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Environmental Economics
ECON3700
Tutorial 4 QUESTIONS
1. Table 1 below contains information on the net benefits of two projects over 4 years.
Table 1: Stream of net benefits for two projects
Net benefits ($) in Year:
1 2 3 4 Total
Project A 20 20 20 20 80
Project B 50 10 10 10 80
2
a. What is the present value of each project assuming a 6% discount rate?
[HINT 1: = ∑
(1+)
=1 ]
[HINT 2: (1 + 0.06)2 = 1.124]
[HINT 3: (1 + 0.06)3 = 1.191]
Project A:
$20 $20 $20 $20
PVA =
1 + 0.06
+
(1 + 0.06)2
+
(1 + 0.06)3
+
(1 + 0.06)4
$20
= +
1.06
$20
+
1.1236
$20
+
1.191
$20
1.262
= 69.30
Project B:
$10 $10 $10 $10
PVB =
1 + 0.06
+
(1 + 0.06)2
+
(1 + 0.06)3
+
(1 + 0.06)4
$50
= +
1.06
$10
+
1.1236
$10
+
1.191
$10
1.262
= 72.39
b. From (a) which project has a higher net present value? Does you answer change
if the discount rate is higher or lower, why/why not?
Project B has a higher net present value. For any positive discount rate Project B
will always be preferred because the net benefits occur sooner than Project A and
the undiscounted net benefits are the same.
2. Table 2 reports likely benefits of costs of three programs on three people with different
incomes. Which of the programs is:
a. Regressive Program 2: Net benefits (difference between benefits and cost) as a
percentage of income are highest for Person C (5%) who has the highest income,
and lowest for Person A with the lowest income (1%).
3
b. Progressive Program 3: Net benefits (difference between benefits and cost) as a
percentage of income are highest for Person A (10%) who has the lowest income,
and lowest for Person C with the highest income (3%).
c. Proportional Program 1: Net benefits (difference between benefits and cost) are
equal to 1% of income for A,B and C.
Table 2: Distributional Impacts of Projects
Income
Person A
5,000
Person B
20,000
Person C
50,000
Program 1
Benefits
150
(3.0)
300
(1.5)
600
(1.2)
Costs 100 (2.0) 100 (0.5) 100 (0.2)
Difference 50 (1.0) 200 (1.0) 500 (1.0)
Program 2
Benefits
150
(3.0)
1,400
(7.0)
5,500
(11.0)
Costs 100 (2.0) 800 (4.0) 3,000 (6.0)
Difference 50 (1.0) 600 (3.0) 2,500 (5.0)
Program 3
Benefits
700
(14.0)
2,200
(11.0)
3,000
(6.0)
Costs 200 (4.0) 1,000 (5.0) 1,500 (3.0)
Difference 500 (10.0) 1,200 (6.0) 1,500 (3.0)
3. Name a revealed preference method for estimating the benefits of environmental policies
and discuss one limitation of this method.
We discussed three methods in Lecture 4:
(a) Travel Cost
(b) Defensive expenditure
(c) Hedonic analysis
Each method differs in the data required for it to be used. A common limitation of
these methods is they can only be used to estimate use values, and they often estimate
a lower bound of willingness-to-pay for environmental quality.