Martha has a job in which she earns $30 per hour. She values Income (Y) and Leisure (I). She has 400 hours a month available to spend working or at leisure. Her utility function is U(I,y) = I^.4y^.6 which  implies that the MU of I is .41^-.6y^.6and MU of Y is .61^.4y^-.4.

a) How many hours a month does Martha work? What is her income?

b) The government institutes a welfare program that guarantees individuals $2000/month. The guarantee is phased out immediately with the first dollar of income earned. How many hours does Martha work? What is her income?

c) The government revises its welfare program so that the phase-out rate is 1/3. Every dollar earned working lowers the transfer from the government by 1/3 dollars. How many hours does Martha work?