where c is consumption and is leisure. Let h be the total hours available to a household. Recall that the worker should split his time h into leisure I and working N such that h=1+N . The household spends on consumption, earns labor income, receives dividend income and pays proportional labor tax, instead of lump-sum tax T for . Let the wage rate per hour worked be w. (a) Write down the household's problem. (b) Find the optimal trade-off condition or equation between consumption and leisure in this example with the specific utility function given above. (c) Solve for optimal c and I in terms of w, t, h, (d) Analyze how a change in affects the consumption, leisure and labor supply choices using the solution in part 3. Explain these results using the income and substitution effects. Make assumptions if necessary. (e) Write down the government budget constraint given the proportional labor tax to finance exogenous public spending G. (f) The federal government decides to cut spending on public goods such as defense. Ana- lyze how this policy change affects the economic decisions (c", 1", and N") of Americans based on your results above