Download problem1_solutions - Agricultural and Resource Economics

Department of Agricultural and Resource Economics
University of California at Berkeley
ENV ECON 1
P. Berck
A. Dey (TA)
INTRODUCTION TO ENVIRONMENTAL ECONOMICS AND POLICY
Problem Set No. 1
(Solutions by Joyce Luh)
Problem 1
1. Demand and supply for milk:
$P
Supply
x
10 —
•
8 —
x
•
6—
• E
4—
x
2 —x
Floor
•
Surplus
|
|
|
20 D 40 60
Q
F
P
x
Demand
•
|
|
|
80 100 120
S
Q
Q
F
The demand curve shows how the quantity that consumers are willing to purchase
varies with the price of milk.
The supply curve shows how the quantities that firms are willing to sell vary with the
price of milk.
2. Equilibrium price = $5.
Equilibrium quantity = 50 units of milk (E).
This point is an equilibrium because, at this price, there is no excess supply or
demand.
3. Price is fixed at $7 (PFloor). At the fixed price, consumers are willing and able to buy
D
S
just 30 units ( QF ) while firms are willing and able to sell 80 units ( QF ). Thus, at the
fixed price, there are 50 units (80 - 30) of surplus production.
4. New demand = old demand + 50 percent = 1.5 x (old demand).
P
Q - new demand
10
8
6
4
2
0
30
60
90
120
$P
Supply
x
$10 —
•
8 —
•
x
•
1
•
6—
E
•x
•
x E0 •
4—
D - new
•
2 —x
•
D - old
|
20
|
|
40 60
|
80
|
|
100 120
Q
The shift in demand results in the new demand schedule and curve plotted above.
The equilibrium price and quantity shifts from E0 to E1 on the graph. The new
equilibrium price increases to about $5.83, and the new equilibrium quantity increases
to about 62.5 units.
While the supply curve has not changed, the eqm quantity supplied has increased
about 12.5 units.
5. The bovine growth hormone will allow firms to profitably produce more milk at all
price levels. Thus, the supply curve will shift out. Assuming that the hormone does
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not alter the quality of the milk produced by cows, demand will not change.
However, the outward shift in supply will lower price and increase both the quantity
supplied and the quantity demanded.
P
S
S
1
..
E
P0
P1
0
E
1
D
Q 0 Q1
Q
Problem 2
1. First, the supply of anchovies shifted in with their disappearance off the coast of Peru.
This caused the equilibrium price to increase dramatically and the quantity demanded
to decrease. Graphically:
$
Supply - post-1972
Supply - pre-1972
P1
P
0
D - anchovies
Q1
Q0
Q - anchovies
2. Because anchovies and soybeans are both rich in protein, they are substitute goods.
Thus, the new higher price in anchovies caused the demand for soybeans to shift out,
increasing both the price and quantity supplied of soybeans. Graphically:
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$
S - soybeans
P1
P0
D - post-1972
D - pre-1972
Q0
Q1
Q - soybeans
3. Because soybeans are an input into the production of cattle (i.e., you need soybeans to
make cows), the supply of cattle in the cattle market shifted in with the increase in the
price of soybeans. The result was higher cattle prices and a lower quantity of cattle
demanded. Graphically:
$
S - post-1972
S - pre-1972
P1
P
0
D - cattle
Q1
Q0
Problem 3
P = 120 - 3Qd
demand
P = 5Qs
supply
In equilibrium, Qs = Qd = Q*, so
P = 120 - 3Q*
P = 5Q*
5Q* = 120 - 3Q*
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Q - cattle
8Q* = 120
Q* = 15.

P = 120 - 3Q* = 120 - 3(15) = 75.
Checking answer: P = 5Q* = 75.
 Equilibrium price = 75cents per pound
Equilibrium quantity = 15 ml pounds.
Problem 4
Suppose that the representative home demander is in the 35 percent income-tax
bracket.
If the governmental subsidy is removed, the effective price of a home increases
25 percent. Demand elasticity = percent change in quantity demanded divided by
percent change in price. Therefore,
%Q
 1.2  %Q  25% 1.2%   30%.
25%
So quantity demanded decreases 30 percent.
(An alternative and perhaps better answer. If the price of housing were 100% before the
reduction, it would be 75% after it. Now on canceling the reduction it goes from .75
to 1.00, a 33% change. Now 33% (1.2) = 39.6 percent.
Problem 5
1. Original P = P0 = $6 per unit.
New P = P1 = $6.06 per unit.
Average P = P = $6.03 per unit.
Original Q = Q0 = $600,000/$6 = 100,000.
New Q = Q1 = $594,000/$6.06 = 98,020.
Average Q = Q = 99,010.
Elasticity based on averages (as in Lipsey and Courant).
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Elasticity of demand = (percent change in Q)/(percent change in P).
Percent change in Q = (98,020 - 100,000)/99,010 = -2 percent.
Percent change in P = (6.06 - 6)/6.03 = 1 percent.
Elasticity of demand = (percent change in Q)/(percent change in P) =
(-2 percent)/(1 percent) = 2.
2. Demand has not changed, so we cannot calculate an elasticity of supply (must have
two points on the same curve to calculate an elasticity).
3.
New equilibrium
S new
En
$6.06
Soriginal
Eo
Old equilibrium
$6
D
Q
90k 100k
Regions
+
= old expenditure = $600 K
Regions
+
= new expenditure = $594 K.
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