1. Obtain the demand functions of x and y for the following utility functions, given m (income), px; and py (prices of x and y, respectively). Are x and y normal, neutral, or inferior?

(a) U = x + py;

(b) U = min [x; 2y];

(c) Given your answer in (b), let m = 15; px = 2; and py = 1: Suppose you cannot consumer more that 4 units of x due to health concerns. What will the effect be on your choice set and units of consumption on x and y?

(d) Lexicographic preference.

2. Assume that your utility function is characterized by U = U(x; y). Suppose that the government wishes to collect a fixed amount of taxes through either HST or income tax.

(a) Analyse and compare their effects on consumers, assuming that y is not subject to HST.

(b) Let U = min [x; y]: What happens to your answer in (a)? Why? Be sure that you highlight your points with help of diagram(s).