ECON 100 Tutorial: Week 17
www.lancaster.ac.uk/postgrad/murphys4/
s.murphy5@lancaster.ac.uk
office hours: 3:00PM to 4:45PM Tuesdays LUMS C85
Question 1(a)
The key things we need to know for Question 1(a) are:
The equation to find the discounted present value of future sums:
𝑃𝑉 =
𝐹𝑉
(1+𝑟)𝑇
Where PV = present value
FV = Future Value
r = interest or discount rate (sometimes it is denoted as i, rather than as r)
T = time, in number of years (sometimes it is denoted as n, rather than as T)
When should a firm make an investment (buy a machine, etc.)?
An investment is good so long as:
cost of the investment < PV of any returns on investment
Question 1(a)
A firm can buy a new machine for £50,000. The firm estimates the revenues that will be
obtained from the machine as
Year
1
2
3
4
follows:
Revenue
10,000 15,000 15,000 20,000
The interest rate is 5%.
Should the firm buy the machine?
To answer this question, we want to compare the present cost of the machine to the
discounted present value of any revenues that we will get from the machine.
𝐹𝑉
𝑃𝑉 =
(1 + 𝑟)𝑇
Question 1(a)
A firm can buy a new machine for £50,000. The firm estimates the revenues that will be
obtained from the machine as
Year
1
2
3
4
follows:
Revenue
10,000 15,000 15,000 20,000
The interest rate is 5%.
Should the firm buy the machine?
To answer this question, we want to compare the present cost of the machine to the
discounted present value of any revenues that we will get from the machine.
The present cost of the machine is £50,000.
The present value of £10,000 one year in the future is:
£10,000 / (1+r) = £10,000 / (1+0.05)
= £10,000 / 1.05
= £9,523.81
The present value of £15,000 two years in the future is:
£15,000 / (1+r) = £15,000 / (1+0.05)^2
= £15,000 * 1.05^2
= £13,605.44
The present value of £15,000 two years in the future is:
£15,000 / (1+r) = £15,000 / (1+0.05)^3
= £12,957.56
The present value of £15,000 two years in the future is:
£20,000 / (1+r) = £20,000 / (1+0.05)^4
= £16,454.05
𝑃𝑉 =
𝐹𝑉
(1 + 𝑟)𝑇
Question 1(a)
A firm can buy a new machine for £50,000. The firm estimates the
revenues that will be
Year
1
2
3
4
obtained from the machine Revenue
10,000 15,000 15,000 20,000
as follows:
The interest rate is 5%. Should the firm buy the machine?
The present cost of the machine is £50,000.
The present value of the four future sums are:
9523.81 + 13605.44 + 12957.56 + 16454.05 = 52,540.86
The sum of the present value of future revenues is greater than the
cost of the machine then the firm should invest in buying the
machine.
Question 1(b)
A firm can buy a new machine for £50,000. The firm estimates the revenues that will
be obtained from the machine as follows:
Year
Revenue
1
10,000
2
15,000
3
15,000
4
20,000
If the interest rate fell to 4%, how would this affect the firm's decision?
Using the exact same method as in part (a), we find that
the present value of the four future sums when the interest rate is 4% would be:
9615.38 + 13,868.34 + 13,334.95 + 17,096.08 = 53,914.75
So, the present value of the future sums would in all four years be higher.
The firm's decision to invest would, therefore, be unaffected by the lower interest
rate, but would be more profitable.
In general:
The lower the discount (interest) rate, the higher the present value of future sums.
Question 1(c)
A firm can buy a new machine for £50,000. The firm estimates the revenues that will be obtained
from the machine as follows:
Year
Revenue
1
9,000
10,000
2
13,500
15,000
3
13,500
15,000
4
18,000
20,000
Keynes argued that the investment decisions of firms depended crucially on what he
called the “animal spirits” of entrepreneurs. That is, their expectations about future
returns would influence their decisions to invest.
Suppose in the case of the firm above managers in the firm now think that revenue
will be 10% lower every year because of a likely recession.
How does this affect the firm's decision to buy the machine when the interest rate is
4%?
Expected revenues are now 9,000; 13,500; 13,500; 18,000
Using the same methods as in part (a), Present values are
8653.85 + 12481.51 + 12001.45 + 15386.48 = 48523.29
Buying the machine is no longer profitable for the firm. The effect of expectations on
investment decisions among firms is still considered to be important.
Relationship between interest rate and demand for capital
We can see that as the interest rate falls, the present value of the
future payout of an investment increases.
If i↑, then PV of a future pay-out↓
So, if PV of a future pay-out↓, then Demand for Investment ↓
And Capital Stock ↓
This shows a negative relationship between the interest rate and
the amount of capital stock that people may wish to buy.
This relationship is Marginal Efficiency of Capital (MEC) curve, that
we see in Question 1(d)
The Marginal Efficiency of Capital (MEC), a Keynesian term, is that
rate of discount which would make the present value of future
returns from an asset equal to that asset’s supply price.
Shifts in the MEC
The following things would cause the MEC to shift to the right (or we
can say, cause investment to become more attractive):
1. Cost of capital becomes cheaper
2. Improvements in technology
3. Optimistic expectations about the future and business confidence
4. Supply of Finance – if banks are more willing to lend money
5. Higher Demand for goods
6. Lower Rates of Taxes
Conversely, the opposite of these things will cause MEC to shift left
and cause investment to become less attractive.
Question 1(d)
Illustrate on a suitable diagram the effect that more pessimistic expectations about
the future among firms would have on the marginal efficiency of capital schedule.
The change in expectations shifts the MEC schedule to the left. For a given interest
rate, the optimal capital stock will be lower.
Practice Short-Answer Question
What are the four functions of money? In economics, are
cheques considered to be a form of money? Why/why not?
Some ways to approach this problem:
1. What exactly is the question asking?
We can break this up into three questions:
a. What are the four functions of money?
– List them and explain them.
b. In economics, are cheques considered to be a form of
money?
c. Why/why not?
– Explain what cheques are vs. what money is.
Practice Short-Answer Question
2.
Come up with an outline for your answer.
a. What are the four functions of money?
Medium of Exchange
Unit of Account
Store of Value
Liquidity
b. In economics, are cheques considered to be a form of money?
No
c. Why/why not?
Not a store of value, not a unit of account.
3. Does the outline address what the question is asking?
4. Use definitions and key terms to fill out your outline.
5. Check again – did you directly answer the questions being
asked?
Practice Short-Answer Question
4. Use definitions and key terms to fill out your outline.
The four functions of money are to be a medium of exchange, a unit of account, a store of
value, and liquidity.
The primary function of money is to be a medium of exchange – this means that buyers and
sellers all are willing to trade goods and services for money. It allows us to walk into a shop
and know that our money will be accepted for the items that the shop is selling.
To serve as a unit of account, means that money serving as a unit of measure or value.
To serve as a store of value means that people can transfer purchasing power from the
present to the future.
To be liquid means that an asset (a store of value) can easily be converted into the economy’s
medium of exchange. Because money is the medium of exchange, it is by definition, the most
liquid asset. Any asset that can easily and with little cost be sold in exchange for money is
considered liquid, i.e. stocks and bonds, whereas things like cars and property take longer to
sell they are therefore less liquid.
Cheques are not considered to be a form of money, in fact they are a note that says that an
individual has a specific amount of money in the bank that the recipient is entitled to receive.
Cheques are a claim to money that allows for transfer of funds.
We do not consider them to be money because they do not meet the primary function of
money – being a medium of exchange. They are not a medium of exchange because when
you hand over a cheque, the seller can not take your cheque and pay somebody else with it.
Debit and Credit Cards are similar to cheques in this way. Similarly, Checques are not used as a
unit of account or a store of value (i.e a check is not an asset).
For more on this topic,
See pgs. 617 – 622 of
Mankiw & Taylor, 2nd Ed.
Exam Advice
It is a Short Answer exam, not an essay exam. That means
be brief and to the point.
Be direct and brief, there’s nothing wrong with using
textbook definitions. Many students thought they needed to
explain things in their own words – if you know the book
definition, write it down, it’s easier for the grader to
recognize as a correct answer.
Other students simply write down a list key words, but don’t
show that they understand what these words mean or use
them in a coherent way. If you just list all of the terms you
heard in class, you won’t get any marks.
More Exam Advice
Most students did a good job of using diagrams. If the question
asks for a diagram, you need to draw one to get full marks. (you
also need to label it correctly; an unlabeled diagram could be
anything.)
If you are working a math problem – write down any equations
that you’re using. You generally would get a mark for having the
equation correct, even if you make a mathematical error later or
don’t have time to finish the question.
Finally, be conscious of time. If you can, have a quick look
through the exam at the beginning and pace yourself – wear a
watch. On the last exam, a lot of students wrote a long essay for
Question 1, then didn’t have time for Question 5. If the question
just asks for a definition, give the definition and move on. If you
don’t know it, move on to something you do know and you can
come back to it later if there’s time.
Question 2(a)
What is the opportunity cost to a consumer or business of
holding notes and coins?
The opportunity cost of holding cash in your hand is the
interest that you could have earned had you kept it in an
interest-earning account instead.
Question 2(b)
For each of the following assets, state whether you believe the asset performs money's
functions as a store of value and a medium of exchange. Explain your answer:
i)
Building society savings accounts
store of value
ii) Ordinary company shares
store of value
iii) Debenture company shares
store of value
iv) Government bonds
store of value
v) Notes and coins
store of value, medium of exchange
vi) UK Treasury bills
store of value
vii) Deposits in commercial bank current accounts
store of value, medium of exchange
viii) Certificates of Deposit
store of value
Question 2(c(i))
A banking system consists of five banks, A, B, C, D and E.
Each operates with a prudential ratio of 5%.
Suppose Eric deposits £1,000 cash in bank A.
What would be the initial increase in lending by Bank A
following the deposit?
The prudential ratio is the proportion of deposits which are
kept at hand. This also might be called the reserve ratio.
A prudential ratio of 5% means that 5% of all deposits are
kept by the bank.
So: 5%*£1,000= £50 is kept on hand by the bank.
So, the bank is able to lend £950 given their prudential ratio.
Question 2(c(ii))
Bank A then lends to Marie who in turn pays cash to Phil, a
customer of Bank B, for a new laptop. He deposits the cash
in his bank account. What would be the increase in bank
lending possible at Bank B following this deposit?
We’re assuming that Bank A lends all £950 to Marie, who
pays Phil the entire sum and that Phil deposits the £950 in
Bank B.
If the £950 is deposited in Bank B, then that bank would
keep 5%*£950 = £47.50 and lend the remaining £902.50.
Question 2(c(iii))
This process continues through Banks C, D and E and then back
to Bank A and so on. What would be the final increase in bank
lending in the banking system?
Assuming a similar pattern in the other banks, £857.38 in Bank C,
£814.51 in Bank D, £773.78 in Bank E and so on.
This is an infinite geometric progression (mentioned in the
lecture). The banking system as a whole will increase lending by:
Increase in bank deposits = initial deposits/(1-the percentage loaned)
Increase in bank deposits= initial deposits/the prudential ratio
Increase in bank deposits = £1,000/0.05
Increase in bank deposits = £20,000
Increase in bank lending = £20,000 - £1,000
Bond Pricing
Question 3 deals with bonds and bond pricing.
Some key terms that we use are:
Face value: Nominal value of the bond
Coupon rate: The percentage of the face value that the bond yields
(pays to bond holders) each year.
Coupon value: The amount the bond yields each year. Note: In some
problems you’re given the coupon rate and have to find the coupon
value. In others you’re just given the coupon value. Pay attention!
Interest rate: The prevailing interest rate is the expected annual rate of
return on bond purchases. It is usually equal to the coupon rate of
new bonds on the market.
Discount rate: When calculating the present value of future gains, this
is the rate you use. For businesses, it is usually set to the interest rate.
Bond Pricing Example (ctd.)
Bond ‘A’ is priced at $1000 with a coupon of 4%, and
the initial prevailing interest rate is 4%.
(a bonds coupon is how much it pays per year, either
an amount or a percentage of its value when issued).
In other words, it pays $40 annually.
After 1 year the interest rate has increased to 4.5%.
A new bond for sale at that time, Bond ‘B’, pays $45
annually. What is the price of Bond ‘B’?
We could guess that it is $1,000, because the
coupon rate is often set to the interest rate at the
time of sale, and 4.5%*$1000=$45.
Bond Pricing
In general, the value of a bond is equal to its annual payout
divided by the discount rate (interest rate)
That is, the value of a bond which gives an infinite stream of
payouts of £45
= £45/.045 = £1000
Bond Pricing
If someone wants to sell Bond ‘A’, it will need to offer a yield
of 4.5%. The coupon (annual $40 payout)always stays the
same, the price must fall to $889in order for the bond’s yield
to remain the same as Bond B. This is because $40/$889 =
4.5%
Question 3(a)
Keynes suggested that the speculative demand for money was linked to the
demand for government bonds.
These bonds are a means for a government to borrow money. In the UK, the
government issues a piece of paper that has a face (or nominal) value of £100
and an associated coupon of a given percentage. This coupon is the money
return on the bond for the bond holder expressed as a percentage of the
bond's face value. For example, if the coupon is 5% the bond holder will
receive a fixed £5 a year. These bonds, once issued by the government, are
then traded on the Stock Exchange. In the case we are considering here, we
will assume the government never repays the £100.
A fixed coupon means that if interest rates change, the return on the bond can
seem either low or high. Suppose interest rates fell to 2%, for example, the
bond would yield a very attractive return.
But this would mean that demand for the bonds on the Stock Exchange would
rise. And we know that means their price would rise from the initial £100. (It's
supply and demand again!) And as the price of the bond rose the return on it
would fall. With a market interest rate of 2%, the price of the bond would
eventually rise to £250. £5 a year is 2% of the new bond price of £250.
Question 3(a)
If the government will never repay the bond, why do people hold
them?
They hold them in the hope of a capital gain if interest rates change as
well as for the (guaranteed) return they receive in the coupon.
Question 3(b again)
Using your results above, derive a formula for the price of
these bonds based on the market interest rate and the
coupon of the bond.
𝐶𝑜𝑢𝑝𝑜𝑛 𝑜𝑓 𝐵𝑜𝑛𝑑
𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐵𝑜𝑛𝑑 =
𝑀𝑎𝑟𝑘𝑒𝑡
𝐼𝑛𝑡𝑒𝑟𝑠𝑡 𝑟𝑎𝑡𝑒
(𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑎𝑠 𝑎 𝑑𝑒𝑐𝑖𝑚𝑎𝑙)
From this formula it can be seen that a rise in the interest
rate will reduce the market price of a bond. In general, the
market price of a bond and the market interest rate are
inversely related.
Question 3(b)
What would be the price of the bond discussed above if the market rate of
interest were:
i)
10%
We can use this equation to find the value of a bond:
𝐶𝑜𝑢𝑝𝑜𝑛 𝑜𝑓 𝐵𝑜𝑛𝑑
𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐵𝑜𝑛𝑑 =
𝑀𝑎𝑟𝑘𝑒𝑡 𝐼𝑛𝑡𝑒𝑟𝑠𝑡 𝑟𝑎𝑡𝑒
The text at the beginning of Q3 tells us this bond gives a coupon of £5/year.
Market price = £5/0.10 = £50
ii)
8%
£5/.08 = £62.5
iii)
4%
iv)
£5/.04 = £125
0.5%
£5/.005 = £1000
Question 3(c)
Why would a fall in interest rates make the bonds less
attractive to speculators and so increase their demand for
money?
A fall in interest rates will increase the price of bonds.
Investors may then speculate that the price will be likely to
fall in the future. Investors therefore shift from holding
bonds to holding money. Note that this assumes bonds to
be a liquid asset that can easily and at relatively low cost be
converted into money. In practice, they actually are.
Question 3(d)
Why would a rise in interest rates make the bonds more
attractive to speculators and so decrease their demand for
money?
A rise in interest rates will cause the price of bonds to fall.
By similar reasoning to the answer in d), a fall in the price of
bonds means that speculators are more likely to want to buy
bonds because they believe their price will increase in the
future. Their demand for money therefore falls as their
demand for bonds rises.
Bonds vs Liquidity Preference Money Supply
So our intuition is that a rise in interest rates will lower the
price and increase the demand for bonds. The demand for
money falls. Money is equivalent to savings, which roughly
equals investment according to the circular flow of money.
So an increase in savings increases I and from our Keyensian
models, increases GDP (Y). When we look at IS-LM
(Investment Saving–Liquidity Preference Money Supply), this
relationship explains why the LM curve has a positive slope.
The LM curve has to do with Liquidity Preference and
Money Supply, and shows a positive relationship between
interest rates, r, and output, Y.
Question 4
The reason barter is not as efficient as money as a medium
of exchange is that it suffers from the problem of:
a) The double coincidence of wants
b) The need to know the rate at which many goods
exchange for each other
c) The difficulty of deciding the cost of repaying loans in
terms of another good
d) All of the above
Question 5
A bank is required by the government to hold 15% of its
assets as cash. If the bank has cash of £150 million and loans
to customers valued at £850 million, which of the following
statements is correct:
a) The bank’s deposits are £1,000 million and it could
increase its lending by £50 million
b) The bank’s deposits are £1,000 million and it cannot
increase its lending
c) The bank’s deposits are £1,000 million and it must reduce
its lending to meet the government’s cash requirement
d) The bank’s deposits are £850 million and it must reduce
its lending to meet the government’s cash requirement
Question 6
A bank receives £1500 in cash as a deposit. If the bank
operates with a prudential ratio of 2% this implies that the
bank could make loans to the value of:
a) £1,500
b) £20,000
c) £73,500
d) £75,000
Question 6
A bank receives £1500 in cash as a deposit. If the bank operates
with a prudential ratio of 2% this implies that the bank could
make loans to the value of:
The amount the bank can loan = (1-prudential rate)*deposit
amount the bank can loan = 0.98* £1500 = £1470
Note, to get the correct answer to this question, the question
should actually be asking what is the increase in money supply
that resulted from the £1500 deposit, but is not inclusive of that
initial deposit.Increase in bank lending = initial deposits/the prudential ratio
a) £1,500
b) £20,000
c) £73,500
d) £75,000
Increase in bank lending = £1500 / 0.02
Increase in bank lending = £75000
Increas e in bank lending minus initial deposit = £75000 - £1500 = £73500
Question 7
In a modern economy the best working definition of the
money supply is:
a) Notes and coins in circulation with the public
b) Notes and coins deposited in the banks
c) Notes and coins in circulation with the public plus
commercial bank deposits
d) Notes and coins deposited in the banks plus commercial
bank deposits
Next Week
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