Imagine Mother Goose is deciding whether or not to steal something from a grocery store at time t. Let's assume that Mother Goose knows the probability she will get caught is p and the probably that she will not get caught is 1p.

If she doesn't get caught, she gets 10 utils at time t and 0 utils at time t+1.

If she does get caught, she gets 0 utils at time t and -x utils at time t+1 as a punishment.

Answer the following:

a Assume that Mother Goose is an exponential discounter with = .95. Solve for what values of x Mother Goose will shoplift (according to a standard Becker model of criminal behavior).

b If p = 0, what values of x will lead to Mother Goose shoplifting? If p = 1, what values of x will lead to Mother Goose shoplifting? If p = .5, what values of x will lead to Mother Goose shoplifting?

c Now suppose that Mother Goose has present bias with = .5 and = .95. Once again, solve for what values of x Mother Goose will shoplift.

d Now imagine that Mother Goose has = .5, = .95, p = .5, and x = 8. Assume that in period t1, Mother Goose has the chance to vote on a law that will increase the severity of criminal punishment (i.e. increase the value of x). Assume that Mother Goose is completely naive, what values of x > 8 in period t1 would Mother Goose be in favor of moving to and for what values of x would Mother Goose be against moving to and for what values of x would Mother Goose be indifferent to move to?

e Same question as (d), but what if Mother Goose is completely sophisticated?

f Same question as (d), but what if Mother Goose is partially naive and thinks that in the future her will be .75 even though her actual is .5?

g For (f), what values of x will Mother Goose have voted for something that makes herself worse off?