Economic 219
Problem Set #4
1. Suppose the real interest rate in the U.S. is 5% per
year and there is no inflation.
- Calculate the price of a bond that pays a fixed payment of
$2 per year for three years. Assume that the first payment comes one year
from now.
- Suppose that in an average year, IBM generates $100 Billion in revenues
and $50 billion in costs. Each year, IBM pays out all its profits as
dividends to stockholders. These dividends are paid at the end of each year.
If IBM has 25 billion shares of stock outstanding, what is the dividend per
share? For simplicity, assume that IBM is expected to go out of business
after three years. Calculate the price of a share of IBM stock.
- Now, suppose that the inflation rate is 10% per year. Redo (a) and (b). (Hint:
for the stock price, remember that a yearly inflation rate of 10% means that
all prices, wages, etc. will rise by 10% per year!).
- What do the above answers tell you about stocks and bonds?
2. Suppose that you are currently a college senior. You are
currently working a part-time job that pays $2,000 per year, but you expect to
earn $20,000 next year, after you graduate. Assume that there is no inflation
and that the interest rate is 10% per year.
- Sketch your budget line for current and future expenditures. Indicate on
your graph a likely consumption choice.
- Suppose that the interest rate suddenly increased to 15%. Show the effect
of the rise in the interest rate on your budget set. Indicate a new
consumption choice on your graph. Explain the reasoning behind your choice.
What happens to your savings?
- Suppose you receive an unexpected inheritance from a long lost Aunt of
$3000. What happens to your current consumption? What happens to your
savings? How would your answer change if you didn’t expect to receive this
inheritance until next year?
3. Suppose you have the following information for the
production of shirts.
| # of Sewing Machines |
# of Shirts (per year) |
| 1 |
100 |
| 2 |
190 |
| 3 |
270 |
| 4 |
340 |
| 5 |
400 |
| 6 |
450 |
| 7 |
490 |
| 8 |
520 |
| 9 |
540 |
| 10 |
550 |
The price of a shirt is $2, and the price of a sewing machine is $1000. The
real interest rate is 5% per year, and sewing machines depreciate at 5% per
year.
- Calculate the value marginal product of capital (the dollar value of MPK)
for sewing machines.
- Calculate the user cost of sewing machines.
- How many sewing machines should the firm purchase?
- Suppose the interest rate rose to 10% per year. How would the firm’s
decision change? Plot the firm’s demand for capital. Plot the firm’s
investment demand.
4. Certain government regulations tend to reduce the
productivity of capital. Show the effects on savings, investment, and the
interest rate of the following plans for de-regulation.
- An immediate, temporary easing of regulations. This temporary break
would last for six months whereas it takes one year to complete any new
investment projects.
- A permanent easing of regulations announced now, but not scheduled
to take place until next year.
5. The outbreak of the bubonic plague – the Black Death –
in 1348 reduced the population in Europe by about 1/3 within a few years. During
this time, wages rose dramatically (doubled by some estimates, but the data is
very sketchy!) while real rents (interest rates) fell by more than 50%, causing
a massive redistribution of wealth from the rich to the poor. How can we explain
this fact with economic theory?