1. Assume that: i. Andrew, a sports fam derives utility 'om attending football and basketball games. ii. The price of each football ticket is $16; the price of a basketball game is $20. iii. Each football game takes 3 hours; each basketball game takes 2 hours. A. Assume that Andrew has $100 per month to spend on football'basketball tickets, and that he has more than enough time to attend all the games he wants. Sketch Andrew's budget constraint. B. Now assume that Andrew can only,r spend 13 hours per month at sporting events, but he has more than enough money.r to attend all the games that he wants. Sketch the budget constraint. C. Now assume that Andrew has only $100 per month to spend and only 18 hours per month available. Sketch the budget constraint, and explain why it can be characterized as having a kink. D. Suppose that Andrew's point of maximum utility occurs at the kink. What can you say about the value of the marginal rate of substitution in equilibrium? What is the MRS if the equilibrium is not at the kink? 2. A.(9N4.2) A young bottled water drinker has $30 to spend stocking up his cellar. He enjoys two particular types of bottled water, one from France (we) that costs $2 a bottle and one from California (we) that costs 40 cents a bottle. How much of each water brand should the consumer purchase if her utility is U(w,, W ) = W B. When she goes online to order, the young woman finds that the price of French water had fallen to $1 a bottle but the price of California water was unchanged. How much of each brand should she purchase now to maximize utility?3.(10N4.4) Mr. Odde Ball enjoys commodities x and y according to the utility function U(x, y) = A. Maximize Mr. Ball's utility if Px = $3 and Py = $4 and his income is $50. B. Consider Mr. Ball's indifference curve either graphically, or by calculating the MRS. What does this tell you about Mr. Ball's behavior? Have you found a true maximum?4.(9N4.8) The lump sum principle discussed in class applies when the government transfers money to people just like it does when they tax people. This problem examines such a situation. A. Use an indifference curve graph to show that an income grant to a person provides more utility than does a subsidy (the government pays part of the price) on good x that costs the same amount to the government. [Hint: a similar graph for taxes is found in Nicholson (9th ed.) p. 107] B. Given a Cobb Douglas expenditure function E(P , P ,U.)=2P/P/U. . Let Px=1 and P.=4. Calculate the extra purchasing power it would take to raise the consumer's utility from U-2 to U=3 with prices constant. C. How much of a price subsidy to good x would be required to raise the consumers utility from U=2 to U=3 while keeping the consumers expenditures constant. D. Given what we know about the lump sum principle, how does the cost of a flat income subsidy compare to the costs of an utility equivalent price subsidy to x ?5. (9N4.5) [Hint: Since this problem involves fixed proportions utility you can't use calculus to find optimal quantities. Mr. Claus gains utility from the consumption of milk and cookies. He is very peculiar about his eating habits, however, always requiring 2 cookies (C) for each glass of milk (M). Thus his utility function can be written: U = min C M Unfortunately since the formation of the elf union Santa's food budget is rather limited. He has only I dollars to spend on cookies which cost Pc each and milk which costs Pm per glass. A. Graph a typical indifference curve Mr. Claus. Show that regardless of the relative prices of the two ingredients Mr. Claus will never alter the ratio of cookies to milk he consumes. B. Given Prices and his constraint find Mr. Claus' optimal consumption of milk and cookies. Depict his choice on an indifference curve graph. C. Find an indirect utility function for Mr. Claus. How much utility does Mr. Claus get if he consumes optimally at the above prices? D. Calculate Mr. Claus' expenditure function
