Problem 3. Consider the same setup as Problem 3 from last week's problem set. Look carefully through the solutions to that problem, including diagrams, before you get started! Preferences are represented by 1 the Cobb-Douglas utility function with a = E' \"('51. x2) = N/ 951372 Suppose that initially m = $40, 191 = $2, 392 = $5. In this problem we consider the impact ofa (potential) price change where the price of good 2 increases to 195 = $10. a) b) Write down the indirect utility function. Find our consumer's utility levels ubefore (under the original prices and income) and uaft'" (after the price of good 2 increases). Write down the expenditure function. Find the Compensating Variation associated with this price change: lfthis price change has already happened (pffter = $2, pg" = $10), how much income do we need to give the consumer to reach their original level of utility, ubefm'e? Compare the answer you got to part b) above to the answer to Problem 3b) on last week's problem set. Which one is larger and why? Find the Equivalent Variation associated with this price change: Before the price change occurs pfefore = $2, pgefore = $5), how much income would the consumer be willing to give up to prevent it from happening? Illustrate your answers to parts b) and d) on two diagrams similar to slides 9 and 10 of Notes #8 from class. Clearly label the old ("before") and new ("after\") budget lines and indifference curves on each diagram