Problem Set 4
I. Optimal Emissions
The Evul Company’s production process generates a cocktail of greenhouse gases.
The Evul Company estimates its Marginal Net Private Benefit from their production
to be related to these gases as follows: MB = 6 – 0.5 E where E is the volume of GHG
emissions.
The local environmental activist organization estimates the social cost of these GHG
emissions as follows: MC = 1.5 E
What is the Pareto efficient volume of emissions for the Evul Company? (show all
work)
MB = MC
6 – 0.5 E = 1.5 E
6 = 2E
E= 3
II. EXTERNALITY PROBLEM -- ANSWERS
D Curve: P = 12 – Q
MC(private) = 4 + Q
MC(social) = 6 + Q
1. What is equilibrium P and Q at market equilibrium, with externality? Label it
“A” on graph. P = $8, Q = 4 units
12 – Q = 4 + Q; 2Q = 12 – 4; Q = 4
P = 12- 4; P = $8
2. What would equilibrium P and Q be at social optimum, with externality?
Label it “B” on graph. P = $9, Q = 3 units
12 – Q = 6 + Q; 2Q = 12 – 6 ; Q = 3
P = 12 – 3; P = $9
3. What is consumer surplus at market equilibrium without externality? Shade
in area with vertical stripes, and calculate amount. $8
[(12-8) x (4 – 0)]/2 = $ 8
4. What is consumer surplus with externality, at social optimum equilibrium?
Shade in area with horizontal stripes, and calculate amount. $4.50
[(12-9) x (3 – 0)]/2 = $ 4.50
5. Is there a deadweight loss from externality at market equilibrium? If so,
shade the area with diagonal stripes and label it “D”.
yes (area of external cost not benefiting, anyone-- consumers or producers); go
up to social MC from market equilibrium to create base of triangle D
6. What is amount of externality per unit?
$2 (6-4)
(Note: Is there a per unit tax that would cause the market to move to the
socially optimal equilibrium? If so, what is the amount?)
Yes, $2 (Shift S curve up by $2, and will generate social optimum as
equilibrium)
III. Public Good
A county wants to decide how many acres of forest to preserve as a nature preserve.
There are 100 residents in the county, each with a demand function: P = 10 - 1.0 Q,
where Q = number of acres preserved and P = per-acre price he/she is willing to pay
for Q acres of nature preserve. Assume the marginal cost (MC) of the nature
preserve is $500 per acre. How many acres will be preserved in an efficient
allocation? What will the P be at this Q? SHOW ALL WORK BELOW:
Q* = 5, P* = $500
This is a public good (nonexcludable, nonrival), so add the 100 demand
curves vertically. This yields P = 1,000 - 100 Q.
This would intersect the marginal cost (MC) curve where P* = $500, so
solve for Q:
500 = 1,000 - 100 Q
100 Q = 500
Q* = 5 acres will be preserved in an efficient allocation
Some considerations this exercise fails to address?
-value of nature preserve to eco-system services accruing to other
individuals including psychic value and benefits from biodiversity;
-value of nature preserve to future residents including psychic value and
benefits from biodiversity;
-value of nature preserve to non-human species plus earth (existence
value), including biodiversity