CHAPTER 10: Intertemporal Choice
MULTIPLE CHOICE
1. If Peregrine in Problem 1 consumes (1, 400, 1, 210) and earns (900, 1, 760) and if the interest rate is
10%, the present value of his endowment is
a.
$2,660.
b.
$2,500.
c.
$2,610.
d.
$5,250.
e.
$6,150.
2. If Peregrine in Problem 1 consumes (1, 400, 1, 440) and earns (900, 2, 040) and if the interest rate is
20%, the present value of his endowment is
a.
$2,940.
b.
$2,600.
c.
$5,720.
d.
$2,840.
e.
$6,620.
3. If Peregrine in Problem 1 consumes (1, 500, 1, 080) and earns (1, 000, 1, 680) and if the interest rate is
20%, the present value of his endowment is
a.
$2,680.
b.
$5,280.
c.
$2,400.
d.
$2,580.
e.
$6,280.
4. If Peregrine in Problem 1 consumes (900, 805) and earns (600, 1, 150) and if the interest rate is 15%,
the present value of his endowment is
a.
$1,600.
b.
$3,440.
c.
$1,705.
d.
$1,750.
e.
$4,040.
5. If Peregrine in Problem 1 consumes (1, 500, 880) and earns (1, 300, 1, 100) and if the interest rate is
10%, the present value of his endowment is
a.
$4,830.
b.
$2,400.
c.
$2,300.
d.
$2,380.
e.
$6,130.
6. Suppose that Molly from Problem 2 had an income of $500 in period 1 and an income of $250 in
period 2. Suppose that her utility function were ca1c1
−
a2, where a = 0.60 and the interest rate were 25%.
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 $300.
c.
increase by $150.
d.
stay constant.
e.
increase by $500.
7. Suppose that Molly from Problem 2 had an income of $400 in period 1 and an income of $690 in
period 2. Suppose that her utility function were ca1c1−a2, where a = 0.80 and the interest rate were 15%.
If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in
period 1 would
a.
stay constant.
b.
increase by $320.
c.
increase by $160.
d.
double.
e.
increase by $400.
8. Suppose that Molly from Problem 2 had an income of $500 in period 1 and an income of $880 in
period 2. Suppose that her utility function were ca1c1−a2, where a = 0.60 and the interest rate were 10%.
If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in
period 1 would
a.
stay constant.
b.
increase by $300.
c.
double.
d.
increase by $150.
e.
increase by $500.
9. Suppose that Molly from Problem 2 had an income of $200 in period 1 and an income of $460 in
period 2. Suppose that her utility function were ca1c1−a2, where a = 0.40 and the interest rate were 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 $80.
b.
increase by $40.
c.
double.
d.
stay constant.
e.
increase by $200.
10. Suppose that Molly from Problem 2 had an income of $600 in period 1 and an income of $880 in
period 2. Suppose that her utility function were ca1c1−a2, where a = 0.80 and the interest rate were 10%.
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 $240.
b.
stay constant.
c.
double.
d.
increase by $480.
e.
increase by $600.
11. Mr. O. B. Kandle, of Problem 8, has a utility function c1c2, where c1 is his consumption in period 1 and
c2 is his consumption in period 2. He has no income in period 2. If he had an income of $50,000 in
period 1 and the interest rate increased from 10 to 15%,
a.
his savings would increase by 5% and his consumption in period 2 would also increase.
b.
his savings would not change but his consumption in period 2 would increase by 1,250.
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 15% and his consumption in period 2
would also decrease.
12. Mr. O. B. Kandle, of Problem 8, has a utility function c1c2, where c1 is his consumption in period 1 and
c2 is his consumption in period 2. He has no income in period 2. If he had an income of $70,000 in
period 1 and the interest rate increased from 10 to 16%,
a.
his savings would increase by 6% and his consumption in period 2 would also increase.
b.
his consumption in both periods would decrease.
c.
his savings would not change but his consumption in period 2 would increase by 2,100.
d.
his consumption in both periods would increase.
e.
his consumption in period 1 would decrease by 16% and his consumption in period 2
would also decrease.
13. Mr. O. B. Kandle, of Problem 8, has a utility function c1c2, where c1 is his consumption in period 1 and
c2 is his consumption in period 2. He has no income in period 2. If he had an income of $40,000 in
period 1 and the interest rate increased from 10 to 12%,
a.
his consumption in both periods would increase.
b.
his savings would increase by 2% and his consumption in period 2 would also increase.
c.
his consumption in both periods would decrease.
d.
his savings would not change but his consumption in period 2 would increase by 400.
e.
his consumption in period 1 would decrease by 12% and his consumption in period 2
would also decrease.
14. Mr. O. B. Kandle, of Problem 8, has a utility function c1c2, where c1 is his consumption in period 1 and
c2 is his consumption in period 2. He has no income in period 2. If he had an income of $60,000 in
period 1 and the interest rate increased from 10 to 17%,
a.
his savings would increase by 7% and his consumption in period 2 would also increase.
b.
his savings would not change but his consumption in period 2 would increase by 2,100.
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 17% and his consumption in period 2
would also decrease.
15. Mr. O. B. Kandle, of Problem 8, has a utility function c1c2, where c1 is his consumption in period 1 and
c2 is his consumption in period 2. He has no income in period 2. If he had an income of $40,000 in
period 1 and the interest rate increased from 10 to 19%,
a.
his savings would not change but his consumption in period 2 would increase by 1,800.
b.
his savings would increase by 9% and his consumption in period 2 would also increase.
c.
his consumption in both periods would decrease.
d.
his consumption in both periods would increase.
e.
his consumption in period 1 would decrease by 19% and his consumption in period 2
would also decrease.
16. Harvey Habit in Problem 9 has a utility function U(c1, c2) = minc1, c2. If he had an income of $430
in period 1 and $860 in period 2 and if the interest rate were 15%, how much would Harvey choose to
spend on bread in period 1?
a.
$945
b.
$210
c.
$315
d.
$1,260
e.
$630
17. Harvey Habit in Problem 9 has a utility function U(c1, c2) = minc1, c2. If he had an income of $1,290
in period 1 and $860 in period 2 and if the interest rate were 15%, how much would Harvey choose to
spend on bread in period 1?
a.
$1,635
b.
$363.33
c.
$545
d.
$2,180
e.
$1,090
18. Harvey Habit in Problem 9 has a utility function U(c1, c2) = minc1, c2. If he had an income of $420
in period 1 and $1,050 in period 2 and if the interest rate were 10%, how much would Harvey choose
to spend on bread in period 1?
a.
$240
b.
$360
c.
$1,440
d.
$1,080
e.
$720
19. Harvey Habit in Problem 9 has a utility function U(c1, c2) = minc1, c2. If he had an income of $645
in period 1 and $1,290 in period 2 and if the interest rate were 15%, how much would Harvey choose
to spend on bread in period 1?
a.
$1,417.50
b.
$315
c.
$1,890
d.
$472.50
e.
$945
20. Harvey Habit in Problem 9 has a utility function U(c1, c2) = minc1, c2. If he had an income of $440
in period 1 and $880 in period 2 and if the interest rate were 20%, how much would Harvey choose to
spend on bread in period 1?
a.
$1,280
b.
$320
c.
$213.33
d.
$960
e.
$640
21. In the village in Problem 10, if the harvest this year is 6,000 bushels of grain and the harvest next year
will be 1,100 bushels and if rats eat 10% of any grain that is stored for a year, how many bushels of
grain could the villagers consume next year if they consume 1,000 bushels of grain this year?
a.
5,600
b.
4,500
c.
7,100
d.
8,400
e.
1,200
22. In the village in Problem 10, if the harvest this year is 6,000 bushels of grain and the harvest next year
will be 900 bushels and if rats eat 10% of any grain that is stored for a year, how many bushels of
grain could the villagers consume next year if they consume 1,000 bushels of grain this year?
a.
6,900
b.
5,400
c.
8,100
d.
4,500
e.
1,000
23. In the village in Problem 10, if the harvest this year is 4,000 bushels of grain and the harvest next year
will be 1,200 bushels and if rats eat 50% of any grain that is stored for a year, how many bushels of
grain could the villagers consume next year if they consume 1,000 bushels of grain this year?
a.
4,050
b.
5,200
c.
2,700
d.
1,500
e.
1,300
24. In the village in Problem 10, if the harvest this year is 4,000 bushels of grain and the harvest next year
will be 1,200 bushels and if rats eat 10% of any grain that is stored for a year, how many bushels of
grain could the villagers consume next year if they consume 1,000 bushels of grain this year?
a.
2,700
b.
5,850
c.
3,900
d.
5,200
e.
1,300
25. In the village in Problem 10, if the harvest this year is 4,000 bushels of grain and the harvest next year
will be 700 bushels and if rats eat 30% of any grain that is stored for a year, how many bushels of
grain could the villagers consume next year if they consume 1,000 bushels of grain this year?
a.
2,800
b.
2,100
c.
4,700
d.
4,200
e.
800
26. Patience has a utility function U(c1, c2) = c1/21 + .080c1/22, where c1 is her consumption in period 1 and
c2 is her consumption in period 2. Her income in period 1 is 3 times 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.
0.75
b.
0.13
c.
0.25
d.
0
e.
0.38
27. Patience has a utility function U(c1, c2) = c1/21 + .083c1/22, where c1 is her consumption in period 1 and
c2 is her consumption in period 2. Her income in period 1 is 3 times 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.
0.20
b.
0
c.
0.10
d.
0.60
e.
0.30
28. Patience has a utility function U(c1, c2) = c1/21 + .087c1/22, where c1 is her consumption in period 1 and
c2 is her consumption in period 2. Her income in period 1 is 5 times 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.
0.75
b.
0
c.
0.08
d.
0.15
e.
0.23
29. Patience has a utility function U(c1, c2) = c1/21 + .083c1/22, where c1 is her consumption in period 1 and
c2 is her consumption in period 2. Her income in period 1 is 5 times 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.
0.10
b.
0
c.
1
d.
0.20
e.
0.30
30. Patience has a utility function U(c1, c2) = c1/21 + .087c1/22, where c1 is her consumption in period
1 and c2 is her consumption in period 2. Her income in period 1 is 2 times 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.
0.08
c.
0.30
d.
0.15
e.
0.23
31. Let i be the rate of inflation and r the nominal interest rate. (We use pi to denote the rate of inflation in
the book.) The (exact) real rate of interest is given by
a.
(r − i)/(i + 1).
b.
(r + i)/(i + 1).
c.
(r + i)/(i − 1).
d.
(r − i)/(i − 1).
e.
r − i/r.