Please solve

2. Consider a representative household in the static consumption-leisure model with well- behaved preferences over consumption, c, and leisure, l, represented by the general utility function a(c,l}. The household faces a price of P on consumption and earns after-tax nominal wages at rate W[1 Tn) on their labor, a, which is the portion of a unitary time endowment not spent on leisure so that 1 = n + l. {3.) Write down the budget constraint for the representative household. (b) Express the consumptionleisure optimality condition in terms of a(c, I]. (c) Using indifference curve analysis. graphically show the optimal choice (c', l\"). Label slopes and intercepts on your graph. [d] Suppose the government wants to tax only consumption instead of taxing wages. Moreover, they do not want affect the aggregate c'fl' ratio. Compute a consumption tax rate '1': in terms of the labor tax rate Tn that would achieve this goal. (e) If the government eliminates labor income tax and instead taxes consumption at the rate you computed in part {d}, is the optimal choice {c', 1"} is aected? Explain