1.The following questions will rely on the concept of "expected productivity", where there is uncertainty to your circumstances, and hence your productivity. Expected productivity is found by multiplying each pos- sible productivity by its probability of occurrence, then adding these products. For example, if there's a 75% chance you have a productivity of 24, and a 25% chance you have a productivity of 16, your expected productivity is

75%(24) + 25%(16)

=18 + 4

=22

1) Suppose you cannot immigrate legally to the United States, and so there is some probability p you are caught and forced to return to Mexico. In this situation, your productivity is reduced by 1 from what it would have been if you had stayed in Mexico, on account of the hassle of trying and failing to immigrate. Assuming you will do whatever maximizes your expected productivity, how high does the probability p of being detected have to be in order to deter you from attempting to immigrate to the United States?

2.Suppose you also have the option of immigrating to California. Workers in the Californian construction industry have the same productivity as Arizonan workers, and so you would earn the same real wage there as in Arizona. However, because it is further away, you have to pay an additional travel cost equivalent to one unit of productivity. If we suppose California is unusually lax at enforcing immigration laws and your probability of being detected is eectively zero, how high would your probability of being caught in Arizona have to be to deter you to immigrate to California instead?