Economics 470/570
Fall 2011
Homework 1
1. You have been put in charge of selecting a new medium of exchange for the economy. Choose something to serve as money, and evaluate it in terms of the properties that a medium of exchange must satisfy in order to be useful.
I choose rocks. The properties are:
Easily standardized, easy to verify value: Standardization would be hard, most rocks are different sizes and it is hard to make them identical. If value is based on, say, weight, then verification shouldn't be too hard, but it would be cumbersome t have to weigh money with every transaction.
Widely accepted: This shouldn't be a problem as there is nothing particularly objectionable about a rock.
Divisible: To some extent, rocks can be broken into smaller pieces, but it might be hard to break off exactly the right size piece. Each one would be a little different.
Easy to carry: Rocks are dense. The weight and bulk would be a disadvantage.
Storable and durable: rocks do well here since they don't deteriorate very easily
Can control the supply: rocks don't do well here, they are easy to find, and every time people wanted to, say, pay rent they'd collect more and more rocks. Eventually, there would be so many circulating that the value of any one rock would fall (that is, the increase in supply would cause inflation undermining the value of the medium of exchange).
2. What is meant by the term "fractionally backed currency"? How does fractionally backed currency come about?
The phrase means that there is more paper money circulating than there is gold and silver backing it (or whatever commodity backs the money. i.e. there is less of it in bank safes than there is paper money in circulation) .
This happens when bankers hold less than 100% reserves against deposits.
3. Suppose that there are 10 individuals, each with $10,000 in savings that they would like to lend, but only if there is little to no chance that they will lose their investment. Suppose there are also 10 different people who want to take out $10,000 loans. (a) Assuming an expected default rate of 10% and an interest rate on loans of 20%, use this example to show how pooling risk through financial intermediation can increase the efficiency of financial markets. (b) Assuming the default rate using financial intermediation is exactly 10%, what is the interest rate at which the return is 0%?
(a) Suppose that the individuals with the savings they would like to lend 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%, 1 of the 10 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 20%. Then, in this case, loans = (10)*($10,000) = $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 9 people pay back $2,000 in interest each, the interest return is $18,000, so the total amount paid back, with interest, is $108,000. Now divide this among the lenders, i.e. divide this by 10 to get $10,800 returned to each person who made a loan. Thus, instead of 1 of the people making loans losing everything, everyone makes 8%.
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).
(b) After default, $90,000 is paid back, so the interest return must be $10,000 to break even. That means that each of the 9 people paying off the loans must pay ($10,000)/9 = $1,111.11, or 11% of the $10,000 loan. Thus, the break even rate is 11% (there is a one penny rounding error in the example).
4. Suppose that there are 10 individuals, each with $10,000 in savings that they would like to lend. Suppose there another person who wants to take out a $100,000 loan. 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.
5. Suppose that there are 100 individuals, each with $1,000 in savings that they would like to lend. However, in any given year 20% 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.
6. 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.)
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.
