Prof. Bryan Caplan

bcaplan@gmu.edu

http://www.bcaplan.com

Econ 812

HW #6

1.  Consider the following gambles:

Gamble 1: 50% chance of \$100, 50% chance of \$0.

Gamble 2: 10% chance of \$50,000, 40% chance of \$10,000, 50% chance of \$1.

Gamble 3: Equal chances of \$100, \$1000, \$10,000, \$100,000, and \$1,000,000.

Fill in the certainty equivalents:

 EU Gamble 1 Gamble 2 Gamble 3 x.5 x x2

2.  An EU maximizer gets \$100 with probability p and \$0 with probability (1-p).  Graph EU as a function of p.

3.  Consider a risk-neutral farmer with the cost function TC=q2.  The market price is 10 with p=.5, and 1 with p=.5.  If the farmer has RE, what is his profit-maximizing output level?  If the farmer beliefs do not satisfy RE (he thinks p=a), solve for lost profit as a function of a.

4.  Suppose your probability of finding a job is given by p=f.5, where f is the fraction of your time that you devote to job search.  Your gross EU of getting a job is 10; your gross EU without a job is 0.  Your net EU=EU(job outcome) - bf2.  Solve for your optimal f.

5.  Suppose your EU=w.5, and insurance is sold at twice the actuarially fair rate.  Your uninsured income is \$40,000 with p=.9, and \$10,000 with p=.1.  Solve for your optimal quantity of insurance.