There are two goods, good 1 and good 2, and a consumer enjoys utility U(x1, x2) from a bundle consisting of x1 units of good 1 and x2 units of good 2. Assume that the prices of the two goods are strictly positive, that is, p1 > 0 and p2 > 0. Given an initial endowment (x1, x2), we consider the following problem: max x10,x20 U (x1, x2) s.t. p1x1 + p2x2 = p1x1 + p2x2.

1. Assume U(x1, x2) = x1 + Bx2 where B > 0 is a constant. Derive the demand for x1 and x2 as functions of p1, p2, x1, and x2.

2. Now, assume U (x1, x2) = x1 + B log x2. Redo part 1. Moreover, discuss what happens if the initial endowment changes to (Cx1, Cx2) where C > 0 is a constant.