Exam 9: Intertemporal Choice

Ophelia says, "If I could lend money at the rates I must pay to borrow, I would. And if I could borrow money at the rates I receive when I lend, I would again. But forsooth, although I spend, I neither borrow nor lend." Contrary to common belief, Ophelia is entirely rational. Draw a diagram to show how Ophelia's remarks can be consistent with rational behavior and smooth convex preferences if she pays a different interest rate when she borrows than she gets when she lends. Explain what happens in words.

Isaiah is a net borrower when the interest rate is 5% and a net saver when the interest rate is 25%. An increase in the interest rate from 5 to 25% may make Isaiah worse off.

If current and future consumption are both normal goods, an increase in the interest rate will necessarily

If the nominal interest rate is 5% and if prices fall by 3% per year, then the real rate of interest is approximately 8%.

A newspaper article claims that more students are choosing 1-year M.B.A. programs instead of 2-year programs because the 2-year programs no longer guarantee a well-paid job. If the length of your M.B.A. program doesn't matter to employers, and you take a job right after completing your M.B.A., the present value of your lifetime earnings is the same whether you take a 1-year or 2-year program.

If the interest rate at which you can borrow is higher than the interest rate at which you can lend, your budget for current and future consumption is a convex set.

The nominal interest rate is 5% and the inflation rate is 6%. A rational consumer will not choose to save.

If the real rate of interest is 12% and the nominal rate of interest is 31%, then the rate of inflation must be about

In a graph that has current consumption on the horizontal axis and future consumption on the vertical axis, the horizontal intercept of the budget line is the present value of all one's income in the two periods.

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 $70,000 in period 1 and the interest rate increased from 10 to 17%,

For every two boxes of strawberries that she consumes, Millicent insists on having one pitcher of cream. She does not, however, insist on consuming the same amount every week. Her utility functions is U = min{s₁, 2c₁} min{s₂, 2c₂}, where s₁ and s₂ are the number of boxes of strawberries she consumes this week and next week and c₁ and c₂ are the number of pitchers of cream she consumes this week and next. Strawberries cost $2 a box and cream costs $1 a pitcher. She has a present value of $100 to spend on these goods in the next two weeks. The weekly interest rate is 1%. How many boxes of strawberries will she consume this week?

Peregrine consumes ($1,300, $1,320) and earns ($1,000, $1,680). If the interest rate is 0.20, the present value of his endowment is

In an isolated mountain village, the only crop is corn. Villagers plan for two time periods. In the first time period each villager will harvest 100 bushels. In the second time period, no corn will be harvested. There is no trade with the rest of the world and no stocks of corn remain from before the first period. Corn can be stored from one time period to the next, but rats eat 25% of what is stored. The villagers all have Cobb-Douglas utility functions U(C₁, C₂) = C₁C₂ and can allocate their own corn between consumption and storage as they wish. If the introduction of cats to the village reduces the rats' predations to 10% of what is stored,

Roger's utility function is U = min{a₁, a₂} min{b₁, b₂}, where a₁ and a₂ are the number of piano lessons he consumes this year and next and b₁ and b₂ are the number of ice skating lessons he consumes this year and next. The price of piano lessons is $10 each and the price of ice skating lessons is $4 each. The prices won't change, but the interest rate is 7%. If Roger consumes 20 piano lessons this year, how many ice-skating lessons will he consume next year?

An increase in the interest rate will necessarily result in a decrease in the present value of a given stream of positive incomes.

Harvey Habit has a utility function U(c1, c2) = min{c₁, c₂}. If he had an income of $880 in period 1 and $1,320 in period 2 and if the interest rate were 0.20, how much would Harvey choose to spend on bread in period 1?

The real interest rate is the interest rate that one receives net of brokerage costs or fees imposed by financial intermediaries.

If the interest rate is less than the inflation rate, a rational person will never save money.

A utility-maximizing consumer would not choose the investment that maximizes the present value of her income stream unless she planned to spend her entire wealth in the first period.

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?