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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.
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.
3.
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.
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).
QD
P
60
70
80
90
100
110
120
130
140
150
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
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
5.
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
25
30
35
40
45
50
6.
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.
Price
Q
R evenue
Elasticity
5
6
7
8
9
10
11
12
13
14
15
;
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.
2.
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).
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.
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).
d. Calculate the GDP deflator as the ratio of the nominal GDP to the real
GDP.
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.
CPI
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
CPI
Inflation
N/A
Nominal
GDP
Real
GDP
GDP
Deflator
GDP Deflator
Inflation
N/A
3.
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
1
Robinho
2 Dimitar Berbatov
3 Andriy Shevchenko
4 Rio Ferdinand:
5
Juan Sebastian Veron:
6
Michael Essien
7
Didier Drogba:
8 Wayne Rooney
9 Shaun Wright-Phillips
10 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
4.
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
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
Frosting
Birthday Cakes
GDP
b. Solve for GDP using the production method
Value Added
Cake Mix
Frosting
Birthday Cakes
GDP
c. Solve for GDP using the income method
Income
Wages
Profit
GDP
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.
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.
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).
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.
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.
b. There is an increase in the wealth of households in the economy of a foreign
trading partner.
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.
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
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 Gap
CPI
Inflation
xxx
107.4 xxx
0.049219808
108.2 0.029795
0.0299929
110.1
0.013160519
107.7
-0.013435423
109.6
-0.063140353
109.5
-0.037229897
109.2
-0.040702363
108.2
Interest Rate
Under
Taylor Rule
xxx
Actual
Interest
Rate
xxx
0.00781
0.00875
0.024375
0.00225
0.00375
0.0013
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%.
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?
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.
ii.
iii.
iv.
Output
Actual
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%
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?
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?
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?
What difficulties did the Bank of Japan have in implementing the Taylor rule
in 1999 and 2000?
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
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
250
$23,608.65
$97,089.53
$222,023.30
$399,276.34
$629,462.71
$913,060.90
$1,250,464.01
$1,642,006.11
$2,087,977.98
$2,588,637.25
300
$19,602.27
$80,613.45
$184,345.99
$331,519.22
$522,642.99
$758,114.63
$1,038,260.49
$1,363,357.96
$1,733,648.48
$2,149,345.96
A.
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?