Exercise #3. Consider the following statements and say whether they are true or false and why. To get credit you should provide a clear justification for your answers. (a) [4 pts.] If two goods are perfect complements and the price of one of them increases, the quantity demanded of both goods decreases. (b) [4 pts.] A non-transitive preference relation can be represented by some utility function. (c) [4 pts.] Consider two goods x and y. If preferences are strictly convex, the absolute value of the marginal rate of substitution between x and y is decreasing along an indifference curve as x increases. (d) [4 pts.] The following Cobb-Douglas utility functions represent two different preference relations: u1 (x,y)=0.3 log(x)+0.6 log(y) u2 (x,y)=0.6 log(x)+1.2 log(y). (e) [4 pts.] If a consumer is making an optimal choice between two goods x and y, then, independently of his preferences, the following condition must always hold: px py = MRS (x,y). (f) [4 pts.] If the following condition holds px py = MRS (x,y) then a consumer must be making the optimal choice between x and y, independently of his preferences. (g) [4 pts.] A cigar is a luxury good for a consumer that has Cobb-Douglas preferences over cigars and food. (h) [4 pts.] Consider two goods x and y, with prices px and py, respectively. A 0.07 percent value tax on these two goods does not affect the relative price of x in terms of y. (i) [4 pts.] The marginal rate of substitution measures the rate at which the market is willing to substitute one good for the other. (j) [4 pts.] An indifference curve represents the collection of all the bundles that a consumer can buy.