4. Consider a representative household in the static consumptionleisure model with a gen eral utility function afar?) that exhibits positiye and diminishing marginal utility in each argument. The household faces a price of P on consumption and earns nominal wages at rate V.\" on their labor, n which is the portion of a unitary time endowment not spent on leisure so that 1 = n- + i. In addition, the household faces a proportional sales tax on consumption at rate Tc and a proportional tax on wage income of TR. {a} "Write down the budget constraint for the representative household. {b} Express the consumptionleisure optimality condition in terms of ul[c._ l]. {c} Express in words the economic meaning of the optimality condition. {d} Using indifference curve analysis. graphically show the optimal choice [c*_. P] given the budget constraint from part {a}. Label slopes and intercepts on your graph. {e} Suppose under present law that the federal wage tax rate is TR 2 .2. while the federal consumption tax rate is Tc 2 I]. Congress wants to lower the wage income tax rate to TR 2 .15, but does not want to alter the aggregate optimal choice of consumption and leisure [c*._ l'\"). Use economic logic based on the households\" optimality condition to explain how they can achieve this using the consumption tax. ff} Compute the consumption tax rate that achieyes the scenario described in part {d}. {g} Suppose Congress only lowers Tn without raising TC. Use your graph from part {c} to show how the optimal choice of aggregate consumption and leisure change, assuming that the substitution effect dominates the income eliect on labor supply