Prof.
Bryan Caplan

bcaplan@gmu.edu

http://www.bcaplan.com

Econ
812

**HW
#2 (please type all answers)**

1. Suppose 50% of all agents in an economy have
U=ln x + ln y, and the other 50% have U=2 ln x + ln y. All agents start with one unit of x and one
unit of y. Find the general equilibrium
relative prices and allocations.

2. Re-do problem #1, assuming that the first
type of agent starts with 2 units of x and 0 of y and the second type of agent
starts with 2 units of y and 0 of x.

3. Re-do problem #1, assuming that all agents
have U=x+y. (Hint: At disequilibrium
prices, agents want to consume only x or only y).

4. Suppose you can redistribute x, but not
y. Returning to problem #1, what exactly
must you do to:

(a)
make the equilibrium utility of the first type of
agents equal to .5,

(b)
give all agents of the second type the same utility,

(c)
and make type-2 agents' utility as high as possible
conditional on (a)?

5. (half page) Use
general equilibrium analysis to explain why barbers earn higher real wages now
than in 1900, even though there has been little technological progress in this
industry.

6. (half page) Explain
how betting markets could be used to resolve a practical controversy of your
choice. Carefully explain the exact bet
or bets that would need to be offered.
Would you be willing to bet against the market?