Practice Midterm #1
Solutions
1) There is an exact expression and a decent approximation.
The exact method compounds the 2% 90 day rate over the entire year
(1.02)^(365/90)
= 1.0837 = 8.37%
The
approximation simply multiplies the 90 day rate by (365/90)
2%
* (365/90) = 8.11%
2) When factors of production are complements, they are used together. Therefore, increasing the supply of one factor improves the productivity of the other factor (and, hence, its price).
3) These differences in returns are easily attributable to the level of risk
associated with each security. Stocks
have a much higher level of risk. Therefore, stockholders must be compensated for this risk
with a higher return.
4) Once again, there is an exact method and an approximation.
First, the exact method:
(1.05)/(1.025)
= 1.024 = 2.4%
Or,
using the Fisher relation
5%
- 2.5% = 2.5%
5) People “smooth” consumption by saving when income is temporarily high and borrowing (or, at least, reducing saving) when income is temporarily low. Therefore, prior to economic expansions, consumers recognize a higher future income and therefore, start top borrow now (raising interest rates). Prior to recessions, consumers recognize that income will be low in the future and therefore, start saving now (thus lowering interest rates).
6)
In dollar terms, obviously ET grossed much more that Gone with
the Wind. However, once you
adjust for inflation, it is no longer the case.
That is, in real terms, Gone With the Wind outsold ET.
7)
Procyclical variables move in the same direction as output (i.e. they
have a positive correlation). For example, consumer expenditures are procyclical. Countercyclical variables move in the opposite direction as
output (i.e. they have a negative correlation). A notable countercyclical variable is unemployment.
8)
Long-term (less liquid) securities tend to pay more than short term (more
liquid) securities to compensate their holders for the fact that they can’t
re-contract the terms of the security very often (this exposes long term
security holder to future changes in the interest rate).
9) Recall that capital and labor are complements. Therefore, increasing the supply of one raises the benefits of the other.
a) The main effect here is an increase in labor supply.
This will raise employment, but lower the real wage.
b) Note that with permanently higher employment, aggregate income is permanently higher as well. Therefore, aggregate savings doesn’t have to adjust (aggregate consumption will be permanently higher). However, with more available labor, the marginal product of capital increases. This increases investment demand and the real interest rate.
10)
With a 4% inflation rate, the three payments will be 250(1.04) = 260 ,
250(1.04)(1.04) = 270.40, and 250(1.04)(1.04)(1.04) = 281.22 respectively.
At a nominal interest rate of 7%, the present value of these payments
will be (approx) $705.
11)
The population of the economy is 100, the labor force (those working or
looking) is 90.
a)
The unemployment rate in a typical month is 8/90 = 8.8%
b)
Participation rate = 90/100 = 90%
c)
There are a total of 63 spells of unemployment each year (5 short term
each month and 3 long term). Of
these 63 spells 60 (95%) are for 1 month and the remaining 3 (5%) are for 12
months. Therefore, average duration
is (.95)1+(.05)12 =
1.55 months.
12)
First, use the identity S=I+(G-T). You
can assume that NX=0. Substituting
in the values for S, G, and T, you can solve for I (I=50).
Now use the Identity Y=C+I+G (again, assume NX=0).
Substituting in the values for Y, I, and G, you can solve for C (C=750).
13)
There are two acceptable explanations for this fact.
We know that when labor productivity increases , labor demand increases.
This should result in a rise in employment (and, hence, output) and a
rise in the real wage.
a)
if labor supply is very flat, the rise in the real wage would be very
small (empirically, this is not the case)
b)
If the increase in labor demand were matched by sn increase in labor
supply (because of intertemporal substitution – workers taking advantage of a
temporary wage increase), we could also get a very small
wage increase
14)
I won’t sketch the graph, but I will describe it.
a) The only points we need to worry about are the extremes. First, suppose that you choose to spend all of your wealth (Present value of lifetime income) today. That would yield 5,000 + 30,000/1.05 = 33,571 dollars of current spending and zero future spending. Alternatively, you could spend noting today and have 5,000(1.05)+30,000 = 35,250 in the future. Connect these two points and you have the budget set. Note that the slope is 1.05, which corresponds to (1+interest rate).
b) Whit higher future, the budget set shifts out (but maintains the same slop). Without a price change, the only relevant effect on the decision process is an income effect. With higher lifetime wealth, you should spend more today and next year. However, since current income hasn’t changed, but current spending has risen, current savings must decline.
15)
a)
|
# of Looms |
MPK |
|
1 |
100 |
|
2 |
80 |
|
3 |
60 |
|
4 |
30 |
|
5 |
15 |
|
6 |
10 |
|
7 |
5 |
c) the user cost of capital is ($1000/$10)*(.05+.10) = 15.
d) The firm should buy 5 looms.
16)
I will describe what the graphs look like
a)
If you work all 80 hours, you will have $800 in income, which you could
use to purchase 400 consumer goods. Therefore, if we put Leisure on the
horizontal axis and consumption on the vertical, (0,400) is one point. If you choose not to work at all, you will have no income
and, hence, no consumption. Therefore,
(80,0) is another point. The
budget set is the line connecting these two points.
Note that the slope is 5 (equal to the real wage).
b)
With the $100 inheritance, you can consume 50 more consumer goods
regardless of you labor choice (the budget line shifts up by 50).
This represents a pure income effect and therefore should reduce labor
supply.
c)
This one is a little tricky. All
points on the budget line where leisure is greater than 40 stay the same. The rest of the budget set rotates up to reflect the higher
“overtime premium”. The impact
on your labor supply decision depends on what your initial choices was.
Case1)
If you were initially consuming more than 40 hours of leisure (ie, working less
than 40 hours a week), your decision is unaffected.
Case
2) If you were initially working exactly 40 hours, you will experience a
substitution effect, but no income effect.
Therefore, you should work more.
Case
3) If your were already working more than 40 hours, you experience both an
income effect and a substitution effect. Therefore,
the effect on your labor supply is ambiguous.
17)
# Hours
MPL