Homework 1
Economics 503
Foundations of Economic Analysis
Practice
Module 1
1.
Luxury Goods We observe the income of the consumers of diamond rings
increase by 10%. We observe that the equilibrium consumption of diamond rings
goes up by 5%. Assume that nothing else happens to cause a change in the
equilibrium in the diamond ring market. Explain why, we can infer that diamond
rings are normal goods, but why we can’t say if they are income elastic luxury
goods or income inelastic. Use at most 1 paragraph and 1 graph.
If diamond rings are luxury goods, a 10% increase in income of diamond ring
consumers will increase demand for diamond rings by more than 10% at any given
price. If the supply curve is sufficiently inelastic, a shift in demand may lead to a
sufficiently large rise in price such that actual diamonds purchase rises by less than
10%. However, if diamond rings were inferior goods, a rise in relevant income would
result in lower demand at any price level, an effect that might be ameliorated to an
extant by a decline in prices, but not completely offset to the extant that actual
purchases would rise.
S
P
10%
D′
D
<10%
Q
2.
Energy Markets For reasons of safety, the Chinese government orders the
closure of 75% of the coal mines currently operating in the PRC. Draw a graph of
the effect of this on closure on the world coal market. Draw a graph of the effect
of this on the world oil market. Explain your graphs in 1 paragraph or less.
Closing most Chinese coal mines would be a large reduction in supply of coal at any
price level. Coal supply would shift in. This would result in an increase in the equilibrium
price of coal. Coal is a substitute for oil. An increase in the price of a substitute would
cause the demand for oil to increase at any price level. In equilibrium, this would lead to
a rise in the price oil.
P
World Coal Market
S′
S
D′
D
Q
P
S
World Oil Market
D′
D
Q
Equilibrium: Algebra The demand for widgets is represented as QD = 100 – 8 P
and the supply of widgets are given by QS = 40 + 4P. Calculate equilibrium price
and quantity. Calculate the change in equilibrium price and quantity if a shift in
the demand curve gives a demand schedule of QD = 124 – 8 P.
The equilibrium price, P*, set quantity demanded equal to quantity supplied.
100  8 P*  40  4 P* 
60  12 P*  P*  5  Q*  100  (8  5)  40  (4  5)  60
In other words, S0 = 40, D0 = 100, d = 8, s = 4
D  S0
s
d
P*  0
, Q* 
D0 
S0
sd
sd
sd
If AD increases to 124 then
3.
124  8P*  40  4 P* 
84  12 P*  P*  7  Q*  124  (8  7)  40  (4  7)  68
4.
Supply Shift Below are short-term and long-term demand schedules for
petroleum as well as a supply schedule. Assume that the supply schedule is the
same in the long-term and the short-term. Calculate the equilibrium level of price
and quantity for oil in the short and the long term within the range of $10 per
barrel (Hint: the answer is the same for the short-term and the long-term). .
Assume that a conflict in the Middle East permanently reduces the amount of oil
that can be supplied at any price level. After the shock, only 94% of the previous
level is supplied at any price level. Calculate the new supply schedules. Assuming
the short-run and long-run demand curves are unchanged, calculate the new price
of oil in the short-term and in the long-term (within a range of $10).
P
60
70
80
90
100
110
120
130
140
150
QD
QS '
Short-term Long-term
83,033.06
89,314.83
81,762.92
82,689.46
80,678.38
77,348.91
79,733.70
72,925.25
78,898.04
69,182.97
78,149.63
65,963.37
77,472.59
63,155.12
76,854.95
60,677.48
76,287.50
58,470.28
75,762.98
56,487.66
New
75256.27
76425.34
77452.7
78370.35
79200.43
79958.9
80657.67
81305.87
81910.65
82477.73
QS
80,059.86
81,303.55
82,396.49
83,372.72
84,255.78
85,062.66
85,806.03
86,495.60
87,138.99
87,742.26
The new supply curve is calculated by multiplying the old supply curve by .94 at every
price point.
Originally, demand is greater than supply whenever the price of oil is lower than $70.
Supply is greater than demand whenever price is above $80. Equilibrium lies between
$70 and $80. After the shock, demand is greater than supply in the short-run
whenever price is below $90. Supply is greater than demand only when price is above
$100. On the other hand, in the long-term, demand is less than new supply if the price
is above $80. Therefore, the long-run price level is still in the same range that it was
previous to the supply shock.
5.
6.
Equilibrium: Tabular A market faces a demand function of the form
Q D  28  .2  P and a supply function of the form Q S  10  .2  P . Use these
functions to fill out a supply and a demand schedule. Identify the equilibrium
price and quantity.
P
Quantity
Quantity
Demanded
Supplied
20
24
14
25
23
15
30
22
16
35
21
17
40
20
18
45
19
19
50
18
20
Revenue and Elasticity Posit a simple demand curve for breakfast cereal of the
form Q = 100 - 5P where Q is the quantity of breakfast cereal and P is the price
per box. Calculate Q and Revenue (R) at each of the following price points. What
is the price elasticity of demand as we move from price point to price point (use
the mid point method)? What is the price point where revenue is largest? Explain
why raising prices above that point does not increase revenues.
5
75
Revenue
375
6
70
420
7
65
455
8
60
480
9
55
495
10
50
500
11
45
495
12
40
480
13
35
455
Price
Q
14
30
420
15
25
375
%ΔR/%ΔP
Elasticity
0.622642
-0.37931
0.52
-0.481481
0.40107
-0.6
0.261538
-0.73913
0.095477
-0.904762
-0.105528
-1.105263
-0.353846
-1.352941
-0.668449
-1.666667
-1.08
-2.076923
-1.641509
-2.636364
;
At price = 10, revenue is largest. At lower prices, elasticity of demand is less elastic than
-1. This means that a 1% rise in prices results in a less than 1% decline in demand which
means that a price rise will increase revenue. At higher prices, demand becomes more
elastic and raising prices above 10 results in bigger declines in demand offsetting higher
prices and reducing revenue.
Module 2
1. Real Hong Kong Box Office. It is 2004. You are analyzing the profitability of
Hong Kong’s movie industry. You hear that Steven Chao’s Kung Fu Hustle is the
top grossing Hong Kong film of all time. You are given a list of local gross box
office receipts for a number of Hong Kong movies.
1. Kung Fu Hustle
2. Shaolin Soccer
3. First Strike
4. Rumble In The Bronx
5. Infernal Affairs
6. God of Gamblers Return
7. Justice My Foot
8. All's Well, End's Well
9. Thunderbolt
10. Mr. Nice Guy
11. Fight Back to School
12. All for the Winner
13. Drunken Master II
14. God of Cookery
15. God of Gambers II
16. Flirting Scholar
17. All's Well, End's Well 1997
Box Office Revenues
HK$60,830,000
HK$60,770,000
HK$57,519,000
HK$56,911,000
HK$55,030,000
HK$52,540,000
HK$49,880,000
HK$48,990,000
HK$45,650,000
HK$45,420,000
HK$43,830,000
HK$41,330,000
HK$40,970,000
HK$40,860,000
HK$40,340,000
HK$40,170,000
HK$40,160,000
Year
2004
2001
1996
1995
2003
1993
1992
1992
1995
1997
1991
1990
1994
1997
1990
1993
1997
Year
CPI
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
63.5
70.8
77.4
84.0
90.8
98.7
104.6
110.6
113.5
109.8
106.6
104.8
101.4
99.3
99.3
(Source: www.Asianboxoffice.com)
Adjust these for inflation using the Hong Kong CPI. Convert all of these film
grosses into 2004 dollars (i.e. use 2004 as the reference year) and rank the films
by their grosses in 2004 dollars.
Box Officet2004$  Box Officet 
CPI 2004 Box Officet

 99.3
CPI t
CPI t
Ex.
2004$
Box OfficeShaolinSoccer

60, 770, 000t
 99.3
104.8
12. All for the Winner
7. Justice My Foot
15. God of Gambers II
8. All's Well, End's Well
6. God of Gamblers Return
11. Fight Back to School
1. Kung Fu Hustle
2. Shaolin Soccer
4. Rumble In The Bronx
5. Infernal Affairs
3. First Strike
16. Flirting Scholar
9. Thunderbolt
13. Drunken Master II
10. Mr. Nice Guy
14. God of Cookery
17. All's Well, End's Well 1997
2.
N_t in 2004 Prices
HK$64,631,007.9
HK$63,993,333.3
HK$63,082,866.1
HK$62,851,511.6
HK$62,109,785.7
HK$61,473,432.2
HK$60,830,000.0
HK$57,580,734.7
HK$57,256,963.5
HK$55,030,000.0
HK$54,604,557.4
HK$47,486,678.6
HK$45,927,507.6
HK$44,805,297.4
HK$40,779,439.4
HK$36,685,334.5
HK$36,056,853.5
Order
in
Current Dollars
12
7
15
8
6
11
1
2
4
5
3
16
9
13
10
14
17
Order
in
Constant Dollars
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Construct a CPI You are given some statistical accounts for the country of
Fruitopia which produces two goods, Apples and Oranges. The accounts contain
information on the price of apples and the price of oranges for the years 1995 to
2005. You are asked to calculate a CPI, nominal GDP, real GDP and the GDP
deflator using 1995 as the base year. Note that there is no investment, government
spending, exports or imports in Fruitopia so GDP is equal to consumption.
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Apples
price
quantity
$1.00
100
$1.10
105
$1.21
110
$1.33
115
$1.46
120
$1.61
125
$1.77
125
$1.95
130
$2.14
135
$2.36
140
$2.59
145
Oranges
price
quantity
$2.00
100
$2.40
105
$2.88
100
$3.46
100
$4.15
100
$4.98
95
$5.97
90
$7.17
90
$8.60
85
$10.32
80
$12.38
75
a. Calculate the CPI. The representative market basket for the Fruitopian
consumer is 100 apples and 100 oranges. Calculate the cost of this market
basket in 1995. The CPI in subsequent years is the price of this same
market basket (100 apples and 100 oranges) relative to price of that basket
in the base year (multiplied by 100).
100  Pt Apple  100  Pt Orange 100  Pt Apple  100  Pt Orange
CPI t 

Apple
Orange
100  P1995
 100  P1995
300
b. Calculate the nominal GDP which is the sum of the market value of apples
(price × quantity) plus the market value of oranges in each period.
GDPt  Pt APPLE  QtAPPLE  Pt ORANGE  QtORANGE
c. Calculate real GDP which is the sum of the market value of apples
calculated using the 1995 price (1 × quantity of apples) plus the value
oranges calculated using the 1995 price (2 × quantity of oranges).
APPLE
ORANGE
Yt  PBASE
 QtAPPLE  PBASE
 QtORANGE  1 QtAPPLE  2  QtORANGE
d. Calculate the GDP deflator as the ratio of the nominal GDP to the real
GDP.
Pt 
Pt APPLE  QtAPPLE  Pt ORANGE  QtORANGE Pt APPLE  QtAPPLE  PtORANGE  QtORANGE

APPLE
ORANGE
PBASE
 QtAPPLE  PBASE
 QtORANGE
1 QtAPPLE  2  QtORANGE
e. Calculate the average inflation rate over the period of 1996-2005 using
both price measures. Which price index increases the most over time?
Explain. Notice that the market basket has switched toward apples whose
price has not risen sharply over time.
P P
CPI t  CPI t 1
 t  t t 1 100% or
 100%
Pt 1
CPI t 1
CPI
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
100
116.6667
136.3333
159.5667
187.0433
219.5717
258.1176
303.836
358.1074
422.5836
499.2405
CPI
Inflation
16.67%
16.86%
17.04%
17.22%
17.39%
17.56%
17.71%
17.86%
18.00%
18.14%
Nominal Real
GDP
GDP Deflator
GDP
GDP
Deflator
Inflation
$300.00
300
100.00
$367.50
315
116.67
16.67%
$421.10
310
135.84
16.43%
$498.67
315
158.31
16.54%
$590.41
320
184.50
16.55%
$674.09
315
214.00
15.99%
$758.92
305
248.83
16.28%
$898.31
310
289.78
16.46%
$1,020.35
305
334.54
15.45%
Avge
$1,155.68
300
385.23
15.15% Avge
17.44% $1,304.85
295
442.32
14.82%
16.03%
3.
1
2
3
4
5
6
7
8
9
10
Deflate Soccer Transfer Fees In European soccer leagues, teams will acquire
players from other clubs by agreeing to pay a transfer fee. The below table shows
the top 10 transfer fees paid by English Premier League sides along with the fee
paid measured in British pounds and the year of the transfer. Use the
accompanying table with the British CPI to convert all transfer fees to 2008
pounds. Who has the highest transfer fee in constant dollar terms?
Player
Robinho
Dimitar Berbatov
Andriy Shevchenko
Rio Ferdinand:
Juan Sebastian Veron:
Michael Essien
Didier Drogba:
Wayne Rooney
Shaun Wright-Phillips
Fernando Torres:
From:
Real Madrid
Tottenham
AC Milan
Leeds
Lazio
Lyon
Marseille
Everton
Manchester City
Atletico Madrid
To
Manchester City
Manchester United
Chelsea
Manchester United
Manchester United
Chelsea
Chelsea
Manchester United
Chelsea
Liverpool
British CPI
2000
2001
2002
2003
2004
2005
2006
2007
2008
93.7
94.7
96.3
97.5
99.1
101.0
104.0
106.2
109.5
Fee
£32.50m
£30.75m
£30m
£29.1m
£28.1m
£24.43m
£24m
£23m
£21m
£20m
Year
2008
2008
2006
2002
2001
2005
2004
2004
2005
2007
CPI
1 Robinho
Real Madrid
Manchester City
£32.50m
32.5
2008
2
Tottenham
Manchester United
£30.75m
30.75
2008
3 Andriy Shevchenko
AC Milan
Chelsea
£30m
30
2006
4
Leeds
Manchester United
£29.1m
29.1
2002
Lazio
Manchester United
£28.1m
28.1
2001
6 Michael Essien
Lyon
Chelsea
£24.43m
24.43
2005
7 Didier Drogba:
Marseille
Chelsea
£24m
24
2004
8
Everton
Manchester United
£23m
23
2004
Manchester City
Chelsea
£21m
21
2005
Atletico Madrid
Liverpool
£20m
20
2007
Dimitar Berbatov
Rio Ferdinand:
5
Juan Sebastian Veron:
Wayne Rooney
9
Shaun Wright-Phillips
10 Fernando Torres:
CPI_REF ANSWER
109.5
109.5
32.5
109.5
109.5
30.75
104
109.5 31.58653846
96.3
109.5 33.08878505
94.7
109.5 32.49155227
101
109.5
99.1
109.5 26.51866801
99.1
109.5 25.41372351
101
109.5 22.76732673
106.2
109.5 20.62146893
26.4859901
Rio Ferdinand
4.
Cakeland GDP An economy called Cakeland produces three products at three
separate products: cake mix, frosting, and birthday cakes. All of the cake mix and
frosting are sold to the birthday cake company. The cake mix and frosting
companies grow all the inputs they need to make their product; their only expense
is wages. Define profits as the value of sales less wages and cost of inputs. The
following charts outline the activities of each of these firms.
Cost of Inputs
Cake Mix
0
Frosting
0
Wages
$30
$40
Sales
$100
$70
a. Solve for GDP using the expenditure method
Final Expenditure
Cake Mix
0
Frosting
0
Birthday Cakes
400
GDP
400
b. Solve for GDP using the production method
Value Added
Cake Mix
$100
Frosting
$70
Birthday Cakes
$230
GDP
$400
c. Solver for GDP using the income method
Income
Wages
$220
Profit
$180
GDP
$400
Birthday Cake
$100 Cake Mix
$70 Frosting
$150
$400
Module 3
1.
Foreign Exchange Market. Diamonds are discovered in Australia. Foreigners
want to buy these diamonds and need Australian dollars to do so. Assume that this
discovery has no particular effect on Australian demand for foreign goods or assets. Draw
two graphs of the Forex market: 1) Demonstrate the effect on the Australian dollar
exchange rate if Australian monetary policy remains unchanged so the exchange rate is
allowed to fluctuate; 2) Demonstrate the effect on the market if the Reserve Bank of
Australia conducts monetary policy to keep the exchange rate from changing.
Spot
Supply
Supply′
1
Spot*
2
Spot**
Demand
YP
Spot
Supply
Supply′
1
Spot*
3
Spot**
Demand′′
2
Supply′′
Demand
Q
Foreigners need Aussie dollars to buy Aussie diamonds. They will supply more US
dollars to the Oz Forex market, pushing down the price of US dollars in that market. If
the Reserve Bank of Australia cuts the interest rate, then Australians will switch to
US$ increasing demand for US$ and US investors will keep their funds at home reducing
the supply of US dollars in OZ Forex market.
2.
Stock Market Liberalization Consider an economy that operates a floating
exchange rate. The government announces that next year, they will liberalize their stock
market which will make investing in that economy more attractive in the future. Describe
the effect of this announcement on the Forex market this year.
Spot
S´
S
D´
D
1
2
Forex
Turnover
If there is a liberalization of the stock market next year, then future foreign investors will
want to acquire domestic dollars then and future domestic investors are likely to keep
their funds at home. This means that the demand vs. supply conditions in the Forex
market will lead to a valuable domestic currency. But a strong currency in the future
would make investing in the domestic bank accounts today relatively attractive, which
will increase the supply of foreign funds to the domestic forex market today and reduce
demand for foreign dollars by domestic investors today. This will cause the domestic
currency to appreciate today.
3.
Currency Board During much of the 1990’s, the South American country of
Argentina implemented a currency board system similar to Hong Kong with the
Argentine peso being fixed 1-to-1 with the US dollar. In January 2002, the Central Bank
of Argentina abandoned the currency peg. Below are interest rates for the US dollar and
money market interest rates for the Argentine Peso from 1995 to 2001.
1996
1997
1998
1999
2000
2001
Peso
US Dollar
Interest
Interest
Rate
Rate
6.23
5.14
6.63
5.2
6.81
4.9
6.99
4.77
8.15
6
24.9
3.48
Calculate the expected exchange rate depreciation in every year (assuming that interest
parity is true).
1996
1997
1998
1999
2000
2001
Peso
US Dollar Expected
Interest
Interest
Depreciation
Rate
Rate
Rate
Alternative1
6.23
5.14
1.09
1.04%
6.63
5.2
1.43
1.36%
6.81
4.9
1.91
1.82%
6.99
4.77
2.22
2.12%
8.15
6
2.15
2.03%
24.9
3.48
21.42
20.70%
Calculate the expected exchange rate depreciation in every year (assuming that interest
parity is true).
Spott 1  Spott
Spott 1  Spott
it  itF 

 it  itF
Spott
Spott
An alternative estimate might be derived directly using
Spott 1
Spott 1  Spott 1  it
1  it 
1  itF  

1

Spott
Spott
1  itF
Module 4
1. Loanable Funds Market Some economists argue that the savings behavior is not
very responsive to the interest rate. Other economists argue that savings is
strongly affected by the interest rate. Use the loanable funds framework for a
large, closed economy. Compare the effect of expansionary fiscal policy (i.e. an
increase in government deficits) on the interest rate and investment in A) an
economy in which the supply of loanable funds (S) was inelastic with respect to
the interest rate; with the effect in B) an economy in which the supply of loanable
funds is very elastic. Draw a graph of each theory to show under which theory
there is a bigger impact on investment and under which theory there is a bigger
impact on the interest rate.
Expansionary fiscal policy, a cut in taxes or an increase in spending, leads to an
increase in the budget deficit. There is a shift out in demand for loanable funds. This
leads to excess demand and upward pressure on interest rates. If supply of loanable
funds is very interest elastic, the higher interest rates will attract much more supply
of loanable funds, and the equilibrium impact will mostly result in higher loanable
funds and slightly higher interest rates. If supply is not interest elastic, the upward
pressure on interest rates will mostly crowd out private sector demand for loanable
funds. The equilibrium impact will be a much higher interest rate and only a little
extra loanable funds.
r
SLF1
B2
r
B1
r
SLF2
A
D'
D
Loanable Funds
Module 5
1. Using aggregate demand, short-run aggregate supply and long-run aggregate
supply curves, explain the process by which each of the following economic
events will move the economy from one long-run macroeconomic equilibrium to
another. Illustrate with diagrams. In each case, what are the short-run and longrun effects on the aggregate price level and aggregate output?
a. There is a decrease in households’ wealth due to a decline in the stock market.
The model starts at point 1. Household consumption drops as wealth declines. This
decreases spending at any given price level (the AD curve shifts in) and reduces the
prices they are willing to pay for goods. The falling price level along the supply curve
reduces firms willingness to produce goods and output declines in equilibrium.
Equilibrium price and output drop to point 2. The relatively low demand for labor in
the recession will put downward pressure on the nominal wage rate. The falling cost
of production reduces the prices that firms demand for their production (i.e the SRAS
curve shifts down). Wages will fall until the labor market equilibrium return relative
wages to their long-term levels. The new long run equilibrium will be at point 3.
SRAS
LRAS
P
SRAS´
1
2
3
AD
AD´
Y
YP
b. There is an increase in the wealth of households in the economy of a foreign
trading partner.
The economy begins at point 1. When foreign households have more wealth, they
increase spending. This shifts out demand for domestic goods. The higher prices of
goods along the supply curve increases production. The new equilibrium is at point 2.
When firms are producing a lot of output, labor demand is high. Wages feel upward
pressure, raising costs. The costs of production are passed along to customers which
in turn reduces equilibrium demand. Eventually, wages rise far enough that the
excess demand for labor is in equilibrium and the economy returns to potential output
at point 3.
LRAS
P
SRAS
3
2
SRAS´
1
AD´
AD
Y
YP
2. In 2005, a hurricane hit New Orleans, Louisiana, an important transportation and
oil refining center in the USA, one of Hong Kong’s key for the petrochemical
industry in that country.
a. Consider the impact of the recent hurricanes that devastated that city as a temporary
supply shock for the USA. Discuss briefly, using one graph, the outcomes that we
would have been likely to see in terms of goods markets in the USA as a result of
this negative business cycle shock.
With the refineries knocked out, the price of oil would rise. With firms energy costs rising,
the price level charged by firms at every level of production would rise. The rising price
levels would dampen consumption and hurt export competiveness and the equilibrium
quantity would fall and prices rise.
P
SRAS
2
SRAS´
1
AD
Y
b.
Analysts are also worried that the natural disaster might have had a negative
impact on consumer confidence. Discuss briefly, using one graph, the differences in
outcomes that we would observe if this demand side effect were stronger from the
outcomes that we would observe if the supply side effects were dominant.
YP
SRAS
P
1
P**
2
AD
´
AD
Y
A decline in consumer confidence would reduce the demand for consumer goods
at any level of prices. This would shrink demand at any price level. If this effect
were dominant the price level would fall.
Module 6
1. The Liquidity Crisis and the Taylor Rule in Hong Kong. You are given the
following Table listing the output gap, the CPI and the overnight HIBOR Rate in
Hong Kong.
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
Output GapCPI
xxx
0.04922
0.029993
0.013161
-0.013435
-0.06314
-0.03723
-0.040702
107.4
108.2
110.1
107.7
109.6
109.5
109.2
108.2
Inflation
xxx
0.029795
0.07024
-0.08719
0.070566
-0.00365
-0.01096
-0.03663
Interest Rate
Actual
Under
Interest
Taylor RuleRate
xxx
xxx
0.084303
0.00781
0.135357
0.00875
-0.10921 0.024375
0.114132
0.00225
-0.02204
0.00375
-0.02005
0.0013
-0.0603
0.0013
a. For each quarter, construct the inflation rate on an annual basis. This is obtained just
P  Pt 1
by constructing the % growth rate of the price that occurs in a given quarter t
Pt 1
and then multiplying the result by 4. An example is constructed in the Table for the
1st Quarter of 2008..
b. Construct a hypothetical interest rate for HK with the Taylor rule using the CPI
inflation. CPI data and an assumption of an inflation target of 2%.
TAYLOR
it
 .025   t  1 2  t  .02  1 2  Output Gapt 
c. Compare the interest rate with that observed in HK. Note that the interest rate has
been below 1% in every quarter except the 2008Q3. Has the interest rate been higher
or lower in HK than that suggested by the Taylor rule?
During the inflationary period during the beginning of 2008, the Taylor rule would
suggest raising interest rates far above those actually observed during that period.
During recessionary later periods, the Taylor rule would have suggested cutting interest
rates. However, these low interest rates would have even been negative which is
impossible in the market place.
2. Does the BOJ have a Taylor Rule? The following table shows numbers for
Japan’s inflation rate, output gap, and the uncollateralized call money interest rate
for the years 1990 to 2000.
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
i.
Output
Actual Target
Gap
Inflation
Interest Rate
3.30%
3.02%
7.56%
4.09%
3.22%
7.48%
2.50%
1.70%
4.82%
0.51%
1.26%
3.18%
-0.87%
0.69%
2.41%
-1.20%
-0.12%
1.15%
2.14%
0.13%
0.48%
2.32%
1.75%
0.52%
-1.48%
0.67%
0.44%
-2.46%
-0.33%
0.06%
-2.57%
-0.71%
0.12%
Inflation
Gap
1.02%
1.22%
-0.30%
-0.74%
-1.31%
-2.12%
-1.87%
-0.25%
-1.33%
-2.33%
-2.71%
Taylor
Rule
7.68%
8.37%
5.30%
3.65%
2.10%
0.71%
2.77%
5.28%
1.76%
-0.23%
-0.86%
Calculate the inflation gap (i.e. the difference between inflation and target
inflation) in each period if Japan had used a target inflation rate of 2% in each
year. What is the average inflation gap during the period 1990-1995
(inclusive) and for 1996-2000?
Average Inflation Gap
90-95
-0.37%
96-00
-1.70%
Calculate the interest target, iTGT, for every period if the Bank of Japan had
used a Taylor rule as specified in class. Compare this with the actual interest
rate. Does the Bank of Japan adjust the target interest rate to domestic
inflation and output?
As inflation has fallen below the target, the central bank has also cut the interest rate.
ii.
iii.
Some have argued that the BOJ was not aggressive enough in cutting interest
rates in the early 1990’s to get the economy out of the slump. What was the
average interest rate during the period 1992-1997? What was the average
interest rate suggested by a Fed-style Taylor rule. Which was larger?
Actual
Implied
Average Interest Target
2.09%
3.30%
During the onset of the recession, the Japanese interest rate target seemed to be
on average lower than that implied by the target. In 1992 and 1993, the interest
rate was slightly above the implied rate.
iv.
What difficulties did the Bank of Japan have in implementing the Taylor rule
in 1999 and 2000?
By 2000, the interest rate had reached a zero lower bound. Even if the Taylor rule
suggests cutting rates, the BoJ cannot.
Module 7
1. Costs of Running a Factory You examine the production of an auto-parts
factory which uses labor, materials and capital machinery referred to as a die
press to produce goods. To start producing any goods, the factory has sunk set-up
costs of $25,000 per year. Up to 300 die presses can be installed in the factory in
increments of 50. The costs of owning and using a die press (including
depreciation and financing costs) in a given year are $5,000 per press. Therefore,
fixed costs are $25,000 plus $5000 times the number of die presses used. Die
presses are varied in increments of 50. In addition, producing goods requires some
variable inputs including materials, energy, and labor. Producing each good
requires material and energy costs of $20 per unit. For various reasons, production
can only be done in batches of 10,000 units. The following Table 1 reports the
variable labor costs of producing different levels of output at different levels of
die-press usage.
Table 1. Variable Labor Costs at the Auto Parts Factory
Production
Level
A.
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
50
$121,904.74
$501,327.80
$1,146,431.10
$2,061,688.19
$3,250,269.77
$4,714,646.67
$6,456,848.58
$8,478,600.52
$10,781,403.97
$13,366,589.17
# of Die Presses
100
150
$60,113.22
$39,751.81
$247,212.94
$163,477.55
$565,323.92
$373,838.72
$1,016,652.16
$672,294.10
$1,602,761.17 $1,059,877.64
$2,324,869.37 $1,537,395.02
$3,183,977.62 $2,105,508.13
$4,180,936.56 $2,764,779.45
$5,316,486.60 $3,515,698.63
$6,591,283.69 $4,358,699.41
200
$29,642.81
$121,904.74
$278,770.47
$501,327.80
$790,347.74
$1,146,431.10
$1,570,071.43
$2,061,688.19
$2,621,646.48
$3,250,269.77
Short-run The factory has set up 100 die presses. Fill in the Table 2 cost
chart for the firm in the short term. Calculate the marginal cost for each
level of production as the cost of producing one more batch (i.e. the cost
of producing another 10,000).
B.
Long-run Now assume that the factory managers can vary the number of
die presses. Calculate the average total cost function for each level of
production for each # of die presses. For each quantity of die-presses,
calculate the minimum average cost. For each level of production,
calculate the minimum average cost and the number of die presses that
would generate the lowest average total cost. Draw a diagram of those
minimum points. Over what range is the firm operating according to
increasing returns to scale? Over what range is the firm operating over
decreasing returns to scale? What is the minimum efficient scale (i.e. what
scale of production will result in the lowest overall level average total cost
when we can vary energy, workers, and # of die presses)? At what number
of die-presses is that minimum achieved?
2
$23,608
$97,089
$222,023
$399,276
$629,462
$913,060
$1,250,464
$1,642,006
$2,087,977
$2,588,637
For each quantity of die-presses, calculate the minimum average cost.
Die Presses
50
100
150
200
250
30
Minimum
ATC
Production
58.82047
10000
56.34413
30000
56.18235
40000
56.19052
60000
56.07806
70000
56.10447
80000
For each level of production, calculate the minimum average cost and the number
of die presses that would generate the lowest average total cost.
Minimum
Scale
ATC
Die Presses
10000 59.69047
50
Returns
to Scale
Increasing
20000 58.61065
100
30000 56.34413
100
Increasing
Roughly Constant
40000 56.18235
150
Roughly Constant
50000 56.30695
200
60000 56.19052
200
70000 56.07806
250
Roughly Constant
Roughly Constant
Roughly Constant
80000 56.10447
300
Roughly Constant
90000 56.20721
300
Decreasing
100000 56.74346
300
Draw a diagram of those minimum points. Over what range is the firm operating
according to increasing returns to scale? Over what range is the firm operating over
decreasing returns to scale?
What is the minimum efficient scale (i.e. what scale of production will result in
the lowest overall level average total cost when we can vary energy, workers, and
# of die presses)? At what number of die-presses is that minimum achieved?
I think two answers are acceptable here. Firs, the lowest scale of production at which the
firm achieves a constant returns to scale at an ATC just a bit more than 56 is 30000
with 100 die presses. On the other hand, the true minimum cost is achieved at 70,000
scale with 250 die presses
Table 2: Cost Chart: 100 Die Presses
# of Die Presses
TFC
TVC
TC
10000 $525,000.00
$260,113.22
$785,113.22
20000 $525,000.00
$647,212.94
$1,172,212.94
Production
30000 $525,000.00
$1,165,323.92
$1,690,323.92
Level
40000 $525,000.00
$1,816,652.16
$2,341,652.16
50000 $525,000.00
$2,602,761.17
$3,127,761.17
60000 $525,000.00
$3,524,869.37
$4,049,869.37
70000 $525,000.00
$4,583,977.62
$5,108,977.62
80000 $525,000.00
$5,780,936.56
$6,305,936.56
90000 $525,000.00
$7,116,486.60
$7,641,486.60
100000 $525,000.00
$8,591,283.69
$9,116,283.69
AFC
AVC
ATC
MC
$52.50
$26.01
$78.51
38.70997
$26.25
$32.36
$58.61
51.8111
$17.50
$38.84
$56.34
65.13282
$13.13
$45.42
$58.54
78.6109
$10.50
$52.06
$62.56
92.21082
$8.75
$58.75
$67.50
105.9108
$7.50
$65.49
$72.99
119.6959
$6.56
$72.26
$78.82
133.555
$5.83
$79.07
$84.91
147.4797
$5.25
$85.91
$91.16
Table 3. Average Total Costs at the Auto Parts Factory
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
.
50
$59.69
$58.82
$67.38
$78.42
$90.51
$103.16
$116.17
$129.42
$142.85
$156.42
100
$78.51
$58.61
$56.34
$58.54
$62.56
$67.50
$72.99
$78.82
$84.91
$91.16
150
$101.48
$66.92
$58.29
$56.18
$56.70
$58.54
$61.15
$64.25
$67.67
$71.34
200
$125.46
$77.35
$63.46
$58.16
$56.31
$56.19
$57.07
$58.58
$60.52
$62.75
250
$149.86
$88.60
$69.90
$61.86
$58.09
$56.47
$56.08
$56.46
$57.37
$58.64
30
$174.46
$100.28
$76.98
$66.41
$60.95
$58.05
$56.62
$56.10
$56.21
$56.74