1.
Suppose that Portage County Wisconsin’s ground water was contaminated with
nitrates, and that two consumers (C1 and C2) live in this famed “sand county”.
Below are their individual marginal willingness to pay functions (also known as
marginal benefit functions) for a public de-nitrification plant where WTP indicates
marginal willingness to pay for each additional unit of treatment and T indicates the
level of treatment.
Treatment is such that higher levels of treatment increase the
purity of water.
WTP
C1
= 5 – ¼ * T
WTP
C2
= 5 – ½ * T
a.
Create a WTP (or marginal benefit) schedule for each consumer at the following
treatment levels:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 in which the first column is T,
the second column is the WTP for the first consumer, the third column is the WTP for
the second consumer, and the 4
th
and 5
th
columns are identified below.
If your
calculated WTP is less than zero, then assume that WTP is zero.
T
WTP
C1
WTP
C2
WTP
C1+C2
MC
0
5
5
10
0
2
4.5
4
8.5
.5
4
4
3
7
1
6
3.5
2
5.5
1.5
8
3
1
4
2
10
2.5
0
2.5
2.5
12
2
0
2
3
14
1.5
0
1.5
3.5
16
1
0
1
4
18
.5
0
.5
4.5
20
0
0
0
5
b.
In the 4
th
column fill in the aggregate WTP for the two consumers for each treatment
level.
[above]
c.
What is the algebraic (linear) formula for this aggregate WTP curve.
Note that there
may be a kink in the WTP function when WTP
C2
falls to zero, so that your formula
may take the form of “Over the range of T from zero to XX, the WTP function
is ????.
From T=XX to YY, the WTP function is ????”.
Why does this kink occur?
Over the range of T from 0 → 10,
WTP
C1+C2
= 10 – ¾*T
Over the range of T from 10 → 20, WTP
C1+C2
= 5 – ¼*T.
Over this range of T,
WTP
C1+C2
= WTP
C1.
There is a kink in the graph when T=10 and WTP
C1+C2
= 2.5 [at
the point (10,2.5)] because C2’s willingness to pay (WTP) falls to zero.
Since the
aggregate WTP curve is formed by combining the WTP curves of C1 and C2, there
will be a kink when T=10 because C2 is no longer willing to pay, and the aggregate