22.6 A welfare program for low-income people offers a family a basic grant of $6,000 per year. This grant is reduced by $.75 for each $1 of other income the family has.

a. How much in welfare benefits does the family receive if it has no other income? If the head of the family earns $2,000 per year? How about $4,000 per year?

b. At what level of earnings does the welfare grant become zero?

c. Assume the head of this family can earn $4 per hour and that the family has no other income. What is the annual budget constraint for this family if it does not participate in the welfare program? That is, how are consumption (C) and hours of leisure (H)

related?

d. What is the budget constraint if the family opts to participate in the welfare program?

(Remember, the welfare grant can only be positive.)

e. Graph your results from parts

(c) and (d).

f. Suppose the government changes the rules of the welfare program to permit families to keep 50 percent of what they earn. How would this change your answer to parts (d)

and (e)?

g. Using your results from part (f), can you predict whether the head of this family will work more or less under the new rules described in part (f)?