Assignment:
1. Explain why the following is true: If preferences are homothetic, then both goods are normal.
2. Explain why the following is false: If both goods are normal, then preferences are homothetic.
3. True or False: For U(X, Y) and the income offer curve is either a vertical line or horizontal line not out of the origin, then the Engels curve for one of the goods will be vertical line not out of the origin.
4. Explain why the following is true: If the Engels curve is upward sloping then the demand curve is downward sloping.
5. Samuel Marchbanks' utility equals the square of x times the square of y and he spends $347 on goody.
a How much does he spend on good x if its price is $113?
6. Robertson Davies has homothetic preferences. He only buys brandy and cigars. He is a profligate old codger and spends all of his income on these two goods. He spends 76% of his income on brandy.
a. If his income increases by $200 how much money does he spend on ciears?
Intertemporal Choice
7. U.S. Senator Daniel Patrick Coin-in-hand is always willing to trade two units of next year's consumption for one unit of this year's consumption. His income this year is $70,000; his income next year is $81,000 for sure. The sticker price of all goods in all time periods is one. There is no inflation. The honorable Senator can borrow and lend at 8% interest.
a Find his optimal intertemporal consumption bundle and his optimal savings.
b. If the rate of interest increases to 10% will he save more?
c. If the rate of interest increases to 20°0 will he save more?
d. At what rate of interest will he increase his savings?
8. Polonius likes all things in moderation. He saves and borrows so that consumption this year equals consumption near year. His income this year is $10,000; next year his income will be $10,000 with certainty. The sticker price of all goods in all time periods is one. There is no inflation. Polonius can borrow and save at 7.25% interest
a Find his optimal intertemporal consumption bundle and his optimal savings.
9. Laertes, Polonius' son, has utility- U-C13 C22. where C1-consumption in the first period and C2= consumption in the second period. He has income of $100,000 in the first period and zero income in the second period. The sticker price of all goods in an time periods is one. There is no inflation. At 8% interest Polonius can be borrower or a lender.
a. Find his optimal intenemporal consumption bundle and his optimal savings.
b. Suppose the interest rate increases to 12%, find his new optimal intertemporal consumption bundle and his optimal savings.
c. Explain why the change in the rate of interest has the above effect on savings.
10. Wilma consumes only blueberries and whipped cream and has utility U=(min{B1,W1}2*(min{B2 , W2}) where B1:=blueberries in the first period, W1= whipped cream in the first period, B2=blueberries in the second period and W2= whipped cream in the second period. Her first period income is $100 and her second period income is $218. She can borrow and lend at 9% interest. The sticker price of all goods in all time periods is one. There is no inflation.
a. Find the optimal blueberries and whipped cream consumed in period one and period 2.
11. Mr. Strunk has utility U=min{B1 , J1} min{B2, J2}, where B1=peanut butter in the first period, B2=peanut butter in the second period, J1=jam in the first period and J2=jam in the second period. The sticker price of all goods in all time periods is one. There is no inflation. His first period income is $100; his second period income is $100. He can borrow and lend at 6% interest.
a. Describe in words the preferences implied by Mr. Strunk's utility Reaction.
b. Find his first period consumption of peanut butter and jam, his second period consumption of peanut butter and jam and the amount of money he saves.
12. Jenny has utility U-C13C2:. Her income is $7000 in this period and $26.500 next period. There is no inflation. She can borrow and lend at 6% interest.
a. Find her optimal present and Muse consumption and her optimal savings.
b. If the interest rate increases to 10% fmd her new optimal present and Astute consumption and her new optimal savings.
c. When is she better off, at 6% or 10% interest?
13. Delores always spends her income and saves so that consumption in the first period equals consumption in the second period. There is no inflation. Originally she maximizes her utility by doing no saving or borrowing.
a. Suppose the interest rate increases: does she save more, borrow more or remain as before?