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Homework 2
Economics 503
Foundations of Economic Analysis
Assigned: Week 2
Due: Week 3
1. 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. 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.
World Coal Market
S′
P
S
D′
D
Q
P
S
World Oil Market
D′
D
Q
3. 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  8P*  40  4 P* 
60  12 P*  P*  5  Q*  100  (8  5)  40  (4  5)  60
In other words, AS = 40, AD = 100, d = 8, s = 4
A D  AS
s
d
P* 
, Q* 
AD 
AS
sd
sd
sd
If AD increases to 124 then
124  8P*  40  4 P* 
84  12 P*  P*  7  Q*  124  (8  7)  40  (4  7)  68
4. 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
Price
Q
8
60
480
9
55
495
10
50
500
11
45
495
12
40
480
13
35
455
14
30
420
15
25
375
%ΔR/%ΔP
Elasticity
0.622642
-0.37931
0.52
-0.48148
0.40107
-0.6
0.261538
-0.73913
0.095477
-0.90476
-0.10553
-1.10526
-0.35385
-1.35294
-0.66845
-1.66667
-1.08
-2.07692
-1.64151
-2.63636
;
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.
5. 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 longrun 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.