Exam 9: Intertemporal Choice

Minnie has an income of $300 in period 1 and will have an income of $625 in period 2. Her utility function is U(c₁, c₂) = c^0.80₁c^0.20₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. The interest rate is 0.25. If she unexpectedly won a lottery which pays its prize in period 2 so that her income in period 2 would be $1,250 and her income in period 1 would remain $300, then her consumption in period 1 would

The intertemporal budget constraint for a consumer can be expressed by setting the present value of her lifetime consumption equal to the future value of her endowment.

Patience has the utility function where c₁ is her consumption in period 1 and c₁ is her consumption in period 2. She will earn 100 units of the consumption good in period 1 and 100 units of the consumption good in period 2. She can borrow or lend at an interest rate of 10%. a. Write an equation that describes Patience's budget. b. If Patience neither borrows nor lends, what will be her marginal rate of substitution between current and future consumption? c. If Patience does the optimal amount of borrowing or saving, what will be the ratio of her period 2 consumption to her period 1 consumption?

Will Wisp will live for exactly two periods. His utility function is U(c₁, c₂) = c₁c₂, where c₁ is consumption in period 1 and c₂ is consumption in period 2. He will have no income in period 2. His income in period 1 is $80,000. If the interest rate rises from 10 to 12%:

The nominal interest rate is 5% and the inflation rate is 6%. A rational consumer

Molly has income $400 in period 1 and income $600 in period 2. Her utility function is c^a₁c^1-a₂, where a = 0.40 and the interest rate is 0.20. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

If apples today are perfect substitutes for bananas today, then apples today must also be perfect substitutes for bananas tomorrow.

Harvey Habit has a utility function U(c₁, c₂) = min{c₁, c₂}, where c₁ and c₂ are his consumption in periods 1 and 2 respectively. Harvey earns $189 in period 1 and he will earn $63 in period 2. Harvey can borrow or lend at an interest rate of 10%. There is no inflation.

Harvey Habit has a utility function U(c₁, c₂) = min{c₁, c₂}. If he had an income of $1,230 in period 1 and $615 in period 2 and if the interest rate were 0.05, how much would Harvey choose to spend on bread in period 1?

An increase in the interest rate cannot make a lender who satisfies WARP become a borrower.

Mandy has an income of $800 in period 1 and will have an income of $500 in period 2. Her utility function is U(c₁, c₂) = c^0.80₁c^0.20₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. The interest rate is .25. If she unexpectedly won a lottery which pays its prize in period 2 so that her income in period 2 would be $1,000 and her income in period 1 would remain $800, then her consumption in period 1 would

If the real interest rate is positive, then a unit of future consumption can be had for the sacrifice of less than 1 unit of current consumption.

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $80,000 in period 1 and the interest rate increased from 10 to 19%,

Molly has income $200 in period 1 and income $920 in period 2. Her utility function is c^a₁c^1-a₂, where a = 0.80 and the interest rate is 0.15. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

Patience has a utility function , where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. Her income in period 1 is twice as large as her income in period 2. At what interest rate will she choose to consume the same amount in period 1 as in period 2?

Luella has to pay an interest rate of 50% to borrow. She only gets an interest rate of 5% if she lends. She is currently endowed with $1,000 in period 1 and $1,050 in period 2. She considers two alternative investment projects. She can only choose one of them. For project A she would have to pay $500 in period 1 and would be paid back $630 in period 2. For project B, she would be paid $500 in period 1 and would have to pay back $525 in period 2. a. Diagram her budget set if she chooses project A. Also show her budget if she chooses project B. b. If she neither borrows nor lends, which project has the higher present value at the interest rate 50%? Which has the higher present value at an interest rate of 5%? c. Draw indifference curves such that she should choose A. d. With different preferences might she choose B?

Kenny Kink's utility function is u(c₁, c₂) = min{c₁, c₂}, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He earns $200 in period 1 and $220 in period 2. Kenny can borrow and lend at an interest rate of 10%, and there is no inflation. The number of dollars that Kenny spends on consumption in the first period must be

Susan is a net borrower when the interest rate is 10% and a net saver when the interest rate is 20%. A decrease in the interest rate from 20% to 10% may make Susan worse off.

Mr. O. B. Kandle will live for only two periods. In the first period he will earn $100,000. In the second period he will retire and live on his savings. Mr. Kandle has a Cobb-Douglas utility function U(c₁, c₂) = c²₁c₂, where c₁ is his period 1 consumption and c₂ is his period 2 consumption. The real interest rate is r.

If a consumer can borrow and lend at the same interest rate, then he can exactly afford a consumption plan if the present value of his consumption equals the present value of his income.