1. 2. 3. Suppose that a consumer has a utility function u(x1, x2) = x1x2, where x is the quantity of good 1 and x2 is the quantity of good 2. The price of good 1 is p per unit, the price of good 2 is p2 per unit, and his money income is m. Find the optimal consumption bundle (x1, x2). (3 points) Derive the demand function for good 1. (2 points) (1) (3) Suppose that he originally faces p = $1 and p2 Then the price of good 1 increases to $4 per unit. (a) (b) (c) = $1, and has m = $1,000. Calculate the compensating variation in income. (5 points) Calculate the equivalent variation in income. (5 points) Calculate the change in (Marshallian) consumer's surplus. If you cannot calculate the change, illustrate it graphically. (5 points) Suppose that a consumer has a quasilinear utility function u(x1, x2) = v(x1)+x2, where x is the quantity of good 1 and x2 is the quantity of good 2. The price of good 1 is p per unit, the price of good 2 is $1 per unit, and his money income is m. (Hint: The quantity demanded of good 1 depends only on the price of good 1, so that we write the demand function for good 1 as x1 = x1(p1).) Now, suppose that the price of good 1 increases from p), to p*. (1) (2) Show that the compensating variation in income and the equivalent variation in income are the same. (10 points) Show that they are both equal to the change in (Marshallian) consumer's surplus. (10 points) In the market for blue popcorn, there are two groups of consumers, group 1 and group 2. The demand function of each consumer in group 1 is given by D(p)=204p. The demand function of each consumer in group 2 is D2(p) 10p. If there are 1,000 consumers in group 1 and 2,000 consumers in group 2, what is the market demand function for blue popcorn? (10 points)