Suppose that in order to engage in some legitimate business, entrepreneurs need permission from a two-level hierarchy of government officials, A and B. However, to receive the permit, they have to bribe the officials. Suppose that the number of entrepreneurs, N, who choose to engage in the said business is a declining function of the total bribe needed to obtain the permit. That is,

N = 600 5(x + y),

where x and y are the bribes demanded by A and B respectively.

(a)Find the Nash equilibrium bribes demanded by A and B.

(b) If the officials can collude, what bribe will they demand?

(c) Some have argued that centralized corruption is less harmful than decentralized corruption. Carefully explain how you will verify this claim in this simple model.

2. Now here is the modification to question 1: When an official collects a total bribe of $ and is caught, he pays a total fine of $, where > 1. The probability that he will be caught is , where 0 < < 1. Thus 1 - is the probability that he is not caught. Assume that < 1.

(a)Find the Nash equilibrium bribes demanded by A and B.

(b) By plotting the officials' best-response functions, illustrate the equilibrium in (a) in a diagram.