ICU winter 2011, Principles of Macroeconomics January 12, 2011
Homework #1 Solution
Problem 1 (8 pts×3) (References: topic 3 and chapter 3)
Note that the neoclassical theory here applies to the long run, so our analyses below are about the long run effects of the corresponding event.
(a) As shown in Figure 1, the decrease in the labor force causes a leftward shift in the labor supply curve (i) and thus raises the real wage (W/P --> (W/P)'). The decrease in the labor force also reduces MPK1, causing a downward shift in the demand for capital line (ii) and reducing the real rental price of capital (R/P --> (R/P)'), as shown in Figure 2.
1 Mathematically, the fact LMPK can be checked using the Cobb-Douglas function (see slide
#29 of the lecture note). Intuitively, the decrease in labor means that there are fewer workers for each unit of capital, which implies that an additional unit of capital produces less output, so MPK falls.
labor (i)
R/P (R/P)'
K' (ii)
E' E
labor demand
E'
K labor
(i)
R/P
(R/P)'
K (ii)
E
E' real rental price
demand for capital supply of capital
E (original equilibrium)
L’ L (W/P)'
W/P
E' (new equilibrium) real wage
labor demand labor supply
capital
Figure 1 Figure 2
E real rental
price
demand for capital supply of capital
L (W/P)'
W/P real wage
labor supply
capital
Figure 3 Figure 4
(b) Because some part of the capital stock was destroyed by the earthquake and tsunami, K decreases. The decrease in K reduces MPL2 and causes a downward shift in the labor demand curve (i), and thus reduces the real wage (W/P --> (W/P)', Figure 3). The decrease in capital causes a leftward shift in the supply of capital line (ii), raising the real rental price of capital (R/P --> (R/P)', Figure 4).
(c) The economy-wide adoption of information technology that helps to improve production function raises both MPL and MPK,3 shifting upward both labor demand line (Figure 5) and demand for capital line (Figure 6). Both the real wage and the real rental price rise as a result.
Problem 2 (10+8×3 pts) (References: topic 3 and chapter 3) 1. The economic meaning of each of the equations (1)~(6):
(1) is the national income identity.
(2) shows that total income (or GDP) is given exogenously at some level
Y
. This reflects the assumption thatY
is determined by the fixed amount of laborL
and capitalK
according to the production functionY F K L ( , )
. (Note also that the technology level is also assumed to be fixed in this model.)(3) and (4) shows that the government expenditure and taxes are given exogenously. This is because they are assumed to be set by the government independently with the state of the economy.
(5) is the consumption function showing that consumption are composed of two
2 The fact KMPL can be checked using the Cobb-Douglas function (see slide #29). Intuitively, the decrease in K means that there is less capital for each worker, which implies that an additional worker produces less output, so MPL falls.
3 This corresponds to the case of A↑ in slide #29 which increases both MPL and MPK. Intuitively, an improve in technology means that for a given amount of labor and capital, each additional worker produces more output, and so does each additional unit of capital, so both MPL and MPK increase.
labor E'
E labor demand labor supply
R/P
K E’
demand for capital (R/P)'
capital E
real rental
price supply of capital
L (W/P)'
W/P
Figure 5 Figure 6
real wage
parts: the first depends positively on disposal income (Y-T) (because people use part of their disposal income to consume) and the second is independent of disposal income and is a constant (
C
0).(6) is the investment function expressing that investment are composed of two parts: the first depends negatively on the real interest rate (r) (because r affects the cost of investment) and the second does not and is a constant (
R
0).2.a. From (3)&(4), public saving = T
G T G1000 1000 0
.To compute private saving and national saving we need to compute consumption (C). Use (2),(4)&(5) and substituting values of parameters to have
0
( ) 250 0.75(5000 1000) 3250
C C a Y T
(i).Thus, using (i) yields, private saving = Y
T C5000 1000 3250 750
, and national saving = Y
C G5000 3250 1000 750
(which is also the sum of private and public saving! See slide#44).2.b. The equilibrium real interest rate can be calculated using I
Y C G, (6) and (i):Y C G I
0br r ( I
0 C G Y ) / b
. Substituting values yields(1000 3250 1000 5000) / 50 5
r
.2.c. When G increases to G
=1250, public saving = T
G 1000 1250 250
, which decreases by 250 - 0 = 250. Note from (i) that C is unchanged, and so is private saving. Because private saving is unchanged, the change national saving is the change in public saving and is a decrease of 250. Finally, similarly to 2b, the equilibrium real interest rate(
0' ) / (1000 3250 1250 5000) / 50 10
r
I
C G Y b
.In summary, the fiscal policy reduces public saving and national saving each by 250, does not affect private saving, and raises the equilibrium interest rate by 5.4
Problem 3 (5 pts×4) (References: topic 5 and chapter 4)
It is convenient to summarize the answer using the following table.
4 You are recommended to draw the graph to confirm that r increases in response to the fiscal policy.
unit of account store of value medium of exc.
(a) a SUICA card no
(A SUICA card does not have its own unit of account, but it uses the currency yen as
the unit.)
yes
(You can store a value, but of only less than
20,000 yen, in a SUICA card.)
yes (You can use a SUICA card to pay for train tickets or to buy
stuff in e.g. Newdays.)
(b) a credit card no
(A credit card does not have its own unit of account, but it uses some currency as the
unit.)
no (You cannot store a value in a credit card.)
yes
(You can use a credit card to buy many things: a book on Amazon, a tour on
Rakuten etc.)
(c) a Rolex watch no
(A Rolex watch does not have its own unit
of account.)
yes
(You can store a value in a Rolex watch.)
yes (In some rare cases, people may accept a
Rolex watch to exchange for something else.) (a) a painting by
Picasso
no (similar to (c))
yes (similar to (c))
yes (similar to (c))
Problem 4 (22pts) (References: topic 5 and chapter 4)
I chose Indonesia as a high-inflation country (with the average rate of 13.0% in the sample period) and Canada as a low-inflation country (with the average rate of 3.5% in the sample period). Figures 7 and 8 show the plots of money growth rate and nominal interest rate against inflation for Indonesia and Canada, respectively. The original series for money growth is “money and quasi money growth”, and for the interest rate is
“lending interest rate.”5 For inflation, GDP deflator is used for Indonesia, and CPI for Canada. The two figures both show positive correlations between money growth and inflation, and between nominal interest and inflation. The results are consistent with the prediction of the quantity theory of money, and the Fisher effect we studied in Topic 5. In addition, we observe that the correlations, especially the nominal interest- inflation one, are somewhat larger for Canada.
5 You can also use deposit interest rate because the two interest rates move very closely with each other.
Figure 7: Money growth & inflation and nominal interest rate & inflation of Indonesia, 1986-2010 (annual data)
Figure 8: Money growth & inflation and nominal interest rate & inflation of Canada, 1980-2010 (annual data)
