Deck 9: Intertemporal Choice

Question 1

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.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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.

Answer 3

False

Question 4

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.

Question 5

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.

Question 6

If the inflation rate doubles and the nominal interest rate remains constant, the real interest rate must be halved.

Question 7

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

Question 8

An increase in the interest rate can make a utility-maximizing lender become a borrower.

Question 9

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.

Question 10

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.

Question 11

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

Question 12

If the nominal interest rate is 3% and if prices fall by 2% per year, then the real rate of interest is approximately 5%.

Question 13

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.

Question 14

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

Question 15

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.

Question 16

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.

Question 17

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

Question 18

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

Question 19

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

Question 20

It would be a mistake to choose the investment that maximizes the present value of your income stream unless you planned to spend your entire wealth in the current time period.

Question 21

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

A) double.
B) increase by $400.
C) increase by $150.
D) stay constant.
E) increase by $120.

Question 22

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?

A) 10
B) 20
C) 22
D) 14.1
E) 6.06

Question 23

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

A) cause savers to save more.
B) cause borrowers to borrow less.
C) reduce everyone's current consumption.
D) make everyone worse off.
E) None of the above.

Question 24

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 $147 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.

A) Harvey will save $102.
B) Harvey will borrow $40.
C) Harvey will neither borrow nor lend.
D) Harvey will save $40.
E) None of the above.

Question 25

If the real rate of interest is 8% and the nominal rate of interest is 28%, then the rate of inflation must be about

A) 36%.
B) 24.26%.
C) 3.50%.
D) 18.52%.
E) 23%.

Question 26

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?

A) 50
B) 20
C) 40
D) 30
E) There is not enough information to be able to tell.

Question 27

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%:

A) his savings will increase by 2% and his consumption in period 2 will increase.
B) his savings will not change but his consumption in period 2 will increase by $800.
C) his consumption in both periods will increase.
D) his consumption in both periods will decrease.
E) his consumption in period 1 will decrease by 12% and his consumption in period 2 will increase.

Question 28

If a consumer views a unit of consumption in period 1 as a perfect substitute (one for one) for a unit of consumption in period 2 and if the real interest rate is positive, the consumer will

A) consume only in period 1.
B) consume only in period 2.
C) consume equal amounts in each period.
D) consume more in period 1 than in period 2 if income elasticity exceeds 1, otherwise consume more in period 2 than in period 1.
E) equalize expenditures but not consumption in the two periods.

Question 29

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

A) more than 200 but less than 220.
B) exactly 200.
C) more than 220.
D) exactly 180.
E) more than 180 but less than 200.

Question 30

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

A) will not save since the real interest rate is negative.
B) will save less than 1% of her income.
C) will save the same amount regardless of the inflation rate; only the nominal interest rate matters.
D) might save despite the negative real interest rate.
E) will necessarily save less if the inflation rate rises and the nominal interest rate does not change.

Question 31

If the price level increases by 80% in one year, then for the real rate of interest to be 10%, the nominal rate of interest would have to be

A) 98%.
B) 70%.
C) 18%.
D) 88%.
E) 72%.

Question 32

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.

A) If the interest rate rises, Mr. Kandle will save more.
B) If the interest rises, Mr. Kandle will save less.
C) He will consume the same amount in each period.
D) A change in the interest rate won't affect his saving.
E) None of the above.

Question 33

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

A) 27.26%.
B) 43%.
C) 2.58%.
D) 16.96%.
E) 22%.

Question 34

Holly's utility function is , where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. In period 2, her income is twice as large as her income in period 1. At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.)

A) 0.30
B) 0.08
C) 0.23
D) 0
E) 0.15

Question 35

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,

A) consumption in the first time period will not change.
B) villagers will consume 5% more corn in each time period.
C) consumption in the first time period will increase but by less than 5%.
D) consumption in the second time period will not change.
E) consumption in the first time period will decrease.

Question 36

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

A) stay constant.
B) double.
C) increase by $320.
D) increase by $400.
E) increase by $320.

Question 37

If the interest rate is 5% and will be 5% forever, the present value of an income stream consisting of $10 a year paid to you on February 11 of every year, starting right now, is $210.

Question 38

Suppose that a person can borrow and lend at an interest rate of 10%. But there is a 5% rate of inflation and the person has to pay an income tax of 30% on all interest income. If the person borrows money, he can deduct interest as an expense. Where current consumption is on the horizontal axis and future consumption is on the vertical axis, the budget line will

A) have a kink at the point of no saving or lending.
B) be a straight line with a slope of about -1.02.
C) be a straight line with a slope of about -1.05.
D) be a straight line with a slope of about -1.35.
E) None of the above.

Question 39

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.

A) Harvey will save $60.
B) Harvey will borrow $60.
C) Harvey will neither borrow nor lend.
D) Harvey will save $124.
E) None of the above.

Question 40

Vanessa's utility function is , where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. In period 2, her income is 4 times as large as her income in period 1. At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.)

A) 0.10
B) 0
C) 0.30
D) 0.80
E) 0.20

Question 41

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?

A) 0
B) 0.25
C) 0.13
D) 0.50
E) 0.38

Question 42

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%,

A) his savings would not change but his consumption in period 2 would increase by $2,450.
B) his consumption in both periods would decrease.
C) his consumption in both periods would increase.
D) his savings would increase by 7% and his consumption in period 2 would also increase.
E) his consumption in period 1 would decrease by 17% and his consumption in period 2 would also decrease.

Question 43

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

A) increase by $160.
B) double.
C) increase by $80
D) stay constant.
E) increase by $200.

Question 44

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%,

A) his savings would increase by 9% and his consumption in period 2 would also increase.
B) his savings would not change but his consumption in period 2 would increase by $3,600.
C) his consumption in both periods would increase.
D) his consumption in both periods would decrease.
E) his consumption in period 1 would decrease by 19% and his consumption in period 2 would also decrease.

Question 45

Peregrine consumes ($700, $880) and earns ($600, $990). If the interest rate is 0.10, the present value of his endowment is

A) $1,590.
B) $1,500.
C) $1,580.
D) $3,150.
E) $3,750.

Question 46

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?

A) $1,860
B) $465
C) $1,395
D) $310
E) $930

Question 47

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?

Question 48

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?

A) 0.40
B) 0.10
C) 0.20
D) 0
E) 0.30

Question 49

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?

A) $1,620
B) $360
C) $540
D) $2,160
E) $1,080

Question 50

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

A) double.
B) increase by $160.
C) increase by $80.
D) stay constant.
E) increase by $400.

Question 51

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

A) $2,400.
B) $2,680.
C) $2,620.
D) $5,280.
E) $6,280.

Question 52

I am always indifferent between a unit of consumption today and tomorrow and the interest rate is 5%.

A) My intertemporal indifference curve is horizontal.
B) My intertemporal indifference curve is a straight line with slope 21.
C) I will spend all of my current and future income on consumption today.
D) I will spend 5% more on consumption today than on consumption tomorrow.
E) I will spend 5% more on consumption tomorrow than on consumption today.

Question 53

Samantha Smoothie's utility function is U(c₁, c₂) = c₁c₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. She earns $200 in period 1 and $220 in period 2. Samantha can borrow and lend at an interest rate of 10% and there is no inflation. The number of dollars that Samantha spends in the second period must be

A) more than 200 but less than 220.
B) exactly 220.
C) more than 220.
D) exactly 200.
E) less than 200.

Question 54

In an isolated mountain village, the harvest this year is 6,000 bushels of grain and the harvest next year will be 900 bushels. The villagers all have utility functions U(c₁, c₂) = c₁c₂, where c₁ is consumption this year and c₂ is consumption next year. Rats eat 40% of any grain that is stored for a year. How much grain could the villagers consume next year if they consume 1,000 bushels of grain this year?

A) 5,850 bushels
B) 3,000 bushels
C) 3,900 bushels
D) 6,900 bushels
E) 1,000 bushels

Question 55

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?

Question 56

Ymir Larson farms near Niffleheim, Minnesota. He works 80 hours a week. He can either grow rutabagas or raise pigs. Every hour that he spends growing rutabagas gives him $2 of income this year. Every hour that he spends raising pigs this year will add $4 to his income next year. In fact, next year's weekly income will be 100 + 4H dollars where H is the number of hours he spends raising pigs this year. Ymir's utility function is U(c₁, c₂) = min{c₁, c₂}, where c₁ and c₂ are his consumption expenditures this year and next year. Ymir doesn't believe in banks and will neither lend money nor borrow money.
a. Draw Ymir's budget line for current and future consumption, labeling key points on it.
b. How many hours a week will he choose to spend raising pigs?
c. How much money will he spend per week on consumption in each year?

Question 57

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.

Question 58

Buzz is a chicken farmer. His earnings will be $100 this year and $100 next year. He can lend money at an interest rate of 20%. Because of a subsidized loan program for chicken farmers, he can borrow money at an interest rate of 10%. No matter what he borrows or lends, his earnings will still be $100 each year.
a. If he is not allowed to either borrow or lend, draw a graph showing his budget between consumption this year and consumption next year. Put numerical labels on the vertical and horizontal intercepts of the budget set.
b. Suppose that Buzz is allowed to borrow up to the present value of next year's earnings at 10% and is also allowed to make loans. Draw Buzz's budget constraint in this case.

Question 59

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 $40,000. If the interest rate rises from 10 to 14%:

A) his savings will increase by 4% and his consumption in period 2 will increase.
B) his consumption in both periods will increase.
C) his consumption in both periods will decrease.
D) his savings will not change but his consumption in period 2 will increase by $800.
E) his consumption in period 1 will decrease by 14% and his consumption in period 2 will increase.

Question 60

In an isolated mountain village, the harvest this year is 3,000 bushels of grain and the harvest next year will be 1,100 bushels. The villagers all have utility functions U(c₁, c₂) = c₁c₂, where c₁ is consumption this year and c₂ is consumption next year. Rats eat 10% of any grain that is stored for a year. How much grain could the villagers consume next year if they consume 1,000 bushels of grain this year?

A) 2,900 bushels
B) 1,800 bushels
C) 4,100 bushels
D) 4,350 bushels
E) 1,200 bushels

Question 61

In an isolated peasant village, the only crop is corn. Good harvests alternate with bad harvests. This year the harvest will be 1,000 bushels. Next year it will be 150 bushels. There is no trade with the outside world. Corn can be stored, but rats will eat 25% of what is stored in a year. The villagers have the Cobb-Douglas utility function U(c₁, c₂) = c₁c₂, where c₁ is consumption this year and c₂ is consumption next year.
a. Draw a budget line for the village with this year's consumption on the horizontal axis and next year's consumption on the vertical axis. On your graph show the quantities at which the budget line intercepts the vertical and horizontal axes.
b. How much will the villagers consume this year?
c. How much will the rats eat?
d. How much will the villagers consume next year?