Consider an individual with the following utility function: U(r, y) = ln(r+ 1) + y. The marginal utility of r is 1/(1 + r); the marginal utility of y is 1. (a) Find the marginal rate of substitution of y for r. Is there anything unusual about the MRSyr? What does this imply about the indifference map? (b) What is the definition of compensating variation (CV)? (c) Find the CV for any level of r where the change is that r is banned. (d) Find the inverse demand curve for r. (e) On a graph show the change in consumer surplus for a ban on r assuming that the price of r is zero and initial consumption is r = 4. (f) For any r what is the change in consumer surplus from a ban, assuming that the price of r is zero? (g) Show that the change in consumer surplus in these circumstances equals the CV! (h) Find the CV for an individual with the following preferences if q is banned and the price of q is zero: U(q, y) = 2q ^1/2 + y