13.3 Derive the compensated labour supply function.

Show that ∂l c/∂w > 0.

In South Africa the government introduces a child support grant to unemployed families of R6000 per year. This grant is reduced by R0.75 for each R1 of other income the family has.

a.

How much in welfare beneits does the family receive if it has no other income? If the head of the family earns R2000 per year? How about R4000 per year?

b.

c.

d.

e.

f.

g.

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

Assume the head of this family can earn R4 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 programme?

What is the budget constraint if the family opts to participate in the welfare programme?

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

Graph your results from parts

(c) and (d).

Suppose the government changes the rules of the welfare programme to permit families to keep 50 per cent of what they earn. How would this change your answers to parts

(d) and (e)?

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)?