Question

1. Student A has preferences represented by U(x1,x2) = min{ax1,bx2}. Suppose good one has a special tax. The government wants good one to be consumed as little as possible, so it imposes a tax on its price when more than x units are bought. Specifically, the price of good one is p1 if less than x units are bought and it is p1(1 + t) when buying more than x units (for all the units bought). Where t indicates the tax imposed to the price (0 < t < 1). The price of good two is p2 regardless of the quantity bought of it. Assume p1 and p2 are strictly greater than zero. Suppose the income of student B is m > 0.

(a) Find the optimal consumption bundle the consumer would chose as a function of p1, p2 and m, that is, find his/her individual demand for good one and two. Hint: Study three cases, based on the budget set and then solve each, put the conditions that are needed for each case. αβ

(b) What happens if now the utility of student A is now U(x1, x2) = x1 x2 . Find the optimal consumption bundle the consumer would chose as a function of p1,p2 and m, that is, find his/her individual demand for good one and two. Hint: Study three cases, based on the budget set and then solve each, put the conditions that are needed for each case.

Answer 1