This problem concerns the runs-created index discussed in the preceding problem. Consider a batter who bats 100 times and always either makes an out, hits for a single, or hits a home run.
(a) Let x be the number of singles and y be the number of home runs in 100 at-bats. Suppose that the utility function U(x, y) by which we evaluate alternative combinations of singles and home runs is the runs created index. Then the formula for the utility function is U(x, y) = ________
(b) Let’s try to find out about the shape of an indifference curve between singles and home runs. Hitting 10 home runs and no singles would give him the same runs-created index as hitting _____ singles and no home runs. Mark the points (0, 10) and (x, 0), where U(x, 0) = U(0, 10).
(c) Where x is the number of singles you solved for in the previous part, mark the point (x/2, 5) on your graph. Is U(x/2, 5) greater than or less than or equal to U(0, 10)? ______. Is this consistent with the batter having convex preferences between singles and home runs?
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