No story. Just the mathematical model of consumer choice. Consider a consumer whose preferences are represented by the following utility function (defined over bundles of exes and whys): u(x, y) = 2√x+y. (a) Are the consumer's preferences convex? 1 point (b) Find the consumer's marginal rate of substitution, and show that its absolute value decreases as the consumption of exes increases. 1 point Py, respec- (c) Find the consumer's demand function of exes. In other words, find her optimal con- sumption level of exes when the unit prices of exes and whys are px and tively, and her income is m. 1 point (d) Find the mathematical expression that describes the consumer's Engel curve for exes, and represent it graphically. 1 point (e) Find the mathematical expression that describes the consumer's income-offer curve, and represent it graphically. 1 point (f) Find the mathematical expression that describes the consumer's demand curve for exes, and represent it graphically. 1 point (g) Suppose that the government levies a per-unit tax (t) on exes, so that their new unit price is p = Px + t. Show that the change in the consumer's demand for exes is entirely due to the substitution effect. You are allowed to ignore corner solutions in this part of the exercise.
