2. Consider a consumer with a utility function over two goods, x and y, given by U(x, y) = 9x1/3y2/3 Suppose our consumer has an income of $60, the price of good x is $4 and the price of good y is $9. Solve for the consumer's profit maximizing consumption levels of x and y. 3. Consider a consumer with a weekly income of $100. Our consumer buys two lottery tickets on his way home every Friday. Each ticket has a 1% chance of being a winner, which would pay out $1,000. Our consumer's utility is a function of only weekly income, w, and it is represented by U(w)=w. The probabilities that each ticket wins are independent of each other. a. Calculate the consumer's expected utility. b. Calculate the consumer's certainty equivalent and interpret. c. Is the consumer risk averse, risk neutral, or risk loving? Explain your answer. d. Calculate the risk premium and interpret.