Sales tax. Consider the standard consumer problem that we have been studying, in which a consumer has to choose consumption of two goods cl and c2 priced (in money) P} and PE, respectively, before any applicable taxes. Many states charge a sales tax on some goods but not on othersfor example, many states charge sales taxes on all goods except food and clothing. Suppose that good 1 carries a per-unit sales tax, while good 2 has no sales tax. Use the variable t, to denote this sales tax, where I} is a number between 0 and l (e.g., so, if the sales tax on good 1 is 15 percent, write I] = 0.15 }. it. Using sales tax fl and consumer income Y, write down the budget constraint of the consumer. Explain economically howfwhy this budget constraint differs from the standard one we have been considering thus far. b. Graphically describe how the imposition of the sales tax on good 1 alters the optimal consumption choice (i.e., how the optimal choice of each good is affected by a policy shift from r, : 0 to I] :5 D). c. Suppose that the consumer's utility function is given by w(, (2) = logg + log c2- Using a Lagrangian, solve algebraically for the consumer's optimal choice of c and c2 as functions of A, P, 1, and Y. Graphically show how, for this particular utility function, the optimal choice changes due to the imposition of the sales tax on good 1