less than half of the market
if A chooses to locate off center.
What is A going to do in this situation?
Well, A might decide, "Hey, I would rather be to the right of Firm B,
somewhere over here."
In that case, A is going to get more than half the market,
and B would get less than half the market.
Following this logic through, one can see that the only position of stability,
that is, the only position in which
neither A nor B can make themselves better off
by a unilateral move,
is where they choose to locate exactly in the middle.
In this case, if A were to move to the right of B,
A would get less than half of the market.
A doesn't want to do that since by locating in the middle,
it gets half the market.
B could move over here, but again,
that's going to reduce B's share of the market,
so neither A nor B want to move
given that both of them are in the middle.
This is called a
when neither player can improve their pay-offs by a unilateral move.
This is a Nash equilibrium, after the famous economist John Nash.
Now, you might say, "Well, what?
Is this a realistic situation, where prices are fixed?"
As we'll see, yes, sometimes it can be.
In France, for example, the booksellers aren't allowed
to charge different prices,
but there are other applications as well.
Let's take a look.
We sometimes do see a principle of minimum differentiation
in location decisions.
Here's a Starbucks, and right next door, we have Peet's.
Now, the prices at Starbucks and Peet's are going to be determined
by national considerations and not set at every individual store.
Thus, this is an example of a location decision,
where prices are fixed.
Notice that, of course, Peet's and Starbucks do try
to differentiate their product in other ways.
But it's hard enough to solve this model in one dimension,
let alone two or more dimensions.
Let's give another application.
Here's an application of politics based upon Anthony Downs' influential book,
An Economic Theory of Democracy
Suppose we think about our space as being from less spending over here
towards more spending over here.
And let's imagine that the Republican Party chooses a position
towards the less spending part of the spectrum.
Notice that the parties here don't really offer prices for their product,
so this is a good application of the fixed priced version of the model.
Now, what are the Democrats going to do?
Well, for very similar reasons to that which we just discussed,
the Democrats will choose to take a position
just to the right of the Republicans.
In this case, the Republicans will get all the voters who want even less spending
than the Republicans are offering,
but the Democrats will get all the voters who want more spending
than the Democrats are offering.
And that's a majority of the voters,
so the Democrats will pick up all of these voters here.
The Democrats will win the election.
What will the Republicans do in response?
Well, the Republicans, rather than losing the election will probably choose
to take a position just to the right of the Democrats.
In this case, the Republicans will get the majority of the votes,
and the Democrats will get the minority.
And the Republicans will win the election.
Once again, just as before,
what is the final consequence of following this logic to its conclusion?
It's that both parties locate in the middle.
Or to be more precise, both parties locate--
choose the position which is most favored by the median voter.
The median voter gets exactly what they want,
even though nobody else does.
This model can be generalized in a number of ways.
For example, I've implicitly assumed that the voters are equally spread out.
But we could have a whole distribution of voters,
and the model will go through.
The parties will want to converge
to the most favored position of the median voter.
We could also talk about primaries and how the parties
have to try and get to the median voter in the primaries,
and that's going to be different than the median voter in the election,
and the difficulty of trying to please the party members
and then to please the general electorate, --
and so forth.
But you get the basic idea
which is that there is an incentive for the parties to move towards --
the preference point of the median voter.
And that's going to make the parties very similar to one another
in their ultimate positions,
no matter what they say in terms of their rhetoric.
Now so far, we've only looked at the model where prices are fixed.
More generally, we want to look at the model where firms choose
both prices and locations.
To do this properly, we need to specify what is the cost to consumers
of moving, of traveling to their closest store.
And we're going to make the assumption that the firms have,
that the consumers have quadratic transportation costs.
This simply means that the cost of walking to the nearest store
increases the farther away the store is,
and it increases at an increasing rate.
Now, remember that we can interpret this model in a lot of different ways,
so we might also interpret this as,
"what's the cost to the consumer of moving away
from their ideal preference point?"
And in this case, the farther they move from their ideal preference point,
the lower the utility of the good,
and the utility is lowering in a quadratic way.
Well, it turns out if you specify the model in this way,
what you get is maximum differentiation.
The firms split as far apart as possible,
they move as far away from one another as possible.
Half of the consumers will then travel to the firm on the right,
half of the consumers will travel to the firm on the left.
Now, what's the intuition here?
The intuition is that --
the farther apart the firms are,
the higher the price they can charge.
When the firms move far away from one another,
each one of them gains monopoly power.
Because they have the monopoly power,
they can charge higher prices.
A consumer right in the middle, for example, is indifferent,
and that consumer could go either to the left
or to the right store.
But every other consumer has a most preferred store.
So consumers which are close to the right, for example,
have very big costs, remember the costs are quadratic,
so they would have very big costs of going to the store on the left.
Same thing, consumers who are close to the leftmost end of Main Street,
they would have really big costs
of going to the store on the right.
That means that the store on the right has monopoly power
over the consumers which are closest to it.
The store on the left has monopoly power
over consumers who are closest to it.
That allows the firms to raise prices.
So there are two opposing forces in these models.
Firms want to move apart
in order to gain monopoly power and raise prices,
firms want to move closer to their competitor
in order to gain more market share,
in order to gain customers.
When we have quadratic transportation costs,
it turns out that maximum differentiation is the solution.
When we had zero pricing power and firms had to charge the same price,
we found minimum differentiation.
Depending upon the balance of costs,
the costs to consumers, and so forth,
and some other technical assumptions,
you can get different solutions to this model,
but those are the two main forces.
When you move apart, you get more monopoly power,
when you move closer, you get more market share.
Let's review.
So in the first version of the model,
we really had too little differentiation.
That is, the stores were located right next to one another.
That doesn't give consumers much of a choice
when the stores are selling identical products
right next to one another.
In the second version of the model, we really had too much differentiation.
The stores were located at the extreme ends of the city,
and a lot of consumers had to travel a long distance
in order to get to the store, and prices were high as well.
Notice that just-right differentiation would actually have the stores located
not in the middle or at the extremes,
but at the one-quarter and three-quarter points.
If you work out the mathematics, it's pretty easy to show
that if the stores were located at one-quarter and three-quarters,
this would actually minimize
the transportation costs for the consumers.
This would be where a social planner would put the stores.
Just a right amount of differentiation, still have some competition
but you also minimize --
the amount of transportation costs.
Notice that, in this model,
we do not have an invisible-hand result.
That is, we can have too little differentiation,
we can have too much differentiation.
If we got just-right differentiation, that would just be by accident.
There are no forces in these models necessarily pushing the stores
to the social optimum.
It's not clear what the policy should be,
whether we might be able to fix that,
how we should adjust to this,
or whether it's even a big problem,
but it is worthwhile pointing out that there is no invisible-hand result
in the Hotelling linear city model.
For further reading, here is Hotelling's original article
and Downs' book, which we've already mentioned.
Shepsle and Bonchek have a nice textbook style analysis of politics,
which uses the median voter theorem as well as other spacial models.
And the applications to industrial organization
to the location of firms,
these are classic topics in industrial organization.
You can find them discussed in almost any textbook.
A leading graduate textbook,
although it's a little bit out of date nowadays,
is John Tirole's book,
Thanks.