Environmental Economics
ECON3700
Tutorial 2 QUESTIONS
1. Consumer A has marginal WTP for apple sauce given by equation 1
MWTPA = 4− 0.8QA (1)
where QA is the quantity of apple sauce that Consumer A currently holds in kg. This
curve is plotted in the solid line in Figure 1.
Figure 1: Consumer A and B Marginal WTP
a. What is Consumer A’s total willingness to pay for 5kg of apple sauce?
You need to calculate the area of the triangle with base 5, height 4.
Area = 0.5* height * base.
= 0.5 * 5 * 4
= 10
b. If the price of apple sauce is $2 per kg, how much apple sauce would Consumer
A want to buy?
The MWTP for 2.5 KG is $2 per kg so if the price is $2 per kg then they will buy
2.5 kg.
2. Consumer B has a demand curve for apple sauce given by equation 2
QB = 7− 1.75P (2)
where QB is the quantity of apple sauce in kg that Consumer B demands at price P .
This curve is plotted in the dashed line in Figure 1.
a. Assume that there are no market failures in the market for apple sauce. Construct
the aggregate marginal willingness-to-pay/ demand curve for the group consisting
of Consumers A and B (you can do this graphically or algebraically).
First, recall that the marginal willingness to pay curve for a private good in a com-
petitive market is just the demand curve, so for Consumer A we can just replace
MWTPA with P .
If you are doing this graphically, remember to add HORIZONTALLY, i.e. at each
price (just pick a few obvious points on the vertical axis), add up the quantities
demanded. The aggregate MWTP curve is shown in 2
If you are doing this algebraically, make sure each demand curve/MWTP curve
has quantity on the left hand side, then substitute into the equation QM = QA+QB
where QM is the market quantity.
We first need to solve for QA as a function of price. From 1:
MWTPA = 4− 0.8QA
QA = 5− 1.25MWTPA
= 5− 1.25P (3)
where the last step comes from recognising that MWTPA = P in a competitive
market with no market failures.
Now we add (3) and (2):
2
Figure 2: Aggregate MWTP/demand curve
QM = QA + QB
= (5− 1.25P ) + (7− 1.75P )
= 12− 3P (4)
b. If the price of apple sauce is $2 per kg, how much apple sauce would be sold in
this market?
At $2 per kg, 6 kg of apple sauce will be bought.
You can read this off the graph in 2 or substitute P = 2 into (4)
c. Suppose the marginal cost of producing apple sauce in this market is constant at
$3 per kg (MC = 3). What is the socially efficient quantity of apple sauce?
The socially efficient rate of output is where MWTP=MC which in a competitive
market is also the intersection of the demand and supply curves. Again, you can
read off the graph or substitute P = 3 in to aggregate demand curve. The socially
efficient quantity is 3 kg of apple sauce (which is also the equilibrium).
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3. Suppose that the following table shows MWTP and MC of apple sauce (i.e. they are
points on continuous curves). Determine the socially efficient quantity of apple sauce.
Show that at any other level, the net benefits to society will be lower than they are at
the efficient level (Question reworked from Chapter 4 of the textbook.)
Output 1 2 3 4 5 6 7 8 9 10
MWTP 20 18 16 14 12 10 8 6 4 2
MC 5 6 7 8 9 10 11 12 13 14
The socially efficient quantity is where MWTP=MC. The curves intersect at an output
of 6 units of apple sauce, so this is the socially efficient quantity of apple sauce.
There are two ways to answer the second part of the question. First, you could calculate
the net benefits at the efficient quantity of apple sauce (total benefits - total costs) then
show that a quantity above or below this has lower net benefits. The second way of
answering the question is the following. Suppose that instead 7 units of output were
produced. Then the last unit of output was produced for a marginal cost of $11, but
the marginal WTP for that unit was only $8, so society would be better off producing
less. Similarly, suppose that 5 units of output were produced. Then it would cost $9
to produce another unit, and the value of that unit is $12, so society would be better
off producing more. At 6 units, MWTP = MC so society cannot do any better by
increasing or decreasing the volume of apple sauce produced.
4. Suppose that the following are points on the demand curve for electricity (in mega
Watt hours (mWh)):
Price Quantity
5 45
10 40
15 35
20 30
25 25
30 20
35 15
40 10
45 5
50 0
Further, suppose that a coal fired generator produces electricity for marginal private
cost of $10/MWh.
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a. Suppose electricity is produced by competitive producers. What price will be
charged and how much electricity will be produced?
In a competitive market the supply curve is given by P = MC and equilibrium is
where demand and supply intersect. At a price of 10/mWh consumers demand
40 so the market will produce Q = 40mWh of electricity.
b. Suppose that smoke is generated in the production of electricity in direct pro-
portion to the amount of electricity generated, and the health damage from the
smoke is $15/mWh generated. What is the name given to this type of market
failure? Illustrate the market failure using a diagram.
Social marginal cost if above private marginal cost so this is an external cost,
otherwise known as a negative externality.
c. What is the socially efficient level of electricity production?
The socially efficient level of production is Q = 25 this is the quantity of electricity
such that SMC = MWTP
5. Suppose you have to decide between two ways of getting to school - driving or catching
the train - and the only difference between these two modes is the time it takes to get
there (i.e. ignore things like whether you can read a book on the train and the cost
of petrol). The train always takes 18 minutes but driving time depends on how many
other cars are on the road according to the information in Table 1.
a. If there are 50 cars on the road would you choose to drive or catch the train?
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Table 1: Traffic and driving travel time
Number of cars* Driving Time
≤ 10 10
11 - 20 10
21-30 10
31-40 11
41-50 12
51-60 14
61-70 18
71-80 24
*Number of cars already on the road (not including you).
If you choose to drive then you will be the 51st car on the road, which will make
the driving time 14 minutes. As this is less than the 18 minutes on the train and
this is the only relevant consideration, you will choose to drive.
b. Is that outcome socially efficient?
No. By adding one additional car to the road the travel time for all the other cars
increases by 2 minutes. So while you save yourself 4 minutes, the other 50 people
on the road now spend an extra 2 minutes each which is a total of 100 minutes. In
aggregate then the cost of commuting has increased by 96 minutes (100 minutes
extra for everyone else and 4 minutes less for you).