Homework 1
Economics 503
Foundations of Economic Analysis
Assigned: Session 2
Due: Session 4
1. Using the demand and supply diagrams (one for each market), show what short-run
changes in price and quantity would be expected in the following markets if chemists
develop a new cheaper method for making jet plane fuel. Each graph should contain the
original and new demand and supply curve, and the original and new equilibrium prices
and quantities. For each market, write one sentence explaining why each curve shifts or
does not shift.
a. The market for air travel. Producers can provide any amount of air travel at a lower
price. The supply curve shifts down. .
S
P
S'
P*
P**
D
Q*
Q**
Q
b. The market for rail travel. Rail travel is a substitute for air travel. As prices of air travel
fall.
P
S
P*
P**
D'
D
Q
Q** Q*
c. The market for hotel rooms at an island resort Hotel rooms at an island resort are
complements.
S
P
P**
P*
D'
D
Q*
Q**
Q
2. Suppose that the demand curve for copper were given by a log-linear demand function
for copper q D  2.75  .03  p and the supply curve were given by a log-linear supply
function q S  2.64  .05  p where q D  ln(Q D ) , q S  ln(Q S ) and p  ln( P) where Q is
measured in millions of tons and P is measured in thousands of US dollars. Solve for the
equilibrium price and quantity level in the copper market. Suppose that the supply shifts
out by 6%, q S  2.70  .05  p and demand shifts out by 5%, q D  2.80  .03  p ; solve for
the new equilibrium price level. Use the mid-point method to calculate the % change in
the price.
q D  2.75  .03  p*  2.64  .05  p*  q S
.11  2.75  2.64  .05  p * .03  p*  .08  p *
p*  11  1.75 
8
q*  2.64  .05  p*  2.64  .55 / 8  2.70875
Solve for the level of P* and Q*, using Excel
Equilbrium
p
1.375 q
P
3.955077 Q
2.70875
15.0105
Originally, a-c = .11. Then, a-c = .1, so Δa-Δc =-.01. Since, p* 
expect the change in equilibrium price level to be p* 
so that p* 
ac
, so we should
bd
a  c
, given that b = .03 and d = .08
bd
a  c
 12.5   a  c   12.5  .01  .125 or approximately -12.5%. So,
.08
solve for
q D  2.8  .03  p*  2.7  .05  p*  q S
p
. Use Excel to get P = P
.1  .08  p * p*  10  1.25
8
= 3.955077 to P1 =3.490343 , so that %P =
( P1  P0 )
3.490343  3.955077
100% 
100%
( P0  P1 )
3.490343  3.955077
2
2
-.46473

100%  .124837  100%  12.4837%
3.72271
1.25
3.490343 , so P goes from P0
3. The accompanying table shows the average daily quantity of postcards sold to tourists at
the airport during each half of 2006 and 2007. Originally, the postcards sold at HK$4
each. However, they were raised to $5 on July 1st, 2006 then raised to $6 on July 1st 2007.
The Airport Authority assumes that the average income of an airport traveler in 2006 was
HK$200,000. They estimate the average income was HK$300,000 in 2007. Assuming
that no other factors affecting the demand for postcards changed (i.e. ceteris parabis)
calculate the price elasticity of demand as prices changes from $4 to $5 and the price
elasticity as prices change from $5 to $6. In both cases, use the mid point method.
Calculate the income elasticity of postcards using the midpoint method.
2006
4000
3000
P=4
P=5
P=6
(Q0  Q1 )
Own price elasticity of demand
(4000  3000)
When P0 = 4.
(5  4)
(4000  3500)
When P0 = 5.
(6  5)
( P1  P0 )
(300000  200000)
( P0  P1 )

1000
1
7000  7  9  1.286
7
1
1
9
9
(5  4)
(4000  3500)

500
(5  6)
Income1  Income0
(4000  3000)
4000
3500
(Q0  Q1 )
(4000  3000)
Q1D  Q0D
Income Elasticity
2007
1
7500  15  11  0.7333
15
1
1
11
11
Q1D  Q0D
when Income0 is 200,000
Income1  Income0
(4000  3000)
(300000  200000)

1000
1
 7  5  0.714
7
100000
1
5
500000
7000
4. The following is a demand table for oil as well as a supply table. Calculate the
equilibrium price in a range of $10. Assume the cross-price elasticity of demand of oil
with respect to the price of coal is 1.5. Is coal a substitute or a complement to oil?
Assume that the price of coal increases by 10%. Calculate the new demand schedule for
oil (you do not need to use the midpoint method) Calculate the new equilibrium.
P
Quantity Supplied Quantity Demanded
60
80,059.86
83,033.06
70
81,303.55
81,762.92
80
82,396.49
80,678.38
90
83,372.72
79,733.70
100
84,255.78
78,898.04
110
85,062.66
78,149.63
120
85,806.03
77,472.59
130
86,495.60
76,854.95
140
87,138.99
76,287.50
150
87,742.26
75,762.98
The equilibrium is between 70 and 80 dollars per barrel. The increase in the price of coal shifts
the demand for oil out by 15%. This means that coal and oil are substitutes. Multiply the
demand curve at every price level by 1.15. At the new demand curve, if the price is 140, there is
excess demand; if the price is 150, there is excess supply. This means that the price goes to a new
equilibrium somewhere between 140 and 150.
P
Quantity Supplied
Quantity Demanded
Quantity Demanded'
60
80,059.86
83,033.06
70
81,303.55
81,762.92
80
82,396.49
80,678.38
90
83,372.72
79,733.70
100
84,255.78
78,898.04
110
85,062.66
78,149.63
120
85,806.03
77,472.59
130
86,495.60
76,854.95
140
87,138.99
76,287.50
95488.02456
94027.35724
92780.14249
91693.76024
90732.74161
89872.07425
89093.47721
88383.19533
87730.62641
150
87,742.26
75,762.98
87127.43083
5. On January 1, 2011, you open up the newspaper and see the 1 year interest rate on US
dollar lending is .1264% ( i = .001264). On the same day, you find 1 year interest rates
on Japanese Yen, Australian dollars and the Euro. You also see the current spot exchange
rate with the US dollar for those three currencies reported as number of currency units
per US$. Use domestic and foreign interest rates, and the current spot rate to calculate the
market’s expectation of the exchange rate on December 31, 2011.
Spot
Interest
Forex
Rate
Rate
US$
0.13%
Japan Yen
0.79%
89.490
Aus. $
4.91% 1.1332729
Euro
0.12% 0.683527
St 1FORECAST
(1  i)
 St 1FORECAST 
St
St
(1  i F )
Since the Japanese Yen has a higher interest rate than the US dollar, the Yen is expected to
drop in value (i.e. the price of US dollars in terms of Yen goes from 89.49 to 90.086). The
Australian dollar has a higher interest rate than the US, so the Aus$ is expected to
depreciate. The Euro Interest rate is slightly lower to that on the dollar and so the currencies
are expected to remain stable in relative value wit the Euro very slightly appreciating.
Uncovered interest parity says (1  i)  (1  i F ) 
Interest
Rate
US$
0.13%
Japan Yen
0.79%
Aus. $
4.91%
Euro
0.12%
Spot
Forex
Rate
Future
Forex
Rate
89.490 90.08648
1.133273 1.187416
0.683527 0.68351
i
iF
0.0013
0.0079 0.0012638
0.0491 0.0012638
0.0012 0.0012638
6. Speculators, both foreign and domestic, believe that domestic interest rates will fall next
year. Draw a graph of the foreign exchange market to show what effect this will have on the
forex rate today.
S
2
S
1
D'
D
FX
The low future interest rates will lead to a weak exchange rate in the future. This will
make the domestic currency less attractive today, reducing demand for US dollars at the
same time that foreign investors will reduce the supply. The exchange rate will depreciate