3. Compensating and Equivalent Variations Jeanine works for a small startup company based in Seattle. She took advantage of relaxed policies about remote work during the pandemic and moved to Bozeman, Montana where the cost of living is much cheaper. She is paid a monthly salary of 55,000, her utiiity is U(1,}F}= (In: + gruff, and the prices of both x and y in Bozeman are 1. Her boss wants to require her to work in person again, but the prices in Seattle are pr = 1 and p}, = 2, and she is not offered a raise as compensation for moving. Jeanine says that she doesn't mind moving, other than the cost of living issue, as she thinks that Bozeman and Seattle are equally attractive places to live. However, she says that having to move is just as bad as having a cut in pay of $1\" per month. She also teils her boss that she wouldn't mind moving it she was given a raise of $i'il per month. [ignore ination and discounting in your analysis; in other words, you can analyze the problem as if you were dealing with a single time period.:| a} Which of H! or $i'il is the compensating variation, and which is an equivalent variation? Explain your answer conceptually. {3 points] b] Which of $1\" or Mr must be the largest in magnitude? Explain the intuition forwhy this must be the case; this answer should be only co nceptualfverbal, as you will do the math to check your intuition in the next part of the problem. {1 points} c} Solve for the values oil\" and N, showing your work. ll points] :11 1liliihat is jeanine's change in consumer surplus associated with her consumption of y when the price increases from 1 to l? {5 points] 4. EXTRA CREDIT In the previous problem, Jeanine's utility function exhibits constant elasticity of substitution, as it is 1. ML?) = (xi + f)? for 1' = 1f2. Imagine that Jeanine's utility was still [ES but with a different value for r. 1ii'll'hat would the limit for the change in consumer surplus calcuiated in part d:| of the previous problem be as 'r approaches [1? [3 points]