Answer this question using diagrams.
Consider a version of the labour-leisure problem, where the household's
whose preferences satisfy the assumptions given in class. The household's
constraints are the same as in the notes with one exception: the government
levies a proportional sales tax on all purchases of consumption goods. Denote
the tax rate by s
(a) Formally write the household's problem.
(b) Draw a representative indifference curve. Show that the indifference
curve you have drawn is consistent with the assumption that the house-
hold's preferences convex? Explain.
(c) Draw a diagram of the budget constraint (be sure to label everything).
Explain, in words, the effect that the tax has on the household's budget
constraint.
(d) Why can we represent the household's budget constraint with an equality
constraint? That is, why don't we allow the household to consume less
than its income? (Relate your answer to our assumptions about the
household's preferences.)
(e) Depict the solution to the household's problem in a diagram.
(f) Suppose the tax rate increases. Illustrate the effects of the tax increase
on the household's optimal consumption and leisure bundle. Explain