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NAME 139
025 75
100
25
50
75
Ambrosia this period
Ambrosia next period
100
50
(b) If Jane planned to spend no red income in the next period and to
borrow as much red currency as it can pay back with interest with next
(d) On the axes below, draw Jane’s blue budget line and its red budget
line. Shade in all of those combinations of current and future ambrosia
consumption that Jane can afford given that it has to pay with both
currencies.
140 INTERTEMPORAL CHOICE (Ch. 10)
025 75
100
25
50
75
Ambrosia this period
Ambrosia next period
100
50
Blue
line
Red line
c
(e) It turns out that Jane finds it optimal to operate on its blue budget
(f) On the following graph, show what happens to Jane’s original budget
NAME 141
025 75
100
25
50
75
Ambrosia this period
Ambrosia next period
100
50
Blue
line
Shaded region
cNew blue
line
Red
line
10.8 (0) Mr. O. B. Kandle will only live for two periods. In the first
period he will earn $50,000. In the second period he will retire and live
(a) If the interest rate rises, will his period-1 consumption increase, de-
(b) Would an increase in the interest rate make him consume more or
less in the second period? More. He saves the same
(c) If Mr. Kandle’s income is zero in period 1, and $ 55,000 in period 2,
would an increase in the interest rate make him consume more, less, or
the same amount in period 1? Less.
10.9 (1) Harvey Habit’s utility function is U(c1,c
2)=min{c1,c
2},where
c1is his consumption of bread in period 1 and c2is his consumption of
bread in period 2. The price of bread is $1 per loaf in period 1. The
interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn
$1,100 in period 2.
142 INTERTEMPORAL CHOICE (Ch. 10)
(a) Write Harvey’s budget constraint in terms of future value, assuming
(b) How much bread does Harvey consume in the first period and how
much money does he save? (The answer is not necessarily an integer.)
(c) Suppose that Harvey’s money income in both periods is the same as
before, the interest rate is still 21%, but there is a 10% inflation rate.
vey’s budget equation for period-1 and period-2 bread, given this new
10.10 (2) In an isolated mountain 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 from one year to the next, but rats
will eat 25% of what is stored in a year. The villagers have Cobb-Douglas
utility functions, U(c1,c
2)=c1c2where c1is consumption this year, and
c2is consumption next year.
(a) Use red ink to draw a “budget line,” showing consumption possibilities
for the village, with this year’s consumption on the horizontal axis and
next year’s consumption on the vertical axis. Put numbers on your graph
to show where the budget line hits the axes.
Next year's consumption
This year's consumption
150
1250
1000
900
1150
1136
1111
Red line
Black line
Blue line
NAME 143
(c) Suppose that a road is built to the village so that now the village is
able to trade with the rest of the world. Now the villagers are able to buy
and sell corn at the world price, which is $1 per bushel. They are also
able to borrow and lend money at an interest rate of 10%. On your graph,
use blue ink to draw the new budget line for the villagers. Solve for the
(d) Suppose that all is as in the last part of the question except that there
is a transportation cost of $.10 per bushel for every bushel of grain hauled
into or out of the village. On your graph, use black ink or pencil to draw
the budget line for the village under these circumstances.
10.11 (0) The table below records percentage interest rates and inflation
rates for the United States in some recent years. Complete this table.
Inflation and Interest in the United States, 1965-1985
Year 1965 1970 1975 1978 1980 1985
(a) People complained a great deal about the high interest rates in
the late 70s. In fact, interest rates had never reached such heights
in modern times. Explain why such complaints are misleading.
144 INTERTEMPORAL CHOICE (Ch. 10)
(b) If you gave up a unit of consumption goods at the beginning of 1985
and saved your money at interest, you could use the proceeds of your
1986. If you gave up a unit of consumption goods at the beginning of
1978 and saved your money at interest, you would be able to use the
beginning of 1979.
10.12 (1) Marsha Mellow doesn’t care whether she consumes in period
1 or in period 2. Her utility function is simply U(c1,c
2)=c1+c2.Her
initial endowment is $20 in period 1 and $40 in period 2. In an antique
shop, she discovers a cookie jar that is for sale for $12 in period 1 and that
she is certain she can sell for $20 in period 2. She derives no consumption
benefits from the cookie jar, and it costs her nothing to store it for one
period.
(a) On the graph below, label her initial endowment, E, and use blue ink
to draw the budget line showing combinations of period-1 and period-2
consumption that she can afford if she doesn’t buy the cookie jar. On the
same graph, label the consumption bundle, A, that she would have if she
did not borrow or lend any money but bought the cookie jar in period 1,
sold it in period 2, and used the proceeds to buy period-2 consumption.
If she cannot borrow or lend, should Marsha invest in the cookie jar?
(b) Suppose that Marsha can borrow and lend at an interest rate of 50%.
On the graph where you labelled her initial endowment, draw the budget
line showing all of the bundles she can afford if she invests in the cookie
jar and borrows or lends at the interest rate of 50%. On the same graph
use red ink to draw one or two of Marsha’s indifference curves.
0204060
80
20
40
60
Period-1 consumption
Period-2 consumption
80
e
a
Blue
line
Red
curves
NAME 145
(c) Suppose that instead of consumption in the two periods being per-
fect substitutes, they are perfect complements, so that Marsha’s utility
function is min{c1,c
2}. If she cannot borrow or lend, should she buy the
much at an interest rate of 100%, should she invest in the cookie jar?
