Question

Suppose the representative household has the following utility function: U (c , l ) = lnc + 12 lnl

where c is consumption and l is leisure. Let h be the total hours available to a household. Recall that the worker should split his time h into leisure l and working N such that h = l + N . The household spends on consumption, earns labor income, receives dividend income π and pays proportional labor income tax τw instead of lump-sum tax T.Let the wage rate per hour worked be w.
Write down the household’s problem.

Answer 1

The household's problem is to maximize utility subject to the labor-leisure budget constraint, taking into account consumption, leisure, labor income, dividend income, labor income tax, and consumption expenditure.

Step-by-step explanation:

The household's problem can be framed as maximizing utility subject to the labor-leisure budget constraint. The utility function given is U(c, l) = ln(c) + 12 * ln(l), where c represents consumption and l represents leisure. The household needs to allocate the total hours available, h, between leisure, l, and working hours, N, such that h = l + N. The household earns labor income, receives dividend income π, pays proportional labor income tax τw, and spends on consumption. The household's problem is to choose the optimal combination of consumption and leisure such that utility is maximized, while satisfying the labor-leisure budget constraint and taking into account taxes and incomes.