ECON 101 Tutorial: Week 22
Shane Murphy
s.murphy5@lancaster.ac.uk
Office Hours: Monday 3:00-4:00 – LUMS C85
Outline
• Roll Call
• Problems
Chapter 25: Problem 1
About 400 years ago, Lenape Native Americans sold
the island of Manhattan for $24. If they had invested
this money at an interest rate of 7% per year, how
much would they have today?
The future value of $24 invested for 400 years at an
interest rate of 7 percent is
(1.07)^400 * $24 =
$13,600,000,000,000 =
$13.6 trillion
Why do I hate this question?
What was the price in real terms? $1000 to $10000
Did the Lenape occupy Manhattan a that time? No
Did Indians have a concept of property rights? Yes
Is 7% a reasonable return on investments from before the 1900s? No
What is the current GDP of Manhattan? ~$1.3 trillion
What would be the annual value of a $13.6 trillion endowment? ~$13.6 trillion * 0.05 = ~$0.68 trillion
What was the annual per capita GDP at the time? $700 for UK, $526 for Ireland, probably around $100-$300 for Indians
Were non-tangible assets (goodwill, alliances) the prime driver of this deal? Yes, for both sides
Are there any other examples of private, 400 year long investments? No
Does the font get any smaller? Not really
Chapter 25: Problem 2
A company that has an investment project that would cost $10 million today
and yield a payoff of $15 million in four years.
a) For interest rates of 8%, 9%, 10%, and 11%, evaluate this project.
The present value of €15 million to be received in four years discounted at an
interest rate of 11 percent is €15 million/(1.11)^4 = €9.88 million.
For an interest rate of 10%, €15 million/(1.10)^4 = €10.25 million
For an interest rate of 9%, €15 million/(1.09)^4 = €10.63 million
For an interest rate of 8%, €15 million/(1.08)^4 = €11.03 million
b) What is the cut-off interest rate where the project changes from profitable
to non-profitable?
The exact cut-off for the interest rate between profitability and nonprofitability is the interest rate that will equate the present value of receiving
€15 million in four years with the current cost of the project (€10 million):
€10 =15/(1 + x)^4
10(1 + x)^4 = 15
(1 + x)^4 = 1.5
1 + x = (1.5)0.25
1 + x = 1.1067
x = 0.1067
Chapter 25: Problem 5
For which kind of stock would you expect a higher
average return: stock in an industry that is sensitive
to economic conditions (such as a car manufacturer),
or in an industry that is insensitive to economic
conditions (such as a water company)?
A stock that is very sensitive to economic conditions
will have more risk associated with it. Thus, we
would expect for that stock to pay a higher return.
To get stockholders to be willing to accept the risk,
the expected return must be larger than average.
Chapter 25: Problem 6
A company faces two kinds of risk. An idiosyncratic
risk is that a competitor might enter its market and
take customers. An aggregate risk is that the
economy might enter a recession and reduce sales.
Which would be more likely to cause shareholders to
demand a higher return?
Shareholders will probably demand a higher return
due to the stock’s idiosyncratic risk. Idiosyncratic risk
is risk that affects only that particular stock. All
stocks in the economy are subject to aggregate risk.
Chapter 25: Problem 7a
One flatmate buys stock only in in companies that
everyone believes will experience big increases in profits
in the future. How do you suppose the PE ration of
these companies compares to others? What are the
disadvantages of buying stock in these companies?
If a flatmate is buying stocks in companies that everyone
believes will experience big profits in the future, the
price-earnings ratio is likely to be high. The price is high
because it reflects everyone’s expectations about the
firm’s future earnings. The largest disadvantage in
buying these stocks is that they are currently overvalued
and may not pay off in the future.
Chapter 25: Problem 7b
If a flatmate buys stock only in companies which are
cheap (low PE ratio), how do earnings prospects of
these companies compare to those of other companies?
What might be the disadvantages of buying stock in
these companies?
Firms with low price-earnings ratios will probably have
lower future earnings. The reason why these stocks are
cheap is that everyone has lower expectations about the
future profitability of these firms. The largest
disadvantage to buying this stock is that the market may
be correct and the firm's stock may provide a low
return.
Chapter 27: Problem 1
M = 500 billion, GDP = 10 trillion, real GDP = 5 trillion
a) What is P, V?
Nominal GDP = P x Y = €10,000 and Y = real GDP = €5,000, so P = (P x Y)/Y =
€10,000/€5,000 = 2.
Since M x V = P x Y, then V = (P x Y)/M = €10,000/€500 = 20.
b) If V is constant and output grows by 5%, what will happen to nominal GDP
and prices if M is constant?
If M and V are unchanged and Y rises by 5 percent, then since M x V = P x Y, P
must fall by 5 per cent. As a result, nominal GDP is unchanged.
c) What money supply should the bank set next year to keep P stable?
To keep the price level stable, the central bank must increase the money
supply by 5 per cent, matching the increase in real GDP. Then, since velocity
is unchanged, the price level will be stable.
d) What money supply should the bank set if it want inflation at 10%?
If the central bank wants inflation to be 10 per cent, it will need to increase
the money supply 15 per cent. Thus M x V will rise 15 per cent, causing P x Y
to rise 15 per cent, with a 10 per cent increase in prices and a 5 per cent rise
in real GDP.
Chapter 27: Problem 2
Suppose that credit card use increases and people hold less
cash.
a) How does this effect money demand?
If people need to hold less cash, the demand for money shifts
to the left, since there will be less money demanded at any
price level.
b) What will happen to prices?
If the central bank does not respond to this event, the shift to
the left of the demand for money combined with no change in
the supply of money leads to a decline in the value of money
(1/P), which means the price level rises
c) What can the central bank do to keep prices stable?
If the central bank wants to keep the price level stable, it
should reduce the money supply
Chapter 27: Problem 7
Michael farms beans and Dorothy farms rice. Both consume equal amounts
of beans and rice. In 2014, the price o beans was 1 and rice was 3.
a) If the prices increase to 2 for beans and 6 for rice, what was inflation?
Were either farmers better or worse off?
When the price of both goods doubles in a year, inflation is 100 percent. The
total cost of purchasing equal amounts of beans and rice equals the quantity
of each good times its price, added together for all goods. That is, if x is the
quantity of beans, which also equals the quantity of rice, then the cost of
beans and rice for the year is x(PB + PR). In the second year, the cost is x(PB'
+ PR'), where the ' mark refers to the price in the second year. Then we can
define a price index with a value of one in the first year. In the second year,
the price index has the value of the cost of goods in the second year divided
by the cost of goods in the first year. Thus the price index in the second year
is x(PB' + PR')/x(PB + PR) = (PB' + PR')/(PB + PR) = (€2 + €6)/(€1 + €3) = €8/€4
= 2. The inflation rate is then (2 - 1)/1 x 100% = 100%. Since the prices of all
goods rise by 100 percent, the farmers get a 100 percent increase in their
incomes to go along with the 100 percent increase in prices, so neither is
affected by the change in prices.
Chapter 27: Problem 7
Michael farms beans and Dorothy farms rice. Both consume
equal amounts of beans and rice. In 2014, the price o beans
was 1 and rice was 3.
b) If in 2015 the price of beans was 2 and of rice was 4, what
was inflation? Were either farmers better or worse off?
If the price of beans rises to €2 and the price of rice rises to €4,
then the price index in the second year is (PB' + PR')/(PB + PR)
= (€2 + €4)/(€1 + €3) = €6/€4 = 1.5, so the inflation rate is (1.51)/1 x 100% = 50%. Michael is better off because his euro
revenues doubled (increased 100 percent) while inflation was
only 50 per cent. Dorothy is worse off because inflation was 50
percent, so the prices of the goods she buys rose faster than
the price of the goods (rice) she sells, which rose only 33
percent.
Chapter 27: Problem 7
Michael farms beans and Dorothy farms rice. Both consume
equal amounts of beans and rice. In 2014, the price o beans
was 1 and rice was 3.
c) If in 2015 the price of beans was 2 and the price of rice was
1.5, what was inflation? Were either farmers better or worse
off?
If the price of beans rises to €2 and the price of rice falls to
€1.50, then the price index in the second year is (PB' + PR')/(PB
+ PR) = (€2 + €1.50)/(€1 + €3) = €3.50/€4 = 0.875, so the
inflation rate is (0.875-1)/1 x 100% = -12.5%. Michael is better
off because his euro revenues doubled (increased 100 percent)
while prices overall fell 12.5 percent. Dorothy is worse off
because inflation was -12.5 percent, so the prices of the goods
she buys didn't fall as fast as the price of the goods (rice) she
sells, which fell 50 percent.
Chapter 27: Problem 7
Michael farms beans and Dorothy farms rice. Both
consume equal amounts of beans and rice. In 2014,
the price o beans was 1 and rice was 3.
d) What matters more, the overall inflation rate or
the relative prices?
The relative price of rice and beans matters more to
Michael and Dorothy than the overall inflation rate.
If the price of the good that a person produces rises
more than inflation, he or she will be better off. If
the price of the good a person produces rises less
than inflation, he or she will be worse off.
Chapter 27: Problem 9
Suppose that people expect inflation to equal 3% but it goes to 5%. How will
this effect the following:
a) The government
Unexpectedly high inflation helps the government by providing higher
inflation tax revenue and reducing the real value of outstanding government
debt.
b) A homeowner with a fixed-rate mortgage
Unexpectedly high inflation helps a homeowner with a fixed-rate mortgage
because he pays a fixed nominal interest rate that was based on expected
inflation, and thus pays a lower real interest rate than was expected.
c) A union worker in the 2nd year of a labour contract
Unexpectedly high inflation hurts a union worker in the second year of a
labour contract because the contract probably based the worker's nominal
wage on the expected inflation rate. As a result, the worker receives a lower
than expected real wage.
d) A retired person who has invested in government savings bonds
Unexpectedly high inflation hurts a retired person that has invested his
savings in government bonds because the higher inflation rate means he is
receiving a lower real interest rate than he had planned for.
Chapter 35: Problem 10
Explain why the following are true, false, or uncertain:
a) The statement that "Inflation hurts borrowers and helps
lenders, because borrowers must pay a higher rate of interest,"
is false. Higher expected inflation means borrowers pay a
higher nominal rate of interest, but it is the same real rate of
interest, so borrowers are not worse off and lenders are not
better off. Higher unexpected inflation, on the other hand,
makes borrowers better off and lenders worse off.
b) The statement that "If prices change in a way that leaves the
overall price level unchanged, then no one is made better or
worse off," is false. Changes in relative prices can make some
people better off and others worse off, even though the overall
price level does not change. See problem 7 for an illustration of
this.
c) The statement that "Inflation does not reduce the purchasing
power of most workers" is true. Most workers' incomes keep up
with inflation reasonably well.