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So now we have our model, it's already set up.

We have a leader, a follower, and we can give them slightly different roles now and

see how we can understand entry with this model.

So assume now that L is the incumbent, and F is a potential entrant.

It's a firm that's interested in entering the market and

breaking the monopoly of the leader.

So there is a cost of entry into this business.

This means that in order to enter you need to invest some initial money,

you need to sign some money.

And we will assume that this is f.

And in order for the firm to enter, there should be a condition.

Firms do not enter unless there is profit to be made.

They do not enter just because they want to be present into the market for

the sake of presence.

They enter because they expect that at some point they will get profit.

So in our model, F will enter if and only iff,

that's why my iff has two fs because it means if and

only if its profit from business exceeds the costs that it has

to pay in order to entry this business, the entry cost.

So unless you make serious profit that will make your investments to pay off,

you will not want to enter in this business.

So we know that the profit for the follower is KF(1- KL- KF).

This again has to be greater than F.

Now L wants to deter, of course,

doesn't like someone entering their territory and sharing their profit.

So therefore they want to deter.

What they have?

They have information.

They have information and they know how the follower,

how the potential entrant, reacts.

How do they know that?

Because they know RF.

RF, of course, is the same like before.

Nothing has changed so far in our model.

And L now starts thinking strategically,

starts thinking that, what if I set my initial investment

which I see that affects the investment of the follower?

What if I set it at these critical level

K* such that I make their profit,

the entrant's potential profit just equal to F?

So assume that if you just break even, you do not enter in this particular amount.

So if I set my investment equal to K*,

then perhaps there is a K* that will make

the entrant to just marginally decide to not enter.

Because I do not want to invest more, investment costs money.

I do not want to invest much more than K* because this will not make it better for

me later, will reduce my profit.

So substituting KL = K* in the reaction function of the follower RF,

and then plugging it into this equation that we

had before that we call it number 1, and

this is setting the profit of the follower equal,

just equal to that, to the entry cost.

So in this case we can get that 1- K*/2,

and all of it squared, should be equal to F.

So if we solve now this relationship with respect to K*,

this is a second degree equation, it's not very difficult to solve.

We will get that K* = 1- 2 x the square root of f.

So there exists a K* which is the level at

which if I set my investment there, if I set my initial capacity at that point,

then the entrant will decide to marginally not enter.

Okay, if I set my investment a little less than that and

my capacity is a little less than K*, then the entrant will decide to enter.

So we have established now that there exists a level

of capacity that if I invest to this capacity,

then the entrant will barely decide to abort, to not enter.

After successful deterrence, the profit for the leader will

be equal to the relationship that we had before but now we will have K*.

And K* we found it to be 1-2 over the square root of f,

which means that we can plug these into the profit function of the leader and

we can calculate the leader's profit.

Now the incumbent will not decide to deter if deterrence is not profitable,

if deterrence doesn't give the incumbent a higher profit than accommodating.

So you want to deter only if deterrence is not too expensive,

if you can afford to deter.

So the incumbent opts to deter if and

only if the profit from deterrence is greater than 1/8.

Why 1/8?

Because 1/8 is the profit that you would get if you accommodate.

And we have established that when we built the model.

We calculated how this 1/8 is coming.

So if the profit from deterrence is higher than

the profit from accommodation, you will always want to deter.

You will always want to throw the other guy out of the market,

to not allow this new firm to enter.

So this can be solved with respect to f which is the only parameter there.

So f has to be greater than 1/189.

That's a pretty small number here.

So the incumbent's choice depends on the entry cost,

how much it costs to the entrant to enter this business.

If f is high, deterrence is easy, it's cheap,

it's affordable for the leader and we'll go for it.

The incumbents always go for deterrence when they can, and

we will see how this relates to other aspects of our life in a later segment,

and it will be very interesting.

But if it's high, it's okay.

But if it's low, the cost of entering is low, is 0,

then probably returns is not going to be possible.

In any case, in any case, if there is a positive entry cost,

it doesn't matter how big it is, assuming that it's big enough

to make the deterrence affordable, it is just affordable.

It is not free.

Deterrence does not come free for the incumbent.

This means that L can price, not higher than 1- K*,

coming from this demand curve given the fact that now is a monopolist again.

So successfully deterred is a loan, has capacity K*.

Therefore, quantity K* saw that the price from the demand curve will be 1- K*.

So this means that cannot charge the monopoly price,

has to charge less than the monopoly price.

So L is alone in the market but still cannot treat this market as a monopolist.

This is a rather interesting result.

It shows why some firms have monopolies, but they do not behave as pure monopolies.

And we have several examples around us of firms that they have a lot of market power

but they do not use it explicitly to exploit the consumers.

The next segment will be about reputation, how it is important in our life but

also in business.

Stay with us.

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3. Dynamic deterrence: preemption

Industrial Organization: Strategy and Competition in Business

Meet the Instructors