Suppose poor households have preferences over consumption (C) and leisure (T) given byu(C,T)=ln(C)+ln(T)

, and they can work at hourly wagewp=5. Assume consumption costs one dollar, and they have 24 hours in a day to allocate to either leisure or working.

Solve for the household's optimal bundle of consumption and leisure, and how much utility they get.

C=

T=

u=

To help the poor, the government offers an income transfer of $20, but because picking up the check takes time, participants can only work up to 5 hours per day if they sign up for the program. (Continue to assume any time not spent working is leisure.)

Find their optimal bundle when the program is in effect.

C=

T=

u=

If the poor have a choice to sign up for the program, will they?

enroll/ not enroll/be indifferent?

What if the program didn't limit their labor supply, and was a pure income transfer of $20? Will they

enroll/ not enroll/be indifferent?

It's possible that the answers above depended on the functional form of the utility function. Suppose that the utility function of the poor wasu(C,T)=C, and that the program limits labor supply. In this case, if the poor had a choice to sign up for the program, would they?

enroll/ not enroll/be indifferent?