Kim is a single head of a household with two children and has the following utility function over consumption, C, and leisure, l:

u(c; l) = c^0.2l^0.8

There are 50 weeks in the work year and 168 hours per week. Assume that Kim earns $10 per hour and has no other sources of income. Normalize the price of consumption goods at $1.

(i) Sketch the family's weekly budget constraint. How many hours a week will Kim work? What will the family's annual consumption be?

(ii) Now suppose that the government gives a yearly basic income of $4,000 to every family regardless of the family's income. Sketch the family's weekly budget constraint. How many hours a week will Kim work?Does the extra $4,000 basic income increase Kim's consumption by$4,000? If yes why and if not then by how much and what has happened to the rest?

(iii) Instead of the above policy, suppose that the government gives a yearly basic income of $4,000 to every family regardless of the family's income but then taxes all earnings at the rate of 30% regardless of the hours of work. Sketch the family's weekly budget constraint. How many hours a week will Kim work? What will the family's annual consumption be?

(iv) The final policy to consider is the current Temporary Aid to Needy families (TANF) which phases out the benefits. That is, it deducts 30 cents from the $4000 yearly benefits for every dollar earned until all the benefit is phased out. Sketch the family's weekly budget constraint.How many hours a week will Kim work?