[Mr.Puff]

Hey guys,

I am trying to calculate the reservation wage for "John" on my problem set. Here is what I know.

John has 112 hours a week available for work or leisure.
His non-labor income is $25.
U(C,L)=C^2+L^2

This is how I did it.
MUc=(dU(C,L)/dC)=2C
MUl=(dU(C,L)/dL=2L
MRS=-(MUc/MUl)=-2C/2L
MRS=-C/L
MRS=-25/112
Reservation wage = 25/112

This is calculated by taking the slope of the indifference curve at H=0 or Leisure = Max and where C=V (non-labor income).

My answer should be correct, but the next question asks, "Will John work at $5 an hour? $10 an hour?" According to my calculations he will... for both.

Here is where I start to question myself... The last part of the problem asks me to calculate the employment rate in a town of 100 people with the same utility function as John. This is assuming that 25 people can earn $5 an hour, 25 can earn $10 an hour, 25 can earn $20 an hour, and 25 can earn $100 an hour. All of these people have a non-labor income of $25 also.

My calculations give an employment rate of 100% because the reservation wage is just so low.

HELP!