There are two options for maintaining monopoly power: entry deterrence and purchase of the rival company.

Consider the market for a homogeneous good, with market demand given by P(Q) = 34 − 4Q

Let there be a single established firm (I) in the market and a single potential entrant (E).

That both competitors have access to the same technology, characterized by the cost function.

Ci(qi) = 2qi + F, with 2 < F < 16

( 2 < F ensures that entry deterrence is preferred over accommodation and

F < 16 ensures that both companies can obtain positive profits under Stackelberg competition).

Consider two scenarios:

Scenario 1:

The incumbent can commit to an amount post-entry and the entrant believes that the incumbent will carry out his threats. However, the holder cannot purchase the participant's share.

Scenario 2:

The holder cannot commit to an amount after entry; the entrant rationally believes that the incumbent will accommodate the entry once the entrant is inside.

However, the holder has the option to purchase the entrant before production.

starts

If the incumbent buys the entrant, it becomes a monopoly.

We want to know which of the two scenarios the owner prefers for which values of F.

SOLVE using calculus please

SHOW STEP BY STEP solution please

Suppose we are in Scenario 2.

The timing of events is as follows.

First, the incumbent decides whether or not to make a purchase offer to the entrant and how much to offer if he does so.

Second, the participant decides whether to accept the offer.

If the entrant accepts, the incumbent pays his offer and becomes a monopolist.

If the entrant declines (or no offer is made in the first place), the firms compete by playing the Stackelberg game (with the incumbent as the leader).

i) How much should the incumbent offer the entrant to stay out?

ii) If the incumbent makes this minimum offer, what will be his final profit (net of the price he paid to purchase the entrant)?