Department of Agricultural and Resource Economics
University of California at Berkeley
EEP1/ECON3
P.Berck
Introduction to Environmental Economics and Policy
Problem Set 5, 2009
Due: Nov 24th
(Luosha, Du and Koichiro Ito)
Total: 21 points
Question 1 (Ch. 11 Exercise Q1) [8 points]
Buchanan Industries receives profits from polluting according to the formula Profits = π = 10Q – Q2, where
Q = pollution emitted (in tons), and profits are measured in dollars. Marginal benefits (MB) of polluting,
derived from this function, are MB = 10 – 2Q. The damages associated with pollution from this facility are
estimated as Damages = D = Q2 + 2Q, where damages are measured in dollars. The marginal damages (costs)
associated with that function are MD = 2Q + 2.
a. [1 point] Draw a graph with the marginal benefits and marginal damage curves. Be sure to label the axes.
$
10
MB
MD
2
0
5
Q
b. [1 point] If Buchanan Industries could ignore the damages it caused, how much Q would it produce?
How much profit would it earn at this level of production? How much would total damages be? What
would be the net benefits, the difference between profits and damages?
If Buchanan can ignore the environmental damages, the pollution level is determined by rule of profit
maximization. Set MB=0, we have 10-2Q=0. Therefore, Q=5, 5 tons of pollution generated. Plug Q=5
into profit function and damage function respectively, we get = 25 and D = 35. And the net benefit
given Q=5 is the difference between profit and damage, which is negative10.
c. [1 point] What is the efficient Q for this industry? How much profit would Buchanan Industries earn at
this level of production? How much would total damages be? What would be the net benefits, the
difference between profits and damages?
Here, we set MB equal to MD to get the efficient Q for the industry. MB = MD, which gives us 10 – 2Q
= 2Q + 2. Therefore, Q=2, which is the intersection between two curves. Again, plug Q=2 into profit
and damage functions, we get = 16 and D = 8. Thus, the net benefit in this case is positive 8.
d. [2 points] Deadweight loss is the difference between the net benefits with the efficient level of pollution
and net benefits with another level of pollution. What is the deadweight loss associated with Buchanan
Industries ignoring damages that its production causes? Show the deadweight loss on your diagram. If
Buchanan Industries would not on its own produce at the efficient Q, is it acting contrary to its own best
interests by producing at the level in (c)?
$
10
MB
MD
Deadweight
Loss
6
0
1
2
Efficient
production
level
5
Q
Production
level in (a)
The deadweight loss = Net Benefits (Q*) – Net Benefits (Q) = 8 – (-10) = 18. Graphically it is the yellow
triangle. Either the mathematical or graphical answer is sufficient. From the production level of 5 to the
level of 2, the industry losses some amount of benefits (represented the blue triangle) and it saves a lot
more costs (the sum of yellow and blue triangles). Blue triangle gets to be canceled out, left yellow
triangle as the deadweight loss. If the industry produces at the efficient level, it is contrary to its own best
interests because producer’s goal is to maximize its profit.
Note: Because the wording of the question is a little unclear about the last part, either of the following
answer is acceptable:
1. If the industry produces the efficient level of output Q*, it is acting contrary to its own best interest
because their objective is to maximize their profit.
2. If the industry produces Q = 5, it is not acting contrary to its own best interest because their objective is
to maximize their profit.
e. [2 points] Those who live near Buchanan Industries propose that Buchanan Industries produce no more
than Q = 1. What is the deadweight loss associated with this level of production? If Q = 1 is an
inefficient level of production, are those who live near the factory acting contrary to their own best
interests by pushing for Q = 1?
$
10
MB
MD
Deadweight
loss
0
1
Production
level in (d)
5
2
Q
Efficient
production
level
By the same reason as part d), the deadweight loss = 8 – 6 = 2. It is the green triangle. Either the
mathematical or graphical answer is sufficient. If Q=1 is the level of production rather than the efficient
level, people who live near the factory follow their best interests because they want less pollution and a
better environment.
f. [1 point] Who benefits from reducing Q from the initial level in (b) to the efficient level in (c)? Who
bears the costs? Is this change Pareto improving?
The residents will benefit from the pollution reduction and the producers will bear the costs. This is not
Pareto improving since only one part gets better off and the other party gets worse off.
Question 2 [6 points]
A monopolist has the following total cost and demand schedules:
Exact
P
Q
TC
TR
MR
MC
Profit
MR
8
5
20
40
2
1
20
3
7
6
21
42
0
1
21
1
6
7
22
42
-2
1
20
-1
5
8
23
40
-4
1
17
-3
4
9
24
36
-6
6
12
-5
3
10
30
30
0
a. [2 points] Determine the monopolist's total revenue for each level of output. On the upper axis (provided
on the next page), plot both total revenue (TR) and total cost (TC).
TR = P*Q – TC. Look at the table and following diagram.
b. [2 points] Determine the marginal revenue (MR) and marginal cost (MC) for each level of output. On the
lower axis, plot MR, MC, and the demand curve.
You can get a full credit using any of the following three definitions for MR.
1. MR(Q) = TR(Q+1) – TR(Q)
2. MR(Q) = TR(Q) – TR(Q-1)
3. Exact MR(Q) = 13-2*Q calculated by using calculus
The table and diagram show the first and third ones. The three definitions produce a slightly different value
because the first and second ones use approximation. You can draw the demand curve simply by using the
combinations of price and quantity in the table.
c. [2 points] What level of output will a profit-maximizing monopolist choose to produce? What price will
he/she charge?
Based on the profit for each quantity in the table, the monopolist can get the maximum profit, 21 when she
produces 6 units and charges the price, 7. Note that MC is equal to Exact MR at Q = 6, although this is not
true for the approximate MR due to its approximation, so you probably do not want to use the condition, MC
= approximate MR to find the profit maximizing Q. Although it is not quite right, you can get a full credit if
you use MC = approximate MR to find the profit maximizing price and quantity. In that case, the profit
maximizing Q is between 5 and 6, and the corresponding P is between 7 and 8.
45
40
35
30
25
20
15
10
5
0
5
6
7
8
9
Q
TC
TR
10
10
8
6
4
2
0
5
6
7
8
9
1
-2
-4
-6
-8
Q
MC
MR
E xact M R
Demand
Notes for the diagrams:
1. You don’t need to draw the exact MR to get a full credit. .
2. The graph of MC and MR can be different if you use the alternative definition.
Question 3 (Ch. 12 Exercise Q1) [7 points]
A builder proposes a skyscraper that would block sunlight to the neighboring houses. The building would
have net benefits to the builder of $100,000. The neighbors, who use some solar heating, would face reduced
property values and increased heating costs totaling $80,000.
a. [2 points] The law clearly stipulates that the neighbors have the right to solar access. Is a
Pareto-improving exchange possible? What do you expect the outcome to be?
Yes, there will be a Pareto-improving exchange. Since the neighbors have the right to solar access and
the total costs resulted from building a skyscraper is less than the net benefit, the builder will pay
neighbors amount of money (will be at least $80,000 but below $100,000). Thus, in short, the likely
outcome is “exchange” and “build the skyscraper”.
b. [1 point] How, if at all, would the outcome be different if the builder had the right to construct the
skyscraper, even if it blocked solar access?
Yes, the outcome will be different if the builder has the right. The outcome will be, the builder builds the
skyscraper and gets the benefit, and neighbors bear the increased heating cost (“build” but “no
exchange”).
c. [2 points] Suppose again that the neighbors have the rights. Because there is a large number of neighbors,
hiring an attorney to negotiate with all of them will be expensive, perhaps as much as $25,000. Is a
Pareto-improving exchange possible? What do you expect the outcome to be?
The total costs of compensating neighbors are the sum of negotiation fee and the increased heating cost
that is $105,000, which is higher than the net benefit of building the skyscraper. Therefore, the outcome
will be “no exchange” and “no build”. Everything will stay the same as before.
d. [2 points] Now suppose that the builder has the rights, and the costs of the lawyer (still $25,000) belong
to the neighbors. Is a Pareto-improving exchange possible? What do you expect the outcome to be?
Compare this scenario with those of the other parts of this problem. What has led to these different
outcomes?
If the builder has the right, neighbors need to hire a lawyer to negotiate with the builder and also pay an
amount of money which is at least equal to the net benefit of building the skyscraper to convince the
builder not to build. The total cost that neighbors bear is $105,000, which is greater than the potential
increased heating cost. Therefore, the outcome is “no exchange” and “build”, same as (b).
There are two factors leading to these different outcomes: 1) who has the right; 2) whether transaction
is low enough to make the exchange of the right possible.