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Treat Bob and Joe as having the same utility function as provided at the beginning of the questionIndifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joes preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also, find b. What is Joes marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive c. Given your answer in part (b), find Joes MRS when q1 4 and q2-4. If one unit of good 1 was taken U2. description of what MRS represents. from Joe, how much of good 2 would he need in compensation to maintain his original level of utility? Fractional units of each good are possible. Graph Joes indifference curve for a utility level of 10. At a minimum, use the 3 bundles of the goods that have the following levels of good 2 (0, 2, & 4) to plot the indifference curve. Does Joe have a diminishing marginal utility for good one? How about for good two? d. e. Is the fact that Bobs indifference curve intersects with the q axis a violation of any of the 5 properties of indifference curves? Briefly support your answer. After considering the preferences represented by this utility function, provide an example of goods that might be reasonably represented by qi and q2 (Hint: think about how the utility Bob derives from consuming good 2 differs from that of good 1). f.

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