Based on the Aghion and Bolton models assupmtions - reservation price equals 100, the incumbent's unit cost of production is 50, the entrant's unit cost is distributed randomly but uniformly on the interval between 0 and 100, there is a Bertrand price competetion in the second period of the game - the expected payoff of the incumbent is:Select one:a.100.b.75.c.50.d.25.e.0.

The Aghion and Bolton model is a model of financial contracting under the assumption of costly state verification. It is used to analyze situations where a firm (the incumbent) faces potential competition from an entrant. The model assumes that the entrant's unit cost is distributed randomly but uniformly on the interval between 0 and 100.

Given the assumptions, we can calculate the expected payoff of the incumbent as follows:

1. In the first period, the incumbent can sell the product at the reservation price of 100, since there is no competition yet. The profit from this sale is 100 - 50 = 50.

2. In the second period, there is a Bertrand price competition. The incumbent will set a price equal to its unit cost of production, which is 50. The entrant will win the market if its unit cost is less than 50, and the incumbent will win if the entrant's unit cost is more than 50. Since the entrant's unit cost is uniformly distributed between 0 and 100, the probability that the incumbent wins is 0.5. Therefore, the expected profit in the second period is 0.5 * (50 - 50) = 0.

Adding up the profits from the two periods, the expected payoff of the incumbent is 50 + 0 = 50.

So, the correct answer is c. 50.