Solution Set 1. 8 points. Draw an indifference curve map representing preferences with the following characteristics: (a) commodity 1 is a bad, (b) commodity 2 is a good, and (c) preferences are convex. Label your axes, and indicate the direction of increasing utility using a sun or arrows. 2. 20 points. Consider a consumer with utility function given by u(x1, x2) = x1 x3 + 10. The consumer has wealth m, and prices are p1 and m. (a) 8 points. Write an expression for this consumer's marginal rate of substitution, as a function of x1 and x2. (b) 8 points. Find the consumer's demand for goods 1 and 2, as functions of the exogenous variables. (c) 4 points. Without working through the math again, how would your answers to parts (a) and (b) change if the utility function were instead 1 2 Mn, x2) = xf' x3 ? Explain your answer in one sentence, using a term for a concept from the course. 3. 12 points. Consider a world with two goods, x1 and x2, and consumer wealth given by m. Assume prices for both goods are positive. Draw the income offer curve and good 2's Engel curve (labeling all axes) given demand with the following characteristics: - For m 4: The consumer chooses a bundle with x2 = O