A consumer has preferences characterized by the utility function u(x1, x2) = In 21 + x2. a)Solve for an expression for this consumer's MRS ,Sketch 3 different indifference curves for this consumer. b) Suppose M = 15, P1 = 1, P2 = 3. Use the tangency condition MRS = - to solve for the optimal amount of good 1. Given this, determine the optimal amount of good 2. Sketch this optimal choice on a graph of the budget set. Include an indifference curve through your optimal point. c) Now increase income to M = 21. Derive the new optimal choice and show it on a graph as in b) d) Explain any difference between the points chosen in b) and c)

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