Suppose that preferences are quasi-lincar: u(x, y) = f(x) + y, and monotonic f'(r) > 0. Denote the price of X by p and let Y be a numeraire p2 = 1. In parts (a) and (b) assume that income m is fixed and high enough for an interior solution. Also recall that with quasi-linear preferences the indifference curves eventually intersect both axes. (a) (5pts) Find the inverse demand curve for X. Under what conditions is X an ordinary good? How does income affect the demand for X? (b) (5pts) Show using a diagram that small changes in p lead to zero income effect for good X. (c) (5pts) Show that a large change in p could lead to a non-zero income effect for X. (hint: the optimum will have to jump from interior to corner point).