# Exercise by liaoqinmei

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```									      Exercises
PT 2
Ch 8: Slutsky Equation
•   For this chapter, you should be able to do the following:
•   Find Slutsky income effect and substitution effect of a specific price
change if you know the demand function for a good.
•   Show the Slutsky income and substitution effects of a price change on
an indifference curve diagram.
•   Show the Hicks income and substitution effects of a price change on
an indifference curve diagram.
•   Find the Slutsky income and substitution effects for special utility
functions such as perfect substitutes, perfect complements, and
Cobb-Douglas.
•   Use an indifference-curve diagram to show how the case of a Giffen
good might arise.
•   Show that the substitution effect of a price increase unambiguously
decreases demand for the good whose price rose.
•   Apply income and substitution effects to draw some inferences about
behavior.
8.1
• As we know, Charlie consumes apples and bananas. Recall that
this utility function is U(xA, xB) = xAxB. The price of apples is \$1,
the price of bananas is \$2, and Charlie’s income is \$40 a day.
Now assume that the price of bananas suddenly falls to \$1.
• (a) How many apples and bananas did Charlie consume a day
before the price change? On a graph with apples on x-axis and
bananas on y-axis, use black ink to draw Charlie’s original
budget line and put the label A on his chosen consumption
bundle.
• (b) If, after the price change, Charlie’s income had changed so
that he could exactly afford his old consumption bundle, what
would his new income be? With this income and the new prices,
how many apples and bananas did Charlie consume a day? Use
red ink to draw the budget line corresponding to this income
and these prices. Label the bundle that Charlie would choose at
this income and the new prices with the letter B.
• (c) Does the substitution effect of the fall in the price
of bananas make him buy more bananas or fewer
bananas? How many more or fewer?
• (d) How many apples and bananas does Charlie buy
actually buy after the price change? Use blue ink to
draw Charlie’s actual budget line after the price
change. Put the label C on the bundle that he actually
chooses after the price change. Draw 3 horizontal
lines on your graph, one from A to the vertical axis,
one from B to the vertical axis, and one from C to the
vertical axis. Along the vertical axis, label the income
effect, the substitution effect, and the total effect on
the demand for bananas. Is the blue line parallel to
the red line or the black line that you drew before?
• (e) The income effect of the fall in the price of
bananas on Charlie’s demand for bananas is the
same as the effect of an (increase, decrease) in his
income of \$10 per day. Does the income effect make
him consume more bananas or fewer? How many
more or how many fewer?
• (f) Does the substitution effect of the fall in the price
of bananas make Charlie consume more apples or
fewer? How many more or fewer? Does the income
effect of the fall in the price of bananas make Charlie
consume more apples or fewer? What is the total
effect of the change in the price of bananas on the
demand for apples?
8.2
• Neville loves wine. When the prices of all
other goods are fixed at current levels,
Neville’s demand function for high quality
claret is q = .02m − 2p, where m is his
income, p is the price of claret (in £), and q
is the number of bottles of claret that he
demands. Neville’s income is £7,500, and the
price of a bottle of suitable claret is £30.
• (a) How many bottles of claret will Neville
• (b) If the price of claret rose to £40, how much
income would Neville have to have in order to be
exactly able to afford the amount of claret and the
amount of other goods that he bought before the
price change? At this income, and a price of £40,
how many bottles would Neville buy?
• (c) At his original income of 7,500 and a price of 40,
how much claret would Neville demand?
• (d) When the price of claret rose from 30 to 40, the
number of bottles that Neville demanded decreased
by 20. The substitution effect (increased, reduced)
his demand by s bottles and the income effect
(increased, reduced) his demand by i bottles.
8.3
Note: Do this problem only if you have read the section entitled “Another Substitution Effect” that describes the
“Hicks substitution effect”.

• Consider the figure below, which shows the budget
constraint and the indifference curves of Zog. Zog is
in equilibrium with an income of \$300, facing prices
pX = \$4 and pY = \$10.
• (a) How much X does Zog consume?
• (b) If the price of X falls to \$2.50, while income and the price of
Y stay constant, how much X will Zog consume?
• (c) How much income must be taken away from Zog to isolate
the Hicksian income and substitution effects (i.e., to make him
just able to afford to reach his old indifference curve at the new
prices)?
• (d) From what point to what point does consumption change
indicating the total effect of the price change?
• (e) From what point to what point corresponds to the income
effect? What movement corresponds substitution effect?
• (f) Is X a normal good or an inferior good?
• (g) On another graph, sketch an Engel curve and a demand
curve for Good X that would be reasonable given the
information in the graph above. Be sure to label the axes on
8.4
• Maude spends all of her income on delphiniums and hollyhocks.
She thinks that delphiniums and hollyhocks are perfect
substitutes; one delphinium is just as good as one hollyhock.
Delphiniums cost \$4 a unit and hollyhocks cost \$5 a unit.
• (a) If the price of delphiniums decreases to \$3 a unit, will
Maude buy more of them? What part of the change in
consumption is due to the income effect and what part is due to
the substitution effect?
• (b) If the prices of delphiniums and hollyhocks are respectively
pd = \$4 and ph = \$5 and if Maude has \$120 to spend, draw her
budget line in blue ink on a graph. Draw also the highest
indifference curve that she can attain in red ink, and label the
point that she chooses as A.
• (c) Now assume the price of hollyhocks fall to \$3 a unit, while
the price of delphiniums does not change. Draw her new budget
line in black ink. Draw the highest indifference curve that she
can now reach with red ink. Label the point she chooses now as
B.
• (d) How much would Maude’s income
have to be after the price of hollyhocks
fell, so that she could just exactly afford
her old commodity bundle A?
• (e) When the price of hollyhocks fell to
\$3, what part of the change in Maude’s
demand was due to the income effect
and what part was due to the
substitution effect?
8.7
• Mr. Consumer spends \$100 per month on
cigarettes and ice cream. Mr. C’s preferences
for cigarettes and ice cream are unaffected
by the season of the year.
• (a) In January, the price of cigarettes was \$1
per pack, while ice cream cost \$2 per pint.
Faced with these prices, Mr. C bought 30
pints of ice cream and 40 packs of
cigarettes. Draw Mr. C’s January budget line
with blue ink and label his January
consumption bundle with the letter J.
•   (b) In February, Mr. C again had \$100 to spend and ice cream still cost
\$2 per pint, but the price of cigarettes rose to \$1.25 per pack. Mr. C
consumed 30 pints of ice cream and 32 packs of cigarettes. Draw Mr.
C’s February budget line with red ink and mark his February bundle with
the letter F.
•   The substitution effect of this price change would make him buy (less,
more, the same amount of) cigarettes and (less, more, the same
amount of) ice cream. Since this is true and the total change in his ice
cream consumption was zero, it must be that the income effect of this
price change on his consumption of ice cream makes him buy (more,
less, the same amount of) ice cream. The income effect of this price
change is like the effect of an (increase, decrease) in his income.
Therefore the information we have suggests that ice cream is a(n)
(normal, inferior, neutral) good.
•   (c) In March, Mr. C again had \$100 to spend. Ice cream was on sale
for \$1 per pint. Cigarette prices increased to \$1.50 per pack. Draw his
March budget line with black ink. Is he better off than in January, worse
off, or can you not make such a comparison? How does your answer
to the last question change if the price of cigarettes had increased to
\$2 per pack?
• (d) In April, cigarette prices rose to \$2 per pack and
ice cream was still on sale for \$1 per pint. Mr. C
bought 34 packs of cigarettes and 32 pints of ice
cream. Draw his April budget line with pencil and
label his April bundle with the letter A. Was he better
off or worse off than in January? Was he better off or
worse off than in February, or can’t one tell?
• (e) In May, cigarettes stayed at \$2 per pack and as
the sale on ice cream ended, the price returned to \$2
per pint. On the way to the store, however, Mr. C
found \$30 lying in the street. He then had \$130 to
spend on cigarettes and ice cream. Draw his May
budget with a dashed line. Without knowing what he
purchased, one can determine whether he is better
off than he was in at least one previous month.
Which month or months?
8.10
• Agatha must travel on the Orient Express from Istanbul to Paris.
The distance is 1,500 miles. A traveler can choose to make any
fraction of the journey in a first-class carriage and travel the
rest of the way in a second-class carriage.
• The price is 10 cents a mile for a second class carriage and 20
cents a mile for a first-class carriage. Agatha much prefers
first-class to second-class travel, but because of a
misadventure in an Istanbul bazaar, she has only \$200 left with
• Luckily, she still has her toothbrush and a suitcase full of
cucumber sandwiches to eat on the way. Agatha plans to spend
her entire \$200 on her tickets for her trip.
• She will travel first class as much as she can afford to, but she
must get all the way to Paris, and \$200 is not enough money to
get her all the way to Paris in first class.
• (a) On a graph, use red ink to show the locus of combinations
of first- and second-class tickets that Agatha can just afford to
purchase with her \$200. Use blue ink to show the locus of
combinations of first and second-class tickets that are
sufficient to carry her the entire distance from Istanbul to Paris.
Locate the combination of first- and second-class miles that
Agatha will choose on your graph and label it A.
• (b) Let m1 be the number of miles she travels by first -class
coach and m2 be the number of miles she travels by second-
class coach. Write down two equations that you can solve to
find the number of miles she chooses to travel by first -class
coach and the number of miles she chooses to travel by
second-class coach.
• (c) How many miles does she travel by second-class coach?
• (d) Just before she was ready to buy her tickets, the price of
second-class tickets fell to \$.05 while the price of first-class
tickets remained at \$.20.
• On the graph that you drew, use pencil to show the
combinations of first-class and second-class tickets that she
can afford with her \$200 at these prices. Also on the same
graph, locate the combination of first-class and second-class
tickets that she would now choose. (Remember, she is going to
travel as much first-class as she can afford to and still make
the 1,500 mile trip on \$200.) Label this point B.
• How many miles does she travel by second class now? (Hint:
For an exact solution you will have to solve two linear equations
in two unknowns.) Is second-class travel a normal good for
Agatha? If not, what type of good is it?
• (e) Just after the price change from \$.10 per mile to
\$.05 per mile for second-class travel, and just before
she had bought any tickets, Agatha misplaced her
handbag. Although she kept most of her money in
her socks, the money she lost was just enough so
that at the new prices, she could exactly afford the
combination of first- and second-class tickets that
she would have purchased at the old prices. How
much money did she lose?
• On the graph you drew previous, use black ink to
draw the locus of combinations of first- and second-
class tickets that she can just afford after discovering
her loss. Label the point that she chooses with a C.
How many miles will she travel by second class now?
• (f) Finally, poor Agatha finds her handbag
again. How many miles will she travel by
second class now (assuming she didn’t buy
any tickets before she found her lost
handbag)?
• When the price of second class tickets fell
from \$.10 to \$.05, how much of a change in
Agatha’s demand for second-class tickets
was due to a substitution effect?
• How much of a change was due to an
income effect?
• In previous chapters, you studied the
behavior of consumers who start out without
owning any goods, but who had some money
• In this chapter, the consumer has an initial
endowment, which is the bundle of goods the
• That is, a consumer can trade away from his
initial endowment by selling one good and
9.1
• Abishag owns 20 quinces and 5 kumquats. She has no income
from any other source, but she can buy or sell either quinces or
kumquats at their market prices. The price of kumquats is four
times the price of quinces. There are no other commodities of
interest.
• (a) How many quinces could she have if she was willing to do
without kumquats? How many kumquats could she have if she
was willing to do without quinces?
• (b) Draw Abishag’s budget set, using blue ink, and label the
endowment bundle with the letter E. If the price of quinces is 1
and the price of kumquats is 4, write Abishag’s budget
equation. If the price of quinces is 2 and the price of kumquats
is 8, write Abishag’s budget equation. What effect does
doubling both prices have on the set of commodity bundles that
Abishag can afford?
• (c) Suppose that Abishag decides to sell 10 quinces.
Label her final consumption bundle in your graph with
the letter C.
• (d) Now, after she has sold 10 quinces and owns the
bundle labeled C, suppose that the price of kumquats
falls so that kumquats cost the same as quinces. On
the diagram above, draw Abishag’s new budget line,
using red ink.
• (e) If Abishag obeys the weak axiom of revealed
preference, then there are some points on her red
budget line that we can be sure Abishag will not
choose. On the graph, make a squiggly line over the
portion of Abishag’s red budget line that we can be
sure she will not choose.
9.2
• Mario has a small garden where he raises eggplant
and tomatoes. He consumes some of these
vegetables, and he sells some in the market.
• Eggplants and tomatoes are perfect complements for
Mario, since the only recipes he knows use them
together in a 1:1 ratio. One week his garden yielded
30 kg of eggplant and 10 kg of tomatoes. At that time
the price of each vegetable was \$5/kg.
• (a) What is the monetary value of Mario’s endowment
of vegetables?
• (b) On a graph, use blue ink to draw Mario’s budget
line. How much does Mario ends up consuming?
Draw the indifference curve through the consumption
bundle that Mario chooses and label this bundle A.
Also note his endowment point.
• (c) Suppose that before Mario makes any trades, the price of
tomatoes rises to \$15/kg, while the price of eggplant stays at
\$5/kg. What is the value of Mario’s endowment now? Draw his
new budget line, using red ink. What will he choose to
consume?
• (d) Now suppose that Mario had sold his entire crop at the
market for a total of \$200, intending to buy back some
tomatoes and eggplant for his own consumption. Before he had
a chance to buy anything back, the price of tomatoes rose to
\$15, while the price of eggplant stayed at \$5. Draw his budget
line, using black ink. What does Mario consume?
• (e) Assuming that the price of tomatoes rose to \$15 from \$5
before Mario made any transactions, what is the change in the
demand for tomatoes due to the substitution effect? What is the
change in the demand for tomatoes due to the ordinary income
effect? What is the change in the demand for tomatoes due to
the endowment income effect? And, lastly, what is the total
change in the demand for tomatoes?
9.3
• Lucetta consumes only two goods, A and B. Her only source of
She doesn’t always get these goods in the proportions in which
she wants to consume them, but she can always buy or sell A at
the price pA = 1 and B at the price pB = 2. Lucetta’s utility
function is U(a, b) = ab, where a is the amount of A she
consumes and b is the amount of B she consumes.
• (a) Suppose that Lucetta’s admirers give her 100 units of A and
200 units of B. In a graph, use red ink to draw her budget line.
Label her initial endowment E.
• (b) What are Lucetta’s gross demands for A? And for B?
• (c) What are Lucetta’s net demands?
• (d) Suppose that before Lucetta has made any trades, the price
of good B falls to 1, and the price of good A stays at 1. Draw
Lucetta’s budget line at these prices on your graph, using blue
ink.
• (e) Does Lucetta’s consumption of good B rise or
fall? By how much? What happens to Lucetta’s
consumption of good A?
• (f) Suppose that before the price of good B fell,
planning to use the money to buy her consumption
bundle later. How much of good B will she choose to
consume? How much of good A?
• (g) Explain why her consumption is different
depending on whether she was holding goods or
money at the time of the price change.
9.7
• Mr. Blog works in a machine factory. He can
work as many hours per day as he wishes at
a wage rate of w. Let C be the number of
dollars he spends on consumer goods and let
R be the number of hours of leisure that he
chooses.
• (a) Mr. Blog earns \$8 an hour and has 18
hours per day to devote to labor or leisure,
and he has \$16 of non-labor income per day.
Write an equation for his budget between
consumption and leisure.
• (b) Use blue ink to draw his budget line in a
graph. His initial endowment is the point
where he does no work and enjoys 18 hours
of leisure per day. Mark this point on the
graph below with the letter A.
• (Remember that although Blog can choose to
work and thereby “sell” some of his
endowment of leisure, he cannot “buy leisure”
by paying somebody else to loaf for him.)
• If Mr. Blog has the utility function U(R,C) =
CR, how many hours of leisure per day will he
choose? How many hours per day will he
work?
• (c) Suppose that Mr. Blog’s wage rate increases to
\$12 an hour, draw his new budget line in red ink. If
he continued to work exactly as many hours as he
did before the wage change, how much more money
would he have each day to spend on consumption?
With this new budget line, how many hours does he
work and how much does his consumption change?
• (d) Suppose that Mr. Blog still receives \$8 an hour
but that his non-labor income rises to \$48 per day.
Use black ink to draw his budget line. How many
hours does he choose to work?
• (e) Suppose that Mr. Blog has a wage of \$w per
hour, a non-labor income of \$m, and that he has 18
hours a day to divide between labor and leisure.
Blog’s budget line has the equation C + wR = m +
18w. Using the same methods you used in the
chapter on demand functions, find the amount of
leisure that Blog will demand as a function of wages
and of non-labor income. (Hint: Notice that this is
the same as finding the demand for R when the price
of R is w, the price of C is 1, and income is m +
18w.)
• What is Mr. Blog’s demand function for leisure?
• And what is Mr. Blog’s supply function for labor?
Ch 10. Intertemporal Choice
• Peregrine consumes (c1, c2) and earns (m1,m2) in
periods 1 and 2 respectively. Suppose the interest
rate is r.
• (a) Write down Peregrine’s intertemporal budget
constraint in present value terms.
• (b) If Peregrine does not consume anything in period
1, what is the most he can consume in period 2?
• (c) If Peregrine does not consume anything in period
2, what is the most he can consume in period 1?
• (d) What is the slope of Peregrine’s budget line?
10.2
• Molly has a Cobb-Douglas utility
function U(c1, c2) = c1α c21− α , where 0
< a < 1 and where c1 and c2 are her
consumptions in periods 1 and 2
respectively. We saw earlier that if utility
has the form u(x1, x2) = x1α x21− α and
the budget constraint is of the
“standard” form p1x1+p2x2=m, then the
demand functions for the goods are x1
= am/p1 and x2 = (1 − a)m/p2.
• (a) Suppose that Molly’s income is m1 in
period 1 and m2 in period 2. Write down her
budget constraint in terms of present values.
• (b) We want to compare this budget
constraint to one of the standard form. In
terms of Molly’s budget constraint, what is
p1? What is p2? What is m?
• (c) If α = .2, solve for Molly’s demand
functions for consumption in each period as
a function of m1, m2, and r. That is, what are
her demand functions for consumption in
period 1 and period 2?
10.3
• Nickleby has an income of \$2,000 this year, and he
expects an income of \$1,100 next year. He can
borrow and lend money at an interest rate of 10%.
Consumption goods cost \$1 per unit this year and
there is no inflation.
• (a) What is the present value of Nickleby’s
endowment? What is the future value of his
endowment? With blue ink, show the combinations of
consumption this year and consumption next year
that he can afford. Label Nickelby’s endowment with
the letter E.
• (b) Suppose that Nickleby has the utility function
U(C1,C2) = C1C2. Write an expression for Nickleby’s
marginal rate of substitution between consumption
will be a function of the variables C1,C2.)
• (c) What is the slope of Nickleby’s budget
line? Write an equation that states that the
slope of Nickleby’s indifference curve is equal
to the slope of his budget line when the
interest rate is 10%. Also write down
Nickleby’s budget equation.
• (d) Solve these two equations. What does
Nickleby will consume? Label this point A on
• (e) Will he borrow or save in the first period?
How much?
• (f) On your graph use red ink to show what Nickleby’s
budget line would be if the interest rate rose to 20%.
Knowing that Nickleby chose the point A at a 10%
interest rate, even without knowing his utility function,
you can determine that his new choice cannot be on
certain parts of his new budget line. Draw a squiggly
mark over the part of his new budget line where that
choice can not be. (Hint: Close your eyes and think
of WARP.)
• (g) Solve for Nickleby’s optimal choice when the
interest rate is 20%. What will he consume?
• (h) Will he borrow or save in the first period? How
much?
10.5
• Laertes has an endowment of \$20 each
period. He can borrow money at an interest
rate of 200%, and he can lend money at a
rate of 0%. (Note: If the interest rate is 0%,
for every dollar that you save, you get back
\$1 in the next period. If the interest rate is
200%, then for every dollar you borrow, you
have to pay back \$3 in the next period.)
• (a) Use blue ink to illustrate his budget set in
the graph below. (Hint: The boundary of the
budget set is not a single straight line.)
• (b) Laertes could invest in a project that would leave him with
m1 = 30 and m2 = 15. Besides investing in the project, he can
still borrow at 200% interest or lend at 0% interest. Use red ink
to draw the new budget set in the graph above. Would Laertes
be better off or worse off by investing in this project given his
possibilities for borrowing or lending? Or can’t one tell without
knowing something about his preferences? Explain.
• (c) Consider an alternative project that would leave Laertes with
the endowment m1 = 15, m2 = 30. Again suppose he can borrow
and lend as above. But if he chooses this project, he can’t do
the first project. Use pencil or black ink to draw the budget set
available to Laertes if he chooses this project. Is Laertes better
off or worse off by choosing this project than if he didn’t
choose either project? Or can’t one tell without knowing more
10.8
• 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 on his savings. His utility
function is U(c1, c2) = c1c2, where c1 is consumption
in period 1 and c2 is consumption in period 2. He can
borrow and lend at the interest rate r = .10.
• (a) If the interest rate rises, will his period-1
consumption increase, decrease, or stay the same?
• (b) Would an increase in the interest rate make him
consume more or less in the second period?
• (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?
10.9
• Harvey’s utility function is U(c1, c2) = min{c1, c2}, where c1 is
his consumption of bread in period 1 and c2 is 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.
• (a) Write Harvey’s budget constraint in terms of future value,
assuming no inflation.
• (b) How much bread does Harvey consume in the first period
and how much money does he save?
• (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. Then in period 2, a loaf of bread will cost \$ 1.10.
Write down Harvey’s budget equation for period-1 and period-2
10.10
• 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, c2) = c1c2
where c1 is consumption this year, and c2 is 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.
• (b) How much corn will the villagers consume this year? How
much will the rats eat? How much corn will the villagers
consume next year?
• (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
amount they would now consume in the first period
and the second period.
• (d) Suppose that all is as in the last part of the questi
on except that there is a transportation cost of \$.10 p
er bushel for every bushel of grain hauled into or out
of the village. On your graph, use black ink or pencil t
o draw the budget line for the village under these circ
umstances.
10.12
• Marsha doesn’t care whether she consumes in period 1 or in
period 2. Her utility function is simply U(c1, c2) = 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 a graph, 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.
• (c) Suppose that instead of consumption in the two
periods being perfect substitutes, they are perfect
complements, so that Marsha’s utility function is
min{c1, c2}. If she cannot borrow or lend, should she
buy the cookie jar? If she can borrow and lend at an
interest rate of 50%, should she invest in the cookie
jar? If she can borrow or lend as much at an interest
rate of 100%, should she invest in the cookie jar?

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