It is exactly 24 hours before Daryl's exams, and she is going to spend the entire time studying. She has an economics exam followed directly by a biology exam, with no time to study in between. Daryl wants to be an economist, so she places more weight on her economics exam score. Her utility is represented by U(E;B) = E^ 2/31 B 1/3 where E is the score on the economics exam and B is the score on the biology exam. Although Daryl cares more about economics (it has a higher exponent in the utility function), she is better at biology. Specifically, for each hour spent studying biology, she will increase her score by 5 points, but her economics score will only increase by 3 points for every hour spent studying economics. (a) Say Daryl will spend hE hours studying economics and hB hours studying biology out of her 24 total hours. What are the constraints on hE and hB in math { that is, what is the budget equation? Explain what it means that the \price" of hE and hB are both equal to 1 in this equation. (b) Rewrite Daryl's utility in terms of hE and hB. That is, how many units of utility does she get when she studies economics for hE hours and biology for hB hours? (c) Given some proposed hE and hB, calculate her Marginal Utility of an extra hour spent on each of Economics and Biology studying (that is, @U @hE and @U..>@hB ). Given that prices are both 1, the \bang-for-the-buck" condition says that Daryl should study at a level where her marginal utility on extra economics studying equals her marginal utility on extra biology studying. What mistake would Daryl be making if her marginal utility on economics studying were, say, higher than that for biology? Write out this bang-for-the-buck equation and simplify the algebra, if you can. (d) How many hours should Daryl optimally spend studying economics? How many hours will she study biology? Hint: Combine the budget equation with the bang- for-the-buck condition. (e) What will Daryl score on each of her exams