Consider a household who lives for only one period. The household is endowed wit

Question

Consider a household who lives for only one period. The household is endowed with h units of time, which can be allocated between leisure I and time spent working. The real wage of the household is tw units of the consumption good per unit of working time (i.e, the consumption good is the numeraire). The household also owns some firm stocks, and hence receives dividend income . Finally, the household pays a lump-sum tax T to the government. The household's preferences over the consumption good and leisure are represented by the utility function u(C'), which is both monotonic and concave. (Hint: C and I are endogenous, and w, h, and T are exogenous.)

Explanation / Answer

8.

(a) If the dividend income of household will increase, then it's total income will increase. Given that both consumption good and leisure both are normal goods, with an increase in income the household will increase the quantity consumed of both, i.e., consumption good and the leisure.

(b) With an increase in wages the household would get higher income even while doing less work, so the household would reduce his work and increase his leisure in the proportion so that it will get total income higher than what it was getting earlier but will reduce its hours of work and increase its leisure time to enjoy its increased income. For example if the household was getting wages of $100 for every day and it was working for 6 days and was earning $ 600 in a week. Now, suppose wage is increased to $150 per day, then he can earn $ 600 as before by working only 4 days that would increase his leisure. But the household would choose to increase its total income so that it could increase itsI consumption as well as leisure by choosing 5 days work and earning of $ 750. Noe, his consumption as well as his leisure are increased.

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