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AEM 250:
Environmental and Resource Economics
Homework 2 Solution Key
1.
P
C1
C2
C1+C2
0
20
10
30
0.5
18
9
27
1
16
8
24
1.5
14
7
21
2
12
6
18
2.5
10
5
15
3
8
4
12
3.5
6
3
9
4
4
2
6
4.5
2
1
3
5
0
0
0
c.
The algebraic equation for the aggregate demand could be obtained by using the intercept
and slope approach used in answering Q1 from HW 1.
Or, one could add the two
equations, using the logic that if price is held constant, the sum of Q
C1
and Q
C2
will yield
aggregate demand.
Q
C1
=
20 – 4*P
Q
C2
=
10  2*P
Q
Aggregate
=
30 – 6*P
Remember that it is always good to cross check your answer, e.g. 30 – 6*(4) = 6, which
corresponds to the demand scheduled above.
d.
To obtain the marginal benefits equation, simply invert the aggregate demand equation to
get:
P = MB = (( 1/6) * Q) + 5
2.
a. & b.
Create individual producer and aggregate supply schedules.
P
S1
S2
S1+S2
0
0
0
0
0.5
0.5
1.5
2
1
1
3
4
1.5
1.5
4.5
6
2
2
6
8
2.5
2.5
7.5
10
3
3
9
12
3.5
3.5
10.5
14
4
4
12
16
4.5
4.5
13.5
18
5
5
15
20
c.
The algebraic equation for the aggregate supply could be obtained by using the intercept
and slope approach used in answering Q1 above.
Or, one could add the two equations,
using the logic that if price is held constant, the sum of Q
C1
and Q
C2
will yield aggregate
supply.
Q
S1
=
P
Q
S2
=
3*P
Q
Aggregate
=
4*P
Remember that it is always good to cross check your answer, e.g. 4*4 = 16, which
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d.
To obtain the marginal costs equation, simply invert the aggregate supply equation to get:
P = MC = ¼ * Q
3.
a.
To calculate market equilibrium, first set MB = MC and solve for Q*:
10 – (1/3) * Q = ½ * Q
30 – Q = 3/2 Q
→
60 – 2Q = 3Q
→
60 = 5Q
→
Q* = 12
Next plug Q* into MB or MC to find P:
MB = 10 – (1/3 * 12) = 10 – 4 = 6 →
P* = 6
MC = ½ * 12 = 6
→
P* = 6
It’s always a good idea to check both equations to be sure you get the
same answer.
b.
To answer b and c it is perhaps easier to derive the supply and demand curves.
To calculate the supply curve, simply resolve the MC function in terms of Q as a function
of P
MC = ½ * Q
Q
S
= 2P
And similarly for the demand curve simply resolve the MB function in terms of Q as a
function of P.
MB = 10 – (1/3 * Q)
Q
B
= 30 – 3P
If you plug in the prices of $5 and $7 for both supply and demand equations, you can find
the exact quantities supplied and demanded at the specific prices.
If the price was $1.00 below the equilibrium price, the quantity demanded would be
greater than the quantity supplied, resulting in a shortage, or excess demand in the
market.
Some consumers would be willing to pay more to obtain the units they want, and
the price would eventually be pushed upwards until MB = MC.
P = 5
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This homework help was uploaded on 02/01/2009 for the course AEM 2500 taught by Professor Poe,g. during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 POE,G.

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