3. Compensating and Equivalent Variations Jeanine works for a small start-up 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 $5,000, her utility is U(x, y) = (x 1/2 + y 1/2), 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 px = 1 and py = 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 $M per month. She also tells her boss that she wouldn't mind moving if she was given a raise of $N per month. (Ignore inflation 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 $M or $N is the compensating variation, and which is an equivalent variation? Explain your answer conceptually. (3 points) b) Which of $M or $N must be the largest in magnitude? Explain the intuition for why this must be the case; this answer should be only conceptual/verbal, as you will do the math to check your intuition in the next part of the problem. (2 points) c) Solve for the values of M and N, showing your work. (10 points) d) What is Jeanine's change in consumer surplus associated with her consumption of y when the price increases from 1 to 2? (5 points)