Week 2 Tutorial Questions (ECF2331)
Ch.4 – Consumption, Savings, and Investment (Good market equilibrium)
- Review question 9 (pg. 178)
- Numerical problem 𝜶 (not in textbook)
- Numerical problem 𝜷 (not in textbook)
- Numerical problem 𝜸 (not in textbook)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 6
CH.4 – CONSUMPTION, SAVINGS, AND INVESTMENT (GOOD MARKET
EQUILIBRIUM)
Review question 9 (pg. 178)
Give two equivalent ways of describing equilibrium in the goods market. Use a diagram to show how
goods market equilibrium is attained.
Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the
aggregate demand for goods (Cd + Id + G).
Since desired national saving (Sd) is Y – Cd – G, an equivalent condition is Sd = Id.
Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of
saving equal to the desired level of investment, as shown in Figure 4.7 in the text.
Numerical problem 𝜶 (not in textbook)
The Northern Kingdom Company (NKC) produces valerian steel fabricators at a cost $100 each. NKC
is trying to decide how many of these machines to buy. NKC expects to produce the following number
of valerian steel swords each year for each level of capital stock shown.
Number of Fabricators
0
1
2
3
4
5
6
Number of valerian steel swords per year
0
100
150
180
195
205
210
Valerian steel swords have a real value of $1 each. NKC has no other costs besides the cost of
fabricators.
Page 2 of 6
a.
Find the expected future marginal product of capital (in terms of dollars) for each level of capital.
The MPKf for the third fabricator, for example, is the real value of the extra output obtained when the
third fabricator is added.
# Fabricators
0
1
2
3
4
5
6
Output
0
100
150
180
195
205
210
MPKf = ∆ 𝐨𝐮𝐭𝐩𝐮𝐭⁄∆# 𝐅𝐚𝐛𝐫𝐢𝐜𝐚𝐭𝐨𝐫𝐬
—
100
50
30
15
10
5
The MPKf is declining.
b.
If the real interest rate is 12% per year and the depreciation rate of capital is 20% per year, find the
user cost of capital (in dollars per fabricator per year). How many fabricators should NKC buy?
We know uc = (r + d)pK = (0.12 + 0.20)  $100 = $32.
NKC should buy two (2) fabricators, since at two fabricators, MPKf = 50 > 32 = uc.
But at three fabricators, MPKf = 30 < 32 = uc.
You want to add fabricators only if the future marginal product of capital exceeds the user
cost of capital.
The MPKf of the third fabricator is less than its user cost, so it should not be added.
c.
Repeat Part (b) for a real interest rate of 8% per year.
When r = 0.08, uc = (0.08 + 0.20) $100 = $28.
Now they should buy three fabricators, since MPKf = 30 > 28 = uc for the third fabricator
and MPKf = 15 > 28 = uc for the fourth fabricator.
Now they should buy three fabricators
Page 3 of 6
Numerical problem 𝜷 (not in textbook)
Assume Australia’s full-employment level of output of 9000, and government purchases are 2000. The
values of the real interest rate, desired consumption and desired investment are given in the following
table.
Real Interest
Rate (%)
2
3
4
5
6
a.
Desired
Consumption
(Cd)
6100
6000
5900
5800
5700
Desired
Investment
(Id)
1500
1400
1300
1200
1100
Why do desired consumption and desired investment fall as the real interest rate rises?
Desired consumption declines as the real interest rate rises because the higher return to
saving encourages higher saving.
Desired investment declines as the real interest rate rises because the user cost of capital
is higher, reducing the desired capital stock, and thus investment.
b.
Find desired national saving for each value of the real interest rate. Add a third column to the table
show the values.
Desired national savings is Sd = Y – Cd – G. We also know Y = 9000 and G = 2000.
So, Sd = 9000 – Cd – 2000 = 7000 – Cd. Now just substitute in each value of Cd to get Sd for
each value of the real interest rate.
Real Interest
Rate (%)
2
3
4
5
6
c.
Desired
Consumption
(Cd)
6100
6000
5900
5800
5700
Desired
Investment
(Id)
1500
1400
1300
1200
1100
Sd =7000 – Cd
900
1000
1100
1200
1300
If the goods market is in equilibrium, what are the values of the real interest rate, desired national
saving, and desired investment? Show that both forms of the goods market equilibrium condition,
Eq’s. (4.7) and (4.8), are satisfied at the equilibrium. Assume that output is fixed at its fullemployment level. Add a fourth column to the table show the values.
Equation (4.7) says that Y = Cd + Id + G at equilibrium. We add another column in the table
and calculate Y for each value of the real interest rate.
Page 4 of 6
Real
Interest
Rate (%)
2
3
4
5
6
Desired
Consumption
(Cd)
6100
6000
5900
5800
5700
Desired
Investment
(Id)
1500
1400
1300
1200
1100
Sd =7000 – Cd
Y = Cd + Id + G
900
1000
1100
1200
1300
9600
9400
9200
9000
8800
Equation (4.8) says that Sd = Id at equilibrium. This is true only at a real interest rate of 5%.
Also note that Equation (4.7) also shows this to be true. We know Y = 9000, and hence this
occurs at a value of the real interest rate at 5%.
Numerical problem 𝜸 (not in textbook)
An economy has full-employment output of 6000. Government purchases, G, are 1200. Desired
consumption and desired investment are given by:
Cd = 3600 – 2000r + 0.10Y
Id = 1200 – 4000r
where Y is output and r is the real interest rate.
a.
Find an equation relating desired national saving, Sd, to r and Y.
We know Sd = Y – Cd – G. Substituting in the above equations, we get:
Sd = Y – (3600 – 2000r + 0.1Y) – 1200
= – 4800 + 2000r + 0.9Y
This equation relates Sd to the real interest rate (r) and output (Y).
b.
Using both versions of the goods market equilibrium condition, Eq’s. (4.7) and (4.8), find the real
interest rate that clears the goods market. Assume that output equals full-employment output.
Using Eq. (4.7)
Y = Cd + Id + G
Y = (3600 – 2000r + 0.1Y) – (1200 – 4000r) – 1200
Y = 6000 – 6000r + 0.1Y
So, 0.9Y = 6000 – 6000r
At full employment, Y = 6000.
Substituting this into the above, we get 0.9  6000 = 6000 – 6000r
Finally, solving for r, we get r = 0.10 (or 10%).
Page 5 of 6
Using Eq. (4.8)
S d = Id
– 4800 + 2000r + 0.9Y = 1200 – 4000r
0.9Y = 6000 – 6000r
When Y = 6000, r = 0.10 (or 10%).
So, we can use either Eq. (4.7) or (4.8) to get to the same result.
c.
Government purchases rise to 1440. How does this increase change the equation describing desired
national saving? Show the change graphically. What happens to the market-clearing real interest
rate?
When G = 1440, desired saving becomes:
Sd = Y – Cd – G = Y – (3600 – 2000r + 0.1Y) – 1440.
This becomes 0.9Y = 5040 – 2000r
Sd is now 240 less for any given r and Y; this shows up as a shift in the Sd from S1 to S2
What about r? Set Sd = Id, we get:
–5040 + 2000r + 0.9Y = 1200 – 4000r
6000r + 0.9Y = 6240
At Y = 6000, this is 6000r = 6240 – (0.9  6000) = 840, and so r = 0.14 (or 14%)
Thus, the market-clearing real interest rate increases from 10% to 14%.
Page 6 of 6
Week 3 Tutorial Questions (ECF2331)
Ch.7 – The Asset Market, Money and Prices (Asset market equilibrium)
- Review question 4 (pg. 310)
- Numerical problem 4 (a and b only) (pg. 310)
- Numerical problem 𝜶 (not in textbook)
- Numerical problem 𝜷 (not in textbook)
- Analytical problem 1 (pg. 311)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 4
CH.7 – THE ASSET MARKET, MONEY
EQUILIBRIUM)
AND
PRICES (ASSET
MARKET
Review question 4 (pg. 310)
What are the four characteristics of assets that are most important to holders of wealth? How does
money compare with other assets for each characteristic?
The four characteristics of assets that are most important to wealth holders are
(1)
(2)
(3)
(4)
expected return,
risk,
liquidity; and
time to maturity.
Money has a low expected return compared with other assets, low risk since it always maintains
its nominal value, is the most liquid of all assets, and has the lowest (zero) time to maturity.
Numerical problem 4 (a and b only) (pg. 310)
Suppose the money demand function is:
𝑀𝑑
= 1000 + 0.2𝑌 − 1000(𝑟 + 𝜋 𝑒 )
𝑃
a.
Calculate velocity if Y = 2000, r = 0.06, and 𝜋 𝑒 = 0.04
We know that V = PY/M = Y/(M/P). But first we need to find what M/P is. Substituting in the
values in the money demand function we get:
𝑴𝒅
𝑷
= 𝟏𝟎𝟎𝟎 + 𝟎. 𝟐(𝟐𝟎𝟎𝟎) − 𝟏𝟎𝟎𝟎(𝟎. 𝟎𝟔 + 𝟎. 𝟎𝟒) = 1300
So, V = 2000/1300 = 1.54
b.
If the money supply (Ms) is 2600, what is the price level?
We know that P =
𝑴𝑺
𝒅
(𝑴 ⁄𝑷)
= 2600/1300 = 2.
Numerical problem 𝜶 (not in textbook)
Consider an economy with a constant nominal money supply, a constant level of real output Y = 100,
and a constant real interest rate r = 0.10. Suppose that the income elasticity of money demand is 0.5
and the interest elasticity of money demand is -0.1.
a.
By what percentage does the equilibrium price level differ from its initial value if output increases to
Y = 106 (and r remains at 0.10)? (Hint: Use Eq. 7.12.)
∆P/P = –𝜼𝒀 ∆Y/Y = –0.5%  6% = –3%. Thus, the price level will be 3% lower.
Page 2 of 4
b.
By what percentage does the equilibrium price level differ from its initial value if the real interest
increases to r = 0.11 (and Y remains at 100)?
∆P/P = –𝜼𝒀 ∆Y/Y = – (–0.1)  0.1 = – 1%. Thus, the price level will be 1% higher.
Numerical problem 𝜷 (not in textbook)
Suppose that the real money demand function is:
𝐿(𝑌, 𝑟 + 𝜋 𝑒 ) =
0.01𝑌
𝑟 + 𝜋𝑒
where Y is real output, r is the real interest rate, and 𝜋 𝑒 is the expected rate of inflation. Real output is
constant over time at Y = $150. The real interest rate is fixed in the goods market at r = 0.05 per year.
a.
Suppose that the nominal money supply is growing at the rate of 10% per year and that this
growth rate is expected to persist forever. Currently, the nominal money supply is M = 300. What
are the values of the real money supply and the current price level? (Hint: What is the value of the
expected inflation rate that enters the money demand function?).
𝚫𝑴
𝝅𝒆 = 𝑴 = 10% (note that both real output and real interest rate are constant/fixed and the
money growth rate is expected to persist forever).
i = 𝒓 + 𝝅𝒆 = 15%
M/P = L = 0.01  150/0.15 = 10.
P = 300/10 = 30.
b.
Suppose that the nominal money supply is M = 300. The central bank announces that from now on
the nominal money supply will grow at the rate of 5% per year. If everyone believes this
announcement, and if all markets are in equilibrium, what are the values of the real money supply
and the current price level? Explain the effects on the real money supply and the current price
level of a slowdown in the rate of money growth.
𝝅𝒆 =
𝚫𝑴
𝑴
= 5%
i = 𝒓 + 𝝅𝒆 = 10%
M/P = L = 0.01  150/0.10 = 15.
P = 300/15 = 20.
The slowdown in money growth reduces expected inflation, increasing real money demand,
thus lowering the price level.
Page 3 of 4
Analytical problem 1 (pg. 311)
What happens to M1 and M2 due to each of the following changes?
a.
You take $500 out of your checking (savings/streamline) account and put it into a passbook
savings account.
M1 decreases by $500, M2 is unchanged (remember that M1 is part of M2).
b.
You take $1000 out of your checking account (savings/streamline) and buy traveler’s checks.
M1 and M2 are both unchanged.
c.
You take $1500 out of your money-market mutual fund and deposit into your checking
(savings/streamline) account.
M1 increases by $1500, M2 is unchanged.
d.
You cash in $2000 in savings bonds and invest the money in a certificate of deposit.
M1 is unchanged, M2 increases by $2000.
Page 4 of 4
Week 4 Tutorial Questions (ECF2331)
Ch.3 – Productivity, Output, and Unemployment (Labor market equilibrium)
- Review question 3 (pg.133)
- Review question 5 (pg.133)
- Numerical problem 𝜶 (not in textbook)
- Numerical problem 3 (part a to b only) (pg.132)
- Analytical problem 2 (pg.133)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 5
CH.3 – PRODUCTIVITY, OUTPUT,
MARKET EQUILIBRIUM )
AND
UNEMPLOYMENT (LABOR
Review question 3 (pg.133)
Define marginal product of capital, or MPK. How can the MPK be shown graphically?
The marginal product of capital (MPK) is the output produced per unit of additional capital. The
MPK can be shown graphically using the production function.
The MPK is just the slope of the production function.
For a fixed level of labor, plot the output provided by different levels of capital; this is the
production function.
Review question 5 (pg.133)
What is the MPN curve? How is the MPN curve related to the production function? How is it related to
labor demand?
The MPN curve shows the marginal product of labor at each level of employment.
It is related to the production function because the marginal product of labor is equal to the slope
of the production function (where output is plotted against employment).
The MPN curve is related to labor demand, because firms hire workers up to the point at which
the real wage equals the marginal product of labor (i.e., 𝐰 ∗ = 𝐍∗ )
Page 2 of 5
Labor demand curve shows relationship between the real wage rate and the quantity of labor
demanded. It is the same as the MPN curve, since 𝒘 = 𝑴𝑷𝑵 at equilibrium.
So, the labor demand curve is identical to the MPN curve, except that the vertical axis is the real
wage instead of the marginal product of labor.
Numerical problem 𝜶 (not in textbook)
The following data give real GDP, Y, capital, K, and labor, N, for the U.S. economy in various years.
Year
1960
1970
1980
1990
2000
2010
Y
3109
4722
6450
8955
12,560
17,784
K
3883
5863
8433
11,460
15,402
18,513
N
66
79
99
119
137
139
Assume that the production function is:
𝑌 = 𝐴𝐾0.3𝑁0.7
a.
By what percentage did U.S. total factor productivity grow between 1960 and 1970? Between 1970
and 1980? Between 1980 and 1990? Between 1990 and 2000? Between 2000 and 2010?
To find the growth of total factor productivity, you must first calculate the value of A in the
production function. This is given by:
𝑨=
𝒀
𝑲𝟎.𝟑 𝑵𝟎.𝟕
Substitute in the values for Y, K, and N for each year. Values are given in column “A”
below.
Next, the growth rate in productivity can be calculated as follows:
𝑨𝒕 − 𝑨𝒕−𝟏
(
) × 𝟏𝟎𝟎
𝑨𝒕−𝟏
Values are given in column “Growth in A (%)” below and plotted in Figure below.
Year
1960
1970
1980
1990
2000
2010
Y
3109
4722
6450
8955
12,560
17,784
K
3883
5863
8433
11,460
15,402
18,513
N
66
79
99
119
137
139
A
13.874
16.42
17.172
19.118
22.234
29.491
Growth in A (%)
18.4%
4.6%
11.3%
16.3%
32.6%
Page 3 of 5
1970
1990
1980
2000
2010
Numerical problem 3 (part a to b only) (pg.132)
Acme Widget, Inc., has the following production function.
Number of workers (N)
0
1
2
3
4
5
6
a.
Number of Widgets Produced (Y)
0
8
15
21
26
30
33
Find the marginal product of labour (MPN) for each level of employment
We calculate the MPN as ∆𝒀⁄∆𝑵, which is given in column “MPN” in the table below.
N
1
2
3
4
5
6
b.
Y
8
15
21
26
30
33
MPN
8
7
6
5
4
3
Acme can get $5 for each widget it produces. How many workers will it hire if the nominal wage is
$38? If it is $27? If it is $22?
We first need to calculate the marginal revenue product of labor (MRPN) when P = 5. This is
given in column “MRPN (P = 5)” below
Page 4 of 5
N
1
2
3
4
5
6
Y
8
15
21
26
30
33
MPN
8
7
6
5
4
3
MRPN (when P = 5)
(MPN × P) = 40
35
30
25
20
15
Thus:
▻ If W = $38:
Hire one worker, since MRPN ($40) is greater than W ($38) at N = 1.
Do not hire two workers, since MRPN ($35) is less than W ($38) at N = 2.
▻ If W = $27:
Hire three workers, since MRPN ($30) is greater than W ($27) at N = 3.
Do not hire four workers, since MRPN ($25) is less than W ($27) at N = 4.
▻ If W = $22: Hire four workers, since MRPN ($25) is greater than W ($22) at N = 4.
Do not hire five workers, since MRPN ($20) is less than W ($22) at N = 5.
Analytical problem 2 (pg.133)
How would each of the following affect the current level of full-employment output? Explain.
a.
A large number of immigrants enter the country.
An increase in the number of immigrants increases the labor force, increasing employment
and increasing full-employment output.
b.
Energy supplies become depleted.
If energy supplies become depleted, this is likely to reduce productivity, because energy is
a factor of production.
So the reduction in energy supplies reduces full-employment output.
c.
New teaching techniques improve the educational performance of high school seniors.
Better education raises future productivity and output, but has no effect on current fullemployment output.
d.
A new law mandates the shutdown of some unsafe forms of capital.
This reduction in the capital stock reduces full-employment output (although it may very
well increase welfare).
Page 5 of 5
Week 5 Tutorial Questions (ECF2331)
Ch.9 – The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis
- Review question 1 (pg. 379)
- Review question 2 (pg. 379)
- Independent question 𝝁 (not in textbook)
- Independent question 𝜸 (not in textbook)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 4
CH.9 – THE IS-LM/AD-AS MODEL: A GENERAL FRAMEWORK FOR
MACROECONOMIC ANALYSIS
Review question 1 (pg. 387)
What determines the position of the FE line? What factors would shift the FE line to the right?
The position of the FE line is determined by the labour market and the production function.
Labour supply and demand determine equilibrium. Using equilibrium in the production
functions gives the full-employment level of output. The FE line is vertical at that point.
The FE line shifts to the right if:
• A beneficial supply shock occurs
• An increase in labour supply
• An increase in the capital stock
Review question 2 (pg. 387)
What relationship does the IS curve capture? Derive the IS curve graphically and show why it slopes as
it does. Give two examples of changes in the economy that would cause the IS curve to shift down and
to the left.
The IS curve shows combinations of the real interest rate (r) and output (Y) that leave the goods
market in equilibrium.
Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the
aggregate demand for goods (Cd + Id + G). Since desired national saving (Sd) is Y – Cd – G, an
equivalent condition is Sd = Id.
Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of
saving equal to the desired level of investment.
For different levels of output, there are different desired saving curves, with different
equilibrium interest rates.
When plotted on a figure showing output and the real interest rate, this forms the IS curve, as
shown in Fig:
Page 2 of 4
The curve slopes downward because as output rises, the saving curve shifts along the investment
curve and the real interest rate declines.
The IS curve could shift down and to the left if:
(1) Expected future output falls, because this increases desired saving;
(2) Government purchases fall, because this increases desired saving;
(3) The expected future marginal product of capital falls, because this decreases desired
investment; or
(4) Corporate taxes increase, because this decreases desired investment.
Review question 𝝁 (not in textbook)
Provide an example of how the price of a non-monetary asset is inversely related to its interest rate or
yield?
Say, for sample, a bond pays $10,000 in one year; its current price is $9615, and its interest rate
is 4%, since ($10,000 - $9615)/$9615 = 0.04 = 4%.
If the price of the bond in the market were to fall to $9524, its yield would rise to 5%, since ($10,000
- $9524)/$9524 = 0.05 = 5%.
Review question 𝜸 (not in textbook)
What relationship does the LM curve capture? Derive the LM curve graphically and show why it slopes
as it does. Give two examples of changes in the economy that would cause the LM curve to shift down
and to the right.
The LM curve shows the combinations of output and the real interest rate that maintain
equilibrium in the asset market. Equilibrium in the asset market occurs when real money demand
equals the real money supply.
Following figure shows the derivation of the LM curve and why it slopes upward.
▻ An increase in output from Y1 to Y2 raises money demand, shifting the money demand
curve from MD(Y1) to MD(Y2).
▻ With money supply fixed at MS, there must be a higher real interest rate to get equilibrium
in the asset market.
▻ This gives two points of the LM curve, plotted on the right half of the figure.
Page 3 of 4
▻ The result is that higher output increases the real interest rate along the LM curve, so the
LM curve slopes upward.
The LM curve would shift down and to the right if the nominal money supply or expected inflation
increased or if the price level or nominal interest rate on money decreased. In addition, the curve
would shift down and to the right if:
(1)
(2)
(3)
(4)
There were a decrease in wealth,
A decrease in the risk of alternative assets relative to the risk of holding money,
An increase in the liquidity of alternative assets, or
An increase in the efficiency of payment technologies.
Page 4 of 4
Week 6 Tutorial Questions (ECF2331)
Ch.9 – The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis
- Independent question 𝝀 (not in textbook)
- Numerical Problem 3 (pg. 388)
- Numerical Problem 4 (pg. 388)
- Analytical problem 1 (pg. 389)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 6
CH.9 – THE IS-LM/AD-AS MODEL: A GENERAL FRAMEWORK FOR
MACROECONOMIC ANALYSIS
Review question 𝝀 (not in textbook)
Define general equilibrium and show the general equilibrium point in the IS–LM diagram. If the economy
isn’t in general equilibrium, what determines output and the real interest rate? What economic forces act
to bring the economy back to general equilibrium?
Recall, the position of the FE line is determined by the labor market and the production function.
Labor supply and demand determine equilibrium employment. Using equilibrium employment in
the production function gives the full-employment level of output. The FE line is vertical at that
point.
General equilibrium is a situation in which all markets in an economy are simultaneously in
equilibrium. This is shown in Figure below as the point at which the FE line and the IS and LM
curves intersect
If the economy is not initially in general equilibrium, output and the real interest rate are
determined by the intersection of the IS and LM curves.
Then adjustment of the price level moves the LM curve until it intersects the FE line and IS curve.
Page 2 of 6
Numerical Problem 3 (pg. 388)
Desired consumption is Cd = 100 + 0.8Y – 500r – 0.5G,
Desired investment is Id = 100 – 500r.
Real money demand is Md/P = Y – 2000i.
Other variables are 𝜋𝑒 = 0.05, G = 200, 𝑌̅ = 1000, and M = 2100.
a.
Find the equilibrium values of the real interest rate, consumption, investment, and the price level.
Recall that in the condition that desired national savings equals desired national
investment shows also that Y = Cd + Id + G.
We use this equation and substitute in Cd, Id and G to get:
Y = [100 + 0.8Y – 500r – 0.5(200)] + [100 – 500r] + 200
Y = 100 + 0.8Y – 500r – 100 + 100 – 500r + 200
Y = 300 + 0.8Y – 1000r
Solving for Y:
Y = 1500 – 5000r (this is the IS curve)
̅ = 1000), we can solve for the full
Now, since full-employment output equals 1000 (i.e., 𝒀
employment equilibrium level of the real interest rate:
1000 = 1500 – 5000r
∴ r = 0.10
Since r = 0.10, we can substitute this into Cd and Id to find equilibrium consumption and
investment:
▻ Cd = 100 + 0.8(1000) – 500(0.10) – 0.5(200) = 750.
▻ Id = 100 – 500(0.10) = 50.
Finally, to find the price level, we use M/P = L = Y – 2000i (but remember: i = r + 𝝅𝒆 )
▻
▻
▻
▻
b.
2100/P = 1000 – 2000(r + 𝝅𝒆)
2100/P = 1000 – 2000(0.10 +0.05)
2100/P = 700
Solving for P, we get P = 3.
Suppose the money supply increases to 2800. Find the equilibrium values of the real interest rate,
consumption, investment, and the price level. (Assume that the expected inflation rate is
unchanged.
To find the price level again, we use M/P = Y – 2000i, where M is now 2800
Page 3 of 6
▻ 2800/P = 700
▻ Solving for P, we get P = 4.
Thus, the increase in the money supply does not change anything except the price level.
Numerical Problem 4 (pg. 388)
Suppose the production function of Nigeria in trillions of international dollars (a reference currency with
the same purchasing power parity as the U.S. dollar and used to compare world currencies) is
Y = A(5N – 0.0025N2)
Where A is productivity. With this production function, the marginal product of labor is:
MPN = 5A – 0.005AN.
Suppose that A = 2. The labour supply curve is:
NS = 55 + 10(1 – t)w,
Where NS is the amount of labor supplied, w is the real wage, and t is the tax rate on wage income,
which is 0.5. Desired consumption and investment are:
Cd = 300 + 0.8(Y – T) – 200r
Id = 258.5 – 250r.
Tax and government purchases are:
T = 0.05Y
G = 50
Money demand is:
Md/P = 0.5Y – 250(r + πe)
The expected rate of inflation, πe, is 0.02 and the nominal money supply M is 9150.
a.
What are the general equilibrium levels of the real wage, employment, and output?
First, look at labor market equilibrium.
Labor supply is NS = 55 + 10(1 – t)w.
Labor demand (ND) comes from the equation w = 5A – (0.005A × ND). Substituting the latter
equation into the former and equating labor supply and labor demand gives N = 100.
Using this in either the labor supply or labor demand equation then gives w = 9.
Page 4 of 6
Using N in the production function gives Y = 950.
b.
For any level of output, Y, find the equation that gives the real interest rate, r, that clears the goods
market; this equation describes the IS curve (Hint: write the goods marker equilibrium condition
and solve for r in terms of Y and other variables). What are the general equilibrium values of the
real interest rate, consumption, and investment?
Look at goods market equilibrium and the IS curve:
Sd = Y – Cd – G = Y – [300 + 0.8(Y – T) – 200r] – G = Y – [300 + (0.4Y – 16) – 200r] – G
= – 284 + 0.6Y + 200r – G.
Setting Sd = Id gives – 284 + 0.6Y + 200r – G = 258.5 – 250r.
Solving this for r in terms of Y gives r = (542.5 + G)/450 - 0.004/3Y.
Thus, When G = 50, this is r = 1.317 - 0.004/3Y.
With full-employment output of 950, using this in the IS curve and solving for r gives r = 0.05.
Plugging these results into the consumption and investment equations gives C = 654 and I =
246.
c.
For any level of output, Y, find an equation that gives the real interest rate that clears the asset
market; this equation describes the LM curve. (Hint: an in part (b) above, write the appropriate
equilibrium condition and solve for r in terms of Y and other variables). What is the general
equilibrium value of the price level?
Look at asset market equilibrium and the LM curve.
Setting money demand equal to money supply gives 9150/P = 0.5Y – 250(r + 0.02).
This can be solved for r = [0.5Y – (5 + 9150/P)]/250.
With Y = 950 and r = 0.05, solving for P gives P = 20.
Page 5 of 6
Analytical problem 1 (pg. 389)
For each of the following changes, what happens to the real interest rate and output in the very short
run, before the price level has adjusted to restore general equilibrium?
a.
Wealth declines.
The decline in wealth shifts the IS curve shifts down and to the left, so r and Y fall.
b.
Money supply declines.
The decline in money supply shifts the LM curve up and to the left, so r rises and Y falls.
c.
The future marginal productivity of capital declines.
The decline in the future marginal productivity of capital shifts the IS curve down and to the
left, so r and Y fall.
d.
Expected inflation rises.
The rise in expected inflation shifts the LM curve down and to the right, so r falls and Y
rises.
e.
Future income rises.
The rise in future income shifts the IS curve up and to the right, so r and Y rise.
Page 6 of 6
Week 7 Tutorial Questions
Ch.12 – Unemployment and Inflation
- Review question 2 (pg. 511)
- Review question 5 (pg. 512)
- Review question 8 (pg. 512)
- Numerical problem 1 (pg. 512)
- Working with macroeconomic data 𝜶
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
CH.12 – UNEMPLOYMENT
AND
INFLATION
Review question 2 (pg. 511)
How does the expectations-augmented Phillips curve differ from the original Phillips curve? According to the
theory of the expectations-augmented Phillips curve, under what conditions should the short-run Phillips
curve relationship appear in the data?
In the original Phillips curve, inflation itself is related to the unemployment rate.
In the expectations-augmented Phillips curve, it is unanticipated inflation (the difference between
actual and expected inflation) that is related to cyclical unemployment (the difference between the
unemployment rate and the natural rate of unemployment).
The short-run Phillips curve appears in the data at times when both expected inflation and the natural
rate of unemployment are fixed.
Review question 5 (pg. 512)
Why do policymakers want to keep inflation low? Who suffers when there is cyclical unemployment?
Policymakers want to keep inflation low because inflation imposes costs on the economy.
Costs of anticipated inflation include shoe leather costs and menu costs.
Costs of unanticipated inflation include unpredictable transfers of wealth between lenders and
borrowers, resources used to reduce the risk of such transfers, and reduced efficiency because of
the difficulty in observing relative prices.
When there is cyclical unemployment, society as a whole loses because of output that is not
produced and the families of the unemployed suffer personal and psychological costs.
Review question 8 (pg. 512)
How does the sacrifice ratio measure the costs of disinflation? Use the expectations-augmented Phillips
curve to explain how expectation can reduce the costs of disinflation.
The sacrifice ratio is the amount of output lost when the inflation rate is reduced by one percentage
point.
▻ For example, if a country has a sacrifice ratio of 0.75, its one percentage point reduction in
inflation will cost 0.75% of a year’s potential GDP.
▻ The lower GDP is associated with higher unemployment rate.
̅ ).
The equation for the expectations-augmented Phillips curve is 𝝅 − 𝝅𝒆 = h(𝒖 − 𝒖
If a central bank announces that next year’s inflation rate will be lower than the current year, people
change their expected inflation rate accordingly. In other words, expected inflation (𝝅𝒆 ) and actual
̅ ) remains unchanged.
inflation (𝝅) fall by the same amount, (𝒖 − 𝒖
Given the natural unemployment rate, disinflation does not raise the unemployment rate, 𝒖.
Numerical problem 1 (pg. 512)
Consider an economy in long-run equilibrium with an inflation rate, 𝜋, of 12% (0.12) per year and a natural
unemployment rate, 𝜋 𝑒, of 4% (0.04). The expectations-augmented Phillips curve is:
𝜋 = 𝜋𝑒 − 2(𝑢 − 𝑢𝑛)
where 𝑢 is the unemployment rate in the current year. Assume that Okun’s law holds so that a 1 percentage
point increase in the cyclical unemployment rate maintained for one year reduces GDP by 3% of fullemployment output.
a.
Consider a two-year disinflation. In the first year, 𝜋 = 0.06 and 𝜋𝑒 = 0.09. In the second year, 𝜋 = 0.06
and 𝜋𝑒 = 0.06. What are the unemployment rates in the first and second years? By what percentage
does output exceed the full-employment in the first and second year respectively? What is the sacrifice
ratio for this disinflation?
We want to first solve the expectations-augmented Phillips curve so that unemployment (𝒖) is our
left-hand-side variable, and since the natural rate of unemployment is 0.04, this gives:
𝝅 = 𝝅𝒆 − 𝟐(𝒖 − 𝟎.𝟎𝟒)
Solving for 𝒖 gives:
𝒖 = 𝟎.𝟎𝟒 + 𝟎.𝟓(𝝅𝒆 – 𝝅) (Eq. 1)
Now, we can determine what the unemployment rates are in years 1 and 2:
Year 1
Substituting in 𝝅 = 𝟎. 𝟎𝟔 and 𝝅𝒆 = 𝟎. 𝟎𝟗 into equation (1) gives:
𝒖 = 𝟎.𝟎𝟒 + 𝟎. 𝟓(𝟎.𝟎𝟗 − 𝟎.𝟎𝟔)
𝒖 = 𝟎. 𝟎𝟓𝟓 (𝟓.𝟓%)
Since the natural rate of unemployment is 0.04 (4%), and the (actual) unemployment rate is
0.055 (5.5%), then obviously the unemployment rate is higher than the natural rate by: 5.5% –
4.4% = 1.5%.
Now, since Okun’s law holds such that a 1%-point increase in the cyclical unemployment rate
maintained for one year reduces GDP by 3% of full-employment output, we can calculate the
‘output shortfall’ by: 3 × (0.055 – 0.04) = 0.045 or 4.5%.
Thus, output is below the full-employment level of output by 4.5% (or we just say, the percentage
that output falls short of the full-employment output is 4.5%)
Year 2
Substituting in 𝝅 = 𝟎. 𝟎𝟔 and 𝝅𝒆 = 𝟎. 𝟎𝟔 into equation (1) gives:
𝒖 = 𝟎. 𝟎𝟒 + 𝟎. 𝟓(𝟎. 𝟎𝟔 − 𝟎. 𝟎𝟔)
𝒖 = 𝟎. 𝟎𝟒 (𝟒%)
So, in this case, the unemployment rate equals the natural rate, since inflation equals
expected inflation
As unemployment is at its natural rate, output is at its full-employment level.
Sacrifice ratio:
With a 4.5 percentage point drop in output and a 6-percentage point decrease in inflation rate,
the sacrifice ratio is 4.5/6 = 0.75.
b.
Now consider a four-year disinflation according to the following table:
Year
𝜋
𝜋𝑒
1
0.09
0.15
2
0.06
0.12
3
0.06
0.09
4
0.06
0.06
What is the unemployment rate in each of the four years? By what percentage does output fall short of
the full-employment output each year? What is the sacrifice ratio for this disinflation?
Using equation (1) above and substituting in the values from the table we get:
Year
𝝅
𝝅𝒆
𝒖 = 𝟎. 𝟎𝟒 + 𝟎. 𝟓(𝝅𝒆 − 𝝅)
1
2
3
4
0.09
0.06
0.06
0.06
0.15
0.12
0.09
0.06
0.07
0.07
0.055
0.04
Output falls short: 3
× (𝒖 − 𝟎. 𝟎𝟒)
0.09
0.09
0.045
0
The total output short fall is the summation of the individual output short falls for each year:
0.09 + 0.09 + 0.045 + 0 = 0.225, or 22.5 percentage points
Inflation drops by 6 percentage points.
Thus, the sacrifice ratio is 22.5/6 = 3.75. Compared with part (a), the sacrifice ratio is
higher for this slow disinflation.
Page 4 of 6
Working with macroeconomic data 𝜶
All data is available through FRED https://fred.stlouisfed.org/. The data identifiers (codes) are provided
below with an underline.
This exercise requires you to diagrammatically illustrate the relationship between unemployment and
inflation. Using annual data for France, generate a scatter plot of the CPI inflation rate (Inflation, consumer
prices) using FPCPITOTLZGFRA against the average unemployment rate (Unemployment Rate: Aged
15-74: All Persons) using LRUN74TTFRA156N. Download both data series into Excel and create a
scatter plot. Make sure the inflation rate is on the vertical axis and the unemployment rate is on the
horizontal axis. Then, add a linear trendline to the chart. Comment on the results in the context of the
Phillips curve.
The Phillips curve shows a negative relationship between unemployment and inflation. On
average, the relationship is verified over the period (the slope of the tendency line conforms to
the Phillips curve). However, Phillips is not a long-term relationship but a short term one. In this
respect the negative relationship seems relevant only for certain periods:
▻ During the oil shocks of 1972–1974, inflation as well as unemployment increased.
▻ After 1974–1978, the decrease of inflation was accompanied by an increase in
unemployment.
The decrease of inflation between 1980 and 2000 was accompanied by a surge of unemployment.
Between 1986 and 1992, inflation and unemployment rise together, between 1993 and 2005 the
decrease of inflation was accompanied by a regular increase on unemployment.
In the 2010s, inflation was contained at a low level in both countries and the shift in unemployment
is no longer related to the evolution of inflation.
The instability of the relationship in the first period could be explained by the fact that inflation
and unemployment have diverse causes and the Phillips relationship could only be applied ‘all
things being equal’. If a strong disturbance occurs, it modifies one of the variables independently.
Since the 2000s, the openness of developed economies has disconnected most prices from the
internal situation and submitted them to international competition. The variation of
competitiveness and productivity is now the main determinant of the level of employment.
Page 5 of 6
Scatter plot for France
16.00
14.00
CPI inflation rate
12.00
10.00
8.00
6.00
y = -0.5304x + 7.6946
4.00
2.00
0.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
average unemployment rate
(URLs for the data series: https://fred.stlouisfed.org/series/FPCPITOTLZGFRA and
https://fred.stlouisfed.org/series/LRUN74TTFRA156N).
Page 6 of 6
Week 9 Tutorial Questions (ECF2331)
Ch.14 – Monetary Policy
- Review question 3 (pg. 611)
- Review question 7 (pg. 611)
- Review question 10 (pg. 611)
- Numerical problem 3 (part a to c only) (pg. 611)
- Analytical problem 1 (pg. 612)
- Working with macroeconomic data 𝜶
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 6
CH.14 – MONETARY POLICY
Review question 3 (pg. 611)
What is the reserve–deposit ratio and how does it affect bank runs?
Because banks lend out some of their deposits, the reserves held by a bank equal only a fraction
of its outstanding deposits.
In a crisis, a large number of depositors may withdraw their deposits simultaneously, exhausting
the bank’s reserves and forcing it to close.
This panicky withdrawal is called a bank run
Review question 7 (pg. 611)
Describe the main sources of uncertainty that affect monetary policymakers and give an example of
each.
The three main sources of uncertainty that affect monetary policymakers are
1. Uncertainty about the current state of the economy
▻ E.g., the fact that different economic variables often give conflicting signals about
the current strength of the economy and the fact that data are often revised, and
the initial releases of the data are much less accurate than later releases of the
data
2. Incompleteness of their models of the economy
▻ E.g., the fact that no one is certain whether a classical model or the Keynesian
model is the best description of the economy, our lack of knowledge about the
slopes and locations of each of the curves in each model, and uncertainty about
the levels of full-employment output and the natural rate of unemployment.
▻ In addition, there is uncertainty about the predominant source of shocks to the
economy.
3. Uncertainty about how the expectations of the public will be affected by economic shocks
and policy actions.
▻ E.g., the idea that the public is not sure of the central bank’s motives, which might
affect their expectations.
Page 2 of 6
Review question 10 (pg. 611)
Describe the Taylor rule. What are the variables that determine the recommended interest rate
according to the rule? How has the rule performed historically?
The Taylor rule (after John Taylor) sets the fed funds rate target depending on recent inflation,
the deviation of output from the level of full-employment output, and the deviation of recent
inflation from its target of 2%.
i = 𝝅 + 0.02 + 0.5y + 0.5(𝝅 – 0.02)
i = the nominal fed funds rate (the Fed’s intermediate target);
𝝅 = the rate of inflation over the previous four quarters;
̅ )/𝒀
̅ = the percentage deviation of output from full-employment output.
y = (𝒀 -𝒀
Hence, the Taylor rule requires that the real fed funds rate, i = 𝝅, respond to
1. the difference between output and full-employment output, and
2. the difference between inflation and its target, here taken to be 2%, or 0.02.
The Fed set the federal funds rate well below the level suggested by the Taylor rule in the late
1960s and 1970s, leading to increased inflation.
In the 1980s, the Fed set the federal funds rate above the level suggested by the Taylor rule,
causing inflation to decline.
In the 1990s, the federal funds rate was set fairly close to that suggested by the rule.
In the 2000s, the federal funds rate has mainly been lower than the level suggested by the Taylor
rule.
Page 3 of 6
Numerical problem 3 (part a to c only) (pg. 611)
When the real interest rate increases, banks have an incentive to lend a greater portion of their
deposits, which reduces the reserve–deposit ratio. In particular, suppose that
res = 0.3 – 2r (Eq. 1)
where res is the reserve–deposit ratio and r is the real interest rate. The currency–deposit ratio is 0.4, the
price level is fixed at 1.0, and the monetary base is THB 2000 billion (Thai Baht). The real quantity of
money demanded is
L(Y,i) = 0.3Y – 1000i (Eq. 2)
where Y is real output and i is the nominal interest rate. Inflation and expected inflation in Thailand are
zero (even negative) so assume that the nominal interest rate and the real interest rate are equal.
a.
If r = i = 0.02, what are the reserve–deposit ratio, the money multiplier, and the money supply? For
what real output, Y, does a real interest rate of 0.02 clear the asset market?
First, calculate the reserve-deposit ratio, and since r = i = 0.10, sub this into Eq. 1
res = 0.3 – 2(0.02) = 0.26
Second, calculate the money multiplier, and since we know the multiplier is given by
Multiplier = (cu + 1)/(cu + res)
∴ Multiplier = (0.4 + 1)/(0.4 + 0.26) = 2.12
Third, calculate the money supply, and since we know the money supply is given by
M = Multiplier × BASE
∴ M = 2.12 × 2000 = THB 4242 billion
Finally, to calculate the output level (Y) that clears the asset market based on an interest rate
of 0.20 is done by setting supply of money = the demand for money (note price level is
constant):
𝑴
=𝑳
𝑷
∴
Solving for Y gives:
𝟒𝟐𝟒𝟐
= 𝟎. 𝟑𝒀 − 𝟏𝟎𝟎𝟎(𝟎. 𝟎𝟐)
𝟏
Y = THB 14,207 billion.
b.
Repeat Part (a) for r = i = 0.05.
Repeating the steps above for r = i = 0.05 gives:
▻ res = 0.3 – 2(0.05) = 0.2
▻ Multiplier = (0.4 + 1)/(0.4 + 0.2) = 2.33
▻ Y = THB 15,700 billion
Page 4 of 6
c.
Suppose that the reserve–deposit ratio is fixed at the value you found in Part (a) and isn’t affected
by interest rates. If r = i = 0.05, for what output, Y, does the asset market clear in this case?
▻ In this case the multiplier is unchanged from part (a) at 2.12, so the money supply is
unchanged at 4242.
▻ Setting M/P = L gives 4242/1 = 0.3Y – (1000 × 0.05), which has the solution Y = THB 14,306
billion.
Analytical problem 1 (pg. 612)
How do the following monetary decisions of the Reserve Bank of Australia (RBA) influence your private
life?
a.
A decrease in interest rates.
The interest rates on your savings and loans will decrease. It will be cheaper to take a new
loan, but savings will get less attractive.
The value of the currency will decrease, and hence, traveling to foreign countries will become
more expensive.
b.
An asset purchase program to support struggling member-states.
The economy will recover; new investments will lead to higher employment and economic
growth.
But the government will need fresh money to finance the huge expenses, which could result
in increased taxes.
c.
A target inflation rate of 2%.
As long as inflation is below the target, the interest rates will stay low too
d.
A fixed exchange rate to the U.S. dollar.
The economy will become highly connected to the U.S. It will be easy to plan journeys to the
U.S. without the risk of a changing currency.
e.
An abolishment of cash.
You will be able to make payments only by credit or debit card. All transactions can be
observed easily and a wallet will not be required.
Page 5 of 6
Working with macroeconomic data 𝜶
All data is available through FRED https://fred.stlouisfed.org/. The data identifiers (codes) are provided
below with an underline.
If money demand is unstable, the Fed may prefer to target interest rates rather than the money supply
itself. When the Fed follows an interest-rate-targeting policy, “Fed watchers” in financial markets and the
media typically look to changes in short-term interest rates rather than changes in the money supply to
gauge the Fed’s intentions. Graph the three-month Treasury bill interest rate (i.e., the 3-Month Treasury
Bill: Secondary Market Rate) using TB3MS and the Unemployment rate using UNRATE. Make sure the
data is monthly. If changes in monetary policy are reflected primarily by changes in the short-term interest
rate, what relationship would you expect to see between these two variables? Does this relationship hold
up in the data?
Theory suggests that the short-term interest rate should be negatively related to the
unemployment rate. This is dues to the fact that in periods in which unemployment is high, Fed
lowers the interest rate to reduced unemployment. But Unemployment will react with a lag. So,
for example, if in period t, unemployment is high, Fed will lower the interest rates (high
unemployment, low Interest rate). Thus, the Fed tends to reduce interest rates to engage in
expansionary monetary policy in recessions, when the unemployment rate rises.
In the figure below, and on average, the short-term interest rate appears to be negatively related
to the unemployment rate, as theory suggests.
Page 6 of 6
Week 10 Tutorial Questions (ECF2331)
Ch.13 – Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy
- Review question 3 (pg. 557)
- Review question 5 (pg. 557)
- Numerical problem 𝜶 (not in textbook)
- Working with macroeconomic data 𝜷
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
CH.13 – EXCHANGE RATES, BUSINESS CYCLES, AND
MACROECONOMIC POLICY IN THE OPEN ECONOMY
Review question 3 (pg. 557)
Define purchasing power parity, or PPP. Does PPP work well empirically? Explain.
Purchasing power parity, PPP, is the idea that similar foreign and domestic goods, or baskets of
goods, should have the same price when priced in terms of the same currency.
Purchasing power parity does seem to explain exchange rates in the long run, but over shorter
periods it doesn’t work well because:
▻ Countries produce very different sets of goods,
▻ Some goods aren’t traded internationally
▻ There are transportation costs and legal barriers.
Review question 5 (pg. 557)
Why is the real exchange rate important in macro- economic analysis? How does it affect net exports?
Explain and give one example.
The rate at which goods and services can be traded for those produced abroad is referred to as the
real exchange rate.
The real exchange rate helps determine the demand for domestic goods in domestic and foreign
markets.
Consequently, the real exchange rate has an impact on net exports and on domestic industries that
produce for export or compare with imported goods in the domestic market.
A high real exchange rate will lead to lower net exports (and vice versa):
▻ For example, cosmetics of the same brand and quality cost 50% less in Germany than in
Austria—a country with the same currency.
This means that exports from the Austrian cosmetic industry to Germany are very low, and many
Austrians travel to Germany to buy cosmetics at cheaper prices.
Numerical problem 𝜶 (not in textbook)
Based on the following information:
Desired consumption
Desired investment
Government purchases
Net exports
Real exchange rate
Full-employment output
a.
Cd = 450 + 0.5Y – 300r
Id = 300 – 450r
G = 150
NX = 225 – 0.15Y – 0.75e
e = 30 + 900r
𝑌̅ = 900
What are the equilibrium values of the real interest rate, real exchange rate, consumption, investment,
and net exports?
Begin by writing the equation for the IS curve which is Sd – Id = NX.
First, substitute in all the relevant information:
Sd = Y – Cd – G = Y – (450 + 0.5Y– 300r) – G.
NX = 225 – 0.15Y – 0.75e = 225 – 0.15Y – 0.75(30 + 900r) = 202.5 – 0.15Y – 675r
Using the relation, Sd – Id = NX, and substituting in all the relevant equations, we get:
Sd− Id
NX
(0.5Y – 450 + 300r – G) – (300 – 450r) = 202.5 – 0.15Y – 675r.
Now, rearranging terms (recall we want r as a function of Y) and simplifying gives the IS curve:
1425r = 952.5 – 0.65Y + G.
Equilibrium value of the real interest rate:
We know Y = 900 and G = 100, so sub into IS relation to get:
1425r = 952.5 – 0.65(900) + 150
∴ r = 0.363
Equilibrium value of real exchange rate:
e = 30 + 900r
e = 30 + 900(0.363)
∴ e = 356.7
Equilibrium value of net exports is:
NX = 225 – 0.15Y – 0.75e
NX = 225 – 0.15(900) – 0.75(0.356.7)
∴ NX = -177.525
Equilibrium value of consumption is:
Cd = 450 + 0.5Y – 300r
Cd = 450 + 0.5(900) – 300(0.363)
∴ Cd = 791.1
Equilibrium value of investment is:
Id = 300 – 450r
Id = 300 – 450(0.363)
∴ Id = 136.35
b.
Now suppose that full-employment output decreases to 850. What are the equilibrium values of the
real interest rate, real exchange rate, consumption, investment, and net exports?
̅ = 850, the IS curve gives 1425r = 925.5 – 552.5 + 150 = 550 so r = 0.386.
With 𝒀
Then:
▻
▻
▻
▻
e = 30 + 900r = 390,
NX = 225 – 0.15Y – 0.75e = 225 – 127.5 – 283.05 = –185.55
Cd = 450 + 0.5Y – 300r= 450 + 425 – 120 = 759.2
Id = 300 – 450r = 126.3.
Hence, the reduction in domestic output:
▻ Increases the real interest rate and real exchange rate, and
▻ Decreases net exports, consumption, and investment.
c.
Suppose that full-employment output remains at 850 and that government purchases increase to
200. What are the equilibrium values of the real interest rate, real exchange rate, consumption, investment, and net exports?
•
With G = 200, the IS curve gives 800r = 952.5 – 552.5 + 200 = 615.5, so r = 0.421.
Then:
▻
▻
▻
▻
e = 30 + 900r = 408.9,
NX = 225 – 0.15Y – 0.75e = – 209.18
Cd = 450 + 0.5Y – 300r = 748.7
Id = 300 – 450r = 110.55
Hence, the rise in government spending:
Page 4 of 5
▻ Increases the real interest rate and real exchange rate, and
▻ Decreases net exports, consumption, and investment.
Working with macroeconomic data 𝜷
All data is available through FRED https://fred.stlouisfed.org/. The data identifiers (codes) are provided
below with an underline.
Plot the exchange rate of the Hong Kong dollar relative to the U.S. dollar using EXHKUS from January
1981 to the present. Was the Hong Kong dollar generally appreciating or depreciating relative to the
U.S. dollar between 1981 and late 1983? What happened after 1983? Research and find an
explanation for the value of the exchange rate after 1983.
The Hong Kong dollar was generally depreciating relative to the U.S. dollar between 1981 and
late 1983 from a low of Hong Kong dollars 5.2 per U.S. dollar in 1981 to 8.1 in 1983.
The Hong Kong dollar was neither appreciating nor depreciating relative to the U.S. dollar after
1983 because of a Fixed exchange rate.
In late 1983, Hong Kong adopted a currency board, pegging the value of the Hong Kong dollar to
the U.S. dollar.
Most countries that adopt a fixed exchange rate is because they what to create for certainty in
future international currency trade and to signal that they are committed to low inflation, by
using a fixed exchange rate as a nominal anchor.
Page 5 of 5
Week 11 Tutorial Questions (ECF2331)
Ch.6 – Long-run Economic Growth
- Numerical Problem 2 (pg. 270)
- Numerical Problem 3 (part a only) (pg. 270)
- Numerical Problem 6 (pg. 217)
- Analytical Problem 1 (pg. 271)
- Working with macroeconomic data 𝜶
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 6
CH.6 – LONG-RUN ECONOMIC GROWTH
Numerical Problem 2 (pg. 270)
From one year to the next, a country’s output rose from 4000 to 4500, its capital stock rose from 10,000
to 12,000, and its labor force declined from 2000 to 1750. Suppose 𝑎𝐾 = 0.3 and 𝑎𝑁 = 0.7
a.
How much did capital contribute to economic growth over the year?
Recall, ∆Y/Y = ∆A/A + 𝑎𝐾∆K/K + 𝑎𝑁∆N/N
So, 𝑎𝐾∆K/K = 0.3 × (2000/10,000) = 6%
b.
How much did labor contribute to economic growth over the year?
𝑎𝑁∆N/N = 0.7 × (-250/2000) = – 8.75%
c.
How much did productivity contribute to economic growth over the year?
Rearranging, ∆Y/Y = ∆A/A + 𝑎𝐾∆K/K + 𝑎𝑁∆N/N so that we have productivity growth on the
right-and side gives:
∆A/A = ∆Y/Y – 𝑎𝐾∆K/K – 𝑎𝑁∆N/N
Thus, ∆A/A = 12.5% – 6% – (–8.75%) = 15.25%
Numerical Problem 3 (part a only) (pg. 270)
For Spain, the following capital stock input, K, and labour input, N, were reported for the following four
years:
Year K (billion Euros) N (million persons)
2000
2000
15.5
2005
3000
19.2
2010
4500
18.7
2015
5500
17.8
The stock input and labour input numbers have been rounded off. Suppose that Spain’s production
function is
where Y is total output.
a.
Y = 15K0.3N0.7
Find total output, the capital–labor ratio, and output per worker in each year. Comment on the results.
Can this production function be written in per worker form? If so, write algebraically the per-worker
form of the production function.
Page 2 of 6
To calculate Y, we just use the production function and substitute in the value of K and N
for each year. For example, for year 2000, Y = 15(2000)0.3(15.5)0.7 = 999.154. We do this for
the remaining years to get the following:
Year K (billion Euros) N (million persons) Y = 15K0.3N0.7
2000
2000
15.5
999.154
2005
3000
19.2
1311
2010
4500
18.7
1453
2015
5500
17.8
1491
The capital-labor ratio is calculated as K/N, while output per worker is calculated as Y/N.
Hence, just divide through the values in get the following:
Year K (billion Euros) N (million persons) Y = 15K0.3N0.7
2000
2000
15.5
999
2005
3000
19.2
1311
2010
4500
18.7
1453
2015
5500
17.8
1491
K/N
129
156
241
309
Y/N
64
68
78
84
Comments on the results:
▻ The high growth in capital and labor between 2000 and 2005 results in a high growth
of the GDP (31.2%)
▻ The growth of output is higher than the growth of labor (24%) but much less than the
growth of capital (50%).
▻ The decrease of N between 2005 and 2015 (−7%) is only partially compensated by the
growth of capital (+83%) as Y grows by 14%.
▻ These variations result from the format of the production function where labor has
more weight (0.7) than capital (0.3).
Finally, the production function can be written in per-worker form. First, we divide the
production function through by N (i.e., to get it into per-worker terms), given by:
𝒀
𝑲𝟎.𝟑 𝑵𝟎.𝟕
𝑲 𝟎.𝟑
= 𝟏𝟓
= 𝟏𝟓 ( )
𝑵
𝑵
𝑵
Note, just use the rules of powers here, i.e.,
▻
𝑵𝟎.𝟕
𝑵
𝟏
≡ 𝑵𝟎.𝟕 × 𝑵−𝟏 ≡ 𝑵𝟎.𝟕−𝟏 ≡ 𝑵−𝟎.𝟑 (or 𝑵𝟎.𝟑 )
𝟏
𝑲𝟎.𝟑
𝑲 𝟎.𝟑
▻ So, 𝑲𝟎.𝟑 × 𝑵𝟎.𝟑 = 𝑵𝟎.𝟑 , and since we have the same power, (𝑵)
.
Page 3 of 6
Numerical Problem 6 (pg. 217)
A country has the per-worker production function:
2/3
𝑦𝑡 = 6𝑘𝑡
where 𝑦𝑡 is output per worker and 𝑘𝑡 is the capital-labor ratio. The depreciation rate is 0.1 and the
population growth rate is 0.1. The saving function is:
𝑆𝑡 = 0.1𝑌𝑡
where 𝑆𝑡 is total national saving and 𝑌𝑡 is total output.
a.
What is the steady-state value of capital-labor ratio?
First, get 𝑺𝒕 in per-worker terms (i.e., divide through by 𝑵𝒕 ): 𝒔𝒕 = 0.1𝒚𝒕 .
𝟐/𝟑
Second, we know that: 𝒚𝒕 = 𝒇(𝒌𝒕 ) = 6𝒌𝒕 .
Third, we also know that in steady state: 𝒔𝒇(𝒌𝒕 ) = (𝒏 + 𝒅)𝒌.
Finally, we are dealing with steady-state, the time t drops. Thus:
𝒔𝒇(𝒌) = (𝒏 + 𝒅)𝒌
0.1 × 6𝒌𝟐/𝟑 = (0.1 + 0.1)𝒌
Now we just solve for k:
𝒌𝟐/𝟑 =
𝟏
𝒌
𝟑
𝒌𝟐/𝟑
= 𝟑
𝒌
𝒌𝟐/𝟑 × 𝒌−𝟏 = 𝟑
𝒌(𝟐/𝟑)−(−𝟏) = 𝟑
𝒌(𝟏/𝟑) = 𝟑
∴ 𝒌 = 𝟐𝟕
b.
What is the steady-state value of output per worker?
Since we now know k = 27, and 𝒚 = 6𝒌𝟐/𝟑 , then 𝒚 = 6(27)2/3 = 6 × 9 = 54.
c.
What is the steady-state value of consumption per worker?
Since we know c = y – (n + d)k, then c = 54 – (0.1+ 0.1) × 27 = 48.6.
Page 4 of 6
Analytical Problem 1 (pg. 271)
How would each of the following changes affect the steady-state values of the capital–labor ratio, output
per worker, and consumption per worker? Use the following graph(s) to show the changes:
a.
A change in the composition of the capital stock raises the depreciation rate.
The rise in d reduces the capital-labor ratio, output per worker, and consumption per worker.
b.
A change in social mores lowers the population growth rate.
The decline in n raises the capital-labor ratio, output per worker, and consumption per
worker.
c.
Government tax policies change to encourage a higher saving rate.
The rise in s raises the capital-labor ratio, output per worker, and consumption per worker.
d.
A supply shock reduces productivity sharply.
The decline in productivity shifts the production function down, reducing the capital-labor
ratio, output per worker, and consumption per worker.
Page 5 of 6
Working with macroeconomic data 𝜶
All data is available through FRED https://fred.stlouisfed.org/. The data identifiers (codes) are provided
below with an underline.
In a steady state output, consumption and capital stock per worker are constant. In other words, there is
no productivity growth. Graph the Total Factor Productivity (TFP) for Japan, Australia and China using
RTFPNAJPA632NRUG, RTFPNAAUA632NRUG, and RTFPNACNA632NRUG, respectively over the
period 1960 to 2017. Do you see evidence of convergence to a steady state for some of these countries?
The following figure plots the TFP at constant national prices, Index 2011=1, Not Seasonally
Adjusted) for the three countries. The productivity levels for Japan and Australia follow similar
trajectories over time (albeit with varying degrees of fluctuations). Discussions will vary.
The productivity of Japan has reached a ceiling during the late 1980s and early 1990s, while
Australia reached a ceiling in the early 2000s. This observation is close to the hypothesis of a
steady state.
China’s productivity is somewhat more chaotic over time, especially from 1960 to 1990. Since
1990, China’s productivity has significantly increased and at similar levels to Japan and Australia.
The argument of convergence is more in favor for Japan and Australia as both series seem to
convergence over time. China seems to have converged from 2010 onwards.
Page 6 of 6
Week 12 Tutorial Questions
Special Topic: Financial Crises and the Economy
- Review Question 1
- Review Question 2
- Review Question 3
- Review Question 4
- Review Question 5
- Discussion Question
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
Page 1 of 4
SPECIAL TOPIC: FINANCIAL CRISES AND THE ECONOMY
Review Question 1
How does asymmetric information help us define a financial crisis?
Asymmetric information problems (adverse selection and moral hazard) are always present in
financial transactions but normally do not prevent the financial system from efficiently channeling
funds from lender-savers to borrowers.
During a financial crisis, however, asymmetric information problems intensify to such a degree
that this flow of funds is halted or severely disrupted, with harmful consequences for economic
activity.
Review Question 2
Why is a financial crisis likely to lead to a contraction in economic activity?
The financial system moves funds from savers to households and business firms who borrow
funds to finance productive investment opportunities such as building new homes and
purchasing equipment.
When it works well, the financial system helps the economy to maintain a high level of economic
activity.
A disruption in the financial system, however, increases asymmetric information and the
associated problems of adverse selection and moral hazard.
As these problems spread, the flow of funds from savers to borrowers diminishes, and this
causes economic activity to contract.
Review Question 3
Describe the three factors that commonly imitate financial crises, and explain how each one contributes
to a crisis.
Financial crises can be started by mismanagement of financial liberalization, the bursting of
asset-price bubbles, and increases in uncertainty that accompany major financial institution
failures.
Relaxing restrictions on the activities of financial institutions and innovating new financial
products may lead financial institution managers to engage in new activities and expose them
to risks for which they lack the expertise to manage effectively.
At the same time, government agencies that oversee financial institutions may lack the
resources to monitor the extent of their risk-taking. Losses that arise from these new activities
reduce the net worth of financial institutions and cause them to cut back on their lending, which
thwarts their ability to channel funds to borrowers with profitable investment opportunities.
Page 2 of 4
The bursting of asset-price bubbles may similarly affect financial institutions and also reduces
the net worth of borrowing firms. This increases the moral hazard risks of lending to those
firms, as they now have less to lose from engaging in risky behaviour. Both of these effects
result in less lending.
Finally, the increased uncertainty that occurs when a major financial institution fails increases
both adverse selection and moral hazard problems and leads to a decline in lending and
economic activity.
Review Question 4
The 2008-09 Global Financial Crisis (GFC) originated in the is the U.S mortgage markets. How did it
spread to the rest of the world?
The crisis originated in a relatively small market of the United States, the subprime mortgage
market.
It spread to the rest of the economy through its effects on mortgage-backed securities and the
burst of the housing bubble.
Financial markets across countries are nowadays very much integrated, and this certainly played
a role in the spreading of the crisis.
Additional, psychological and “irrational behavior” (e.g., panic) reasons can also justify the
contagion.
Review Question 5
None of the major central banks across the world responds to asset-price bubbles. Why?
The main reason is probably the fact that it is hard to identify asset bubbles, especially those
caused by excessive optimism.
However, some claim that asset bubbles caused by credit booms are identifiable, and as a result
central banks should promptly act in order to avoid these dangerous bubbles. There is a debate
on this, and economists advocating non-intervention state that monetary policy has little
instruments to target specific markets, i.e., those where asset bubbles are forming.
Therefore, targeting asset bubbles by raising interest rates may prevent the bubbles, but at the
same time it may harm the economy by creating unnecessary distortions.
Page 3 of 4
Discussion Question
Related article:
The Federal Reserve System, “Monetary Policy Report to the Congress, July 2008”:
http://www.federalreserve.gov/monetarypolicy/mpr_20080715_part2.htm.
In this section of the report (Part 2), you can find an exhaustive analysis of the U.S. economy during the
most virulent phase of the 2007–2009 financial crisis.
Discussion Question:
What are the lessons from the 2007–2009 financial crisis about the process of financial innovation?
Answers will vary in this discussion.
Generally, the 2007–2009 financial crisis left many lessons for both financial market participants
and policy makers.
One of them is that the process of financial innovation should be considered as a potentially great
tool (e.g., answering to the needs of both savers and investors) to enhance the efficiency of the
financial system but also as a dangerous process if exploited without enough information.
The securitization process that led to the creation of mortgage backed securities (MBS) is a good
example: It served the needs of both savers and investors for some time, but when financial
institutions decided to issue MBS backed by subprime mortgages, the seeds of the crisis were
planted.
It is quite likely that new financial products will be created in the future; the lesson to derive from
the most recent crisis is that these products should be used carefully, as it will be difficult by
nature (they will be “new” and therefore people will have no experience in pricing them) to assess
their degree of liquidity and risk.
This creates a challenge for financial market participants, but also for policy makers.
Page 4 of 4