Burglar

Bob, is a rational criminal, and is trying to figure out the amount he is trying to steal, x. Bob

has two other partners who provide him with the expertise and equipment to commit a crime, but

in exchange Bob must evenly split the amount he

steals with these two partners. You are given the

following information about the expected punishment for Bob:

y(x) =?

p(x) = (1/12,000)x

f(x) = 2 x

a. Determine Bob's payoff function. Draw a diagram with x on the horizontal axis and $ on the vertical axis. Include the payoff curve, and the expected punishment curve. What optimal amount x*, does Bob decide to steal?

b. Determine Bob's payoff, probability of detection, and the criminal fine he would pay if he got caught.