Homework #5

I?!\" (5 points) The price of a KFC bucket is $10 and the price of one video game is $50. Find Cartman's optimal consumption bundle. (5 points) What is the total utility of Cartman's optimal consumption bundle? (5 points) Cartman's grandma gives him $50 for his birthday. How should Cartman spend it? Explain. 3. (I Opor'nrs) Jake is consuming two goods: good Y and good X. We know that his preferences over two goods satisfy rationality (of course), monotonicity and the diminishing MRS assumptions. We also know that for him X is an inferior good and Y is a normal good. Draw Jake's preferences for X and Y (put Y on the horizontal axis). Use (hypothetical) budget constraint (5) and optimal choice(s) to demonstrate that good X is inferior and good Y is normal. 4. (20poinns) John and Jane are avid readers and consume only electronic books and paper books. For John e-books and paper books are perfect substitutes that he likes equally well. That is, John does not care which format (electronic or paper) the book is in, he only cares about having as many books of either kind as he can afford For Jane the two goods are less substitutable. She also likes paper books more than the electronic ones. A. (6190mm) Draw the indifference curves that represent John's and Jane's preferences for e-books and paper books on separate graphs. Put paper books on the horizontal axis. How are the two graphs different? B. ( 7 points) Suppose both John and Jane have the same income (M) and buy their e-books and paper books at the same market at respective prices Pm and Pro. Suppose also that paper books cost a little bit more, that is, Pm)- P23. Add the budget constraints to the graphs from A and show the optimal choices. Can you tell who would optimally buy more electronic books, John or Jane? Explain. C. (7 points) Suppose the price of paper books and incomes stay the same, while the price of electronic books increases so that Pas =PPB- Find the new optimal consumption bundle(s) for each consumer. What are the substitution and income effects of this price change on consumption of paper books for each consumer? What consumer has larger substitution effect and why? 5. (15 points) Eric Theodore Cartman consumes only Kentucky Fried Chicken (KF C) in buckets and video games. His preferences are described in the table below. For given quantity of each good it gives the marginal utility, keeping the quantity of the other good xed. Cartman has income m=$80 that he can spend on KFC and games. Quantity of each Marginal utility of Marginal utility good one bucket of of one video KFC ame 1 60 200 2 50 100 3 40 SO 4 30 25 5 20 10 6 10 5 7 + 0 0