9 Consider the utility function u(x1, x2) = 3 ln(x1) + 2 ln(x2). Initially p1 = $1 and p2 = $2. Income is $ 15. 1. Derive the optimal consumption bundle. [05 pts] 2. If the price of good 1 doubles to $ 2, derive the new consumption bundle. [03 pts] 3. Now suppose u(x1, x2) = xax1a. Given M ,P1, P2 derive the ordinary demand function for 12 the two goods. Further suppose a = 43, P1 = $1, P2 = $2 and Y = $100. Draw the budget set and show the optimal point chosen by this consumer. Include a reasonable sketch of an indifference curve through the optimal point. [06 pts] 4. Andy utility function is u(x1, x2) = 3x1 + 5x2. What are his marginal utility for the two goods? Suppose that he has an income of $40 and can purchase x1 at $2 and x2 at $4. What bundles of x1 x2 should he purchase to maximize her utility? Why? [06 pts]