Economics 470/570
Fall 2008
Homework #1
1. Suppose that there are 100 individuals, each with $1,000 in savings
that they would like to lend. Suppose there are also 100 different people who
want to take out $1,000 loans. Assuming an expected default rate of 10%, use
this example to show how pooling risk through financial intermediation can
increase the efficiency of financial markets.
Suppose that the individuals with the savings to be lent out are risk averse.
In particular, suppose that they are not willing to risk losing all of their
savings, at least not at an interest rate anyone would be willing to pay. There
might be some individuals who would take a chance anyway, but for the most part
loan activity would be expected to be low. This is because (a) it would be hard
for individuals to find each other, so matching borrowers and lenders is
difficult, (b) individuals aren't experts at assessing credit risk, so when they
meet some stranger in (a) will they be willing to lend them money? How do they
find out if they are a good risk? And (c) even if these problems are solved,
there still wouldn't be any loans because with a default rate of 10%, 10 of the
100 people will lose everything and that's not a risk they are willing to take.
Now suppose that there are intermediaries. Also suppose they make loans at
15%. Then, in this case, loans = (100)*($1,000) = $100,000. But not all of it is paid back. Subtract off defaults of 10%, i.e. subtract $10,000 leaving a payback of $90,000.
Next, add interest to the $90,000. Since 90 people pay back $150 in interest
each, the interest return is $13,500, so the total amount paid back, with
interest, is $103,500. Now divide this among the lenders, i.e. divide this by 100 to get
$1,035 returned to each person who made a loan. Thus, instead of 10 people
losing everything, everyone makes 3.5%.
Overall, then:
Without an intermediary: Few, if any loans are made.
With an intermediary: Risk falls, the chances of losing everything falls, so
more loans are made. The increase in loans increases investment, which in turn
increases output. Hence, the economy is more efficient with intermediaries than
without (and the intermediaries may also lower default risk because of their
expertise at assessing the credit worthiness of borrowers, an effect I did not
include in the example).
2. Suppose that there are 100 individuals, each with $1,000 in savings
that they would like to lend. Suppose there are 10 different people who want to
take out $10,000 loans. Use this example to show how pooling small deposits
through financial intermediation can increase the efficiency of financial
markets.
In this case, in order for loans to be made without an intermediary, 10
people have to find each other, then find someone who wants to borrow money,
then find a way to assess their credit worthiness, draw up legal documents,
etc. Thus, the transactions costs are high in this case, default risk might be high, and that would stifle
loans reducing investment and output.
With an intermediary, these problems can be solved. The intermediary collects
deposits, pools them together, and then loans the money to worthy borrowers
using pre-existing contracts, etc. Since everyone can find the intermediary,
the problem of borrowers and lenders finding each other is resolved, the intermediary is an expert at assessing
risk so it can reduce default risk, and it can exploit economies of scale to draw up legal documents, etc.
Because the costs are and default risk are lower when an intermediary is involved, more loans are
made and output is higher. Hence, it's more efficient.
3. Suppose that there are 100 individuals, each with $1,000 in savings
that they would like to lend. However, in any given year 10% of them will need
the money for emergencies. Because of this possibility, and the dire
consequences if they cannot access their money at such a time, they are
unwilling to lend the money for long periods of time. Explain how financial
intermediation can solve this problem of "borrowing short and lending long" and
increase the efficiency of financial markets.
This is a case of matching short-term deposits with long-term loans. Suppose
that borrowers want to take out 30 year loans, but no individual lender is
willing to tie their money up for longer than a year. In this case, without an
intermediary, productive loans would not get made since nobody can part with
their money for so long.
But an intermediary solves this problem by replacing the people who take out
their funds with new depositors (think of a university town where a quarter of
the people leave each year, but are replaced with new students). Even though the
money of individual depositors rolls over fairly fast relative to the length of
the loan, the intermediary has a constant pool of funds on hand, and that allows
it to make the loans. Since these are loans that wouldn't get made otherwise,
and since loans turn into productive investment and lift output, having an
intermediary involved increases efficiency.
4. Besides pooling risk, pooling small deposits, and pooling over time,
what else do financial intermediaries do to increase the efficiency of financial
markets?
I've already discussed these above, so I will simply list them here.
Basically, intermediaries lower transactions costs and default risk. That is,
they lower transactions costs by lowering search costs (borrowers and lenders
finding each other), by lowering the costs of drawing up contracts and other
documents (they pay once for a general contract, then spread the cost over many,
many loans), and through having the means and knowledge to check the credit
worthiness of borrowers (they do it faster and cheaper). And, by using their
accumulated expertise at checking credit worthiness, they lower default rates.
5. Briefly, what does the phrase “increase the efficiency of financial
markets” mean?
The phrase means that, with the same amount of resources in the economy,
output will be higher with intermediaries than without. Intermediaries help us to use the
existing stock of resources more efficiently (by making it possible for
productive loans to be made that would otherwise not occur they increase
investment and output.)
