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The economy consists of Sandra and Max. Their utility is increasing with income I, but decreasing in hours of work h. Specifically, their utility function is equal to U^i = 6√Iᵢ-hᵢ, where i denotes the individual (S=Sandra, M=Max). Max earns $30 per hour of work and Sandra earns $20 per hour of work. Labor income is their only source of income.
a. How many hours do Max and Sandra work each month? What is the total welfare if the social welfare function is W = UM + US Now suppose the government uses lump-sum taxes and transfers to redistribute income (each additional dollar of tax on one person means an additional dollar of transfer to the other person).
b. If Max has to pay $2,220 in lump-sum taxes and Sandra receives $2,220 in lump-sum transfers, how many hours will each of them work?
c. What is the total welfare if the social welfare function is W = U^M + U^S?
d. Explain the intuition why the welfare is different in (c) than in (a).

Sagot :

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