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(30 points) Justine derives utility from peanut butter (b) and jelly (j) sandwiches. For Justine, a sandwich only provides utility if it contains the exact amount of (b) and (3'). That is, adding more b without more j renders no additional utility, and viceversa. (a) (5 points) What utility function can be used to represent Justine preferences? (b) (5 points) Is the utility function concave? (Hint: You can Show this with a gmph.) (c) (10 points) How many peanut butter and jelly sandwiches will Justine consume if of b is $0.5 and the price of j is $1.5, and she has income equal to $10? ((1) (10 points) The government introduce a new tax to reduce the consumption of peanut butter and jelly due to health concerns. As a result of this policy, the price of j increase to $2.5 and the price of b is now $1.5, calculate the compensating variation and use it to evaluate the welfare effect of the tax policy on Justine's welfare