Prof.
Bryan Caplan
bcaplan@gmu.edu
http://www.bcaplan.com
Econ
812
HW
#6
1. Consider the following gambles:
Gamble
Gamble
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 



x^{2} 



2. An EU maximizer gets $100 with probability p
and $0 with probability (1p). Graph EU
as a function of p.
3. Consider a riskneutral farmer with the cost
function TC=q^{2}. The market
price is 10 with p=.5, and 1 with p=.5.
If the farmer has RE, what is his profitmaximizing 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)  bf^{2}. 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.
6. Do your beliefs about your overall academic
performance satisfy RE? (1 paragraph)
7. Use search theory to explain optimal
testtaking strategy. (1 paragraph)
8. After reading Caplan's Economic Journal piece,
pick the belief typical of economists that you agree with the least. Where are your fellow economists going
wrong? Is this systematic or random
error? (half a page)