Homework 2
Economics 503
Foundations of Economic Analysis
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%.
Explain why, ceteris paribus, we can infer that diamond rings are normal, 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 cross price elasticity of oil with respect to Sport Utility Vehicles is -.1. The
governments of the world agree to a tax on SUV’s which raise the price of SUV’s
world-wide by 10%. Calculate the size of the shift in the demand curve for oil that
results. The short-term price elasticity of demand for oil is -.061. The short-term
price elasticity of supply for oil is .04. Calculate the short-run effect (in % terms)
of the tax increase on the equilibrium price and quantity of oil sold in the world
market in. The long-term price elasticity of demand for oil is .3; the long-term
price elasticity of supply is .35. Calculate the long run % change in the
equilibrium change in the price and quantity caused by this tax.
The cross price elasticity is -.1. This means a 10% rise in the price of SUV’s reduces
demand for oil by -.1*10% = -1%. This shifts demand at any given price level by 1%.
However, a shift down in demand would result in a decline in both price and quantity.
1
 1% . Since the
The change in the equilibrium price is given as by % P*  S
e  eD
supply curve is not shifted, we will experience a movement along the supply curve.
Therefore the changes in equilibrium quantity will be eS * %P* .
In the short run, with eS = .04 and eD = -.061 we would see the price increase by %P*
= -9.9% and the quantity increase by %Q* = -.04*9.9% = - .396%.
In the long run, with eS = .35 and eD = -.3, the long-term price change will be %P*l
1/.65 * -1% = -1.538% and the quantity change will be %Q* = .35*-1.538% = -.538%.
4. Posit a simple demand curve for breakfast cereal of the form Q = 100 - 5P.
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? Calculate the %
change in revenue relative to the % change in prices as the price changes. 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. 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 shortrun 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 $5).
Price
10
15
20
25
30
35
40
45
50
55
60
65
70
Demand
Short-term Long-term
31,060.3 48,317.8
30,301.5 40,259.2
29,774.4 35,370.7
29,371.9 31,991.4
29,047.0 29,471.5
28,775.2 27,496.4
28,541.7 25,892.8
28,337.4 24,556.2
28,155.8 23,419.1
27,992.6 22,435.9
27,844.4 21,574.4
27,708.8 20,811.1
27,583.8 20,128.6
Lower
Supply
Supply
26032.06 27,693.7
26457.7 28,146.5
26763.92 28,472.3
27003.87 28,727.5
27201.53 28,937.8
27369.77 29,116.8
27516.35 29,272.7
27646.3 29,411.0
27763.06 29,535.2
27869.1 29,648.0
27966.27 29,751.3
28055.95 29,846.8
28139.24 29,935.4
Originally, demand is greater than supply whenever the price of oil is lower than $30.
Supply is greater than demand whenever price is above $35. Equilibrium lies between
$30 and $35. After the shock, demand is greater than supply in the short-run
whenever price is below $55. Supply is greater than demand only when price is above
$60. Short-run equilibrium price is between $55 and $60. In the long-run,
equilibrium price is between $35 and $40.