Lind on Measuring Benefits
© Allen C. Goodman, 2002
Suppose
• We have 2 types of land, half
polluted (p), half not (u).
• Pp = 100; Pu = 200
• If a program of air pollution
control equalizes productivity
everywhere, rent may end up
at 150.
• If so total property values
remain same.
• Does this mean there were no
benefits?
Analysis
• Assume class of programs w/ output specific to particular
locations.
• How do we measure benefits?
• Two major findings
– Benefits of a project can be approximating by measuring net
increase in profits of activities located on land directly affected by
project.
– W/ zero profits, total change in productivity equals change in land
values.
Analysis
aij = maximum rent ind. i would pay for parcel j.
Alternatively:
aij = Net earnings of firm i at parcel j exclusive of land cost.
n activities, n parcels
pj = rental value of parcel j.
Activity locates at parcel j ONLY IF:
(2.3) aij  pj AND
(2.4) aij - pj  aik - pk
Analysis
Define consumer surplus (or profit) as sij.
sij aij – pj.
SO, the total benefit from land is
(2.5) aij = sij + pj
Land is ENHANCED if there is some aij > aij for some
parcels, and aij = ij for the rest.
Let:
A = ajj
(2.7) A a jp(j)
(2.8) A - a jp(j)- a j j
Analysis
(2.5) aij = sij + pj
Let:
A = ajj
(2.7) A a jp(j)
(2.8) A - a jp(j)- a j j
From (2.5)
(2.9) A - s  jp(j) - s j j ) + p  j - pj)
What does this mean?
Change in total land values = change in productivity ONLY if
surplus terms = 0, or surplus terms don’t change!
Essentially an open city argument.
Benefit Measurement
Lind shows that any cycle of relocation NOT involving a
parcel of land affected by the project will leave net
productivity unchanged. We need to consider ONLY
parcels that are directly affected, where land is improved.
Benefits can be measured by considering in surplus of those
activities alone that move onto improved land.
Suppose we have 3 unimproved parcels
Din productivity = [a12 – a11] + [a23 – a22] + [a31 – a33]
Since there is no improvement,
Din productivity = [a12 – a11] + [a23 – a22] + [a31 – a33]
From the equilibrium conditions:
(2.3) aij  pj AND
(2.4) aij - pj  aik - pk
[ajj+1 – ajj]  p  j+1 – p  j
New rents
AND
[ag1 – p 1]  [agg – p g]
Suppose we have 3 unimproved parcels
[ajj+1 – ajj]  p  j+1 – p  j
AND
[ag1 – p 1]  [agg – p g]
ALSO
[ajj+1 – ajj]  p j+1 – p j
AND
[ag1 – p 1]  [agg – p g]
New rents
Old rents
Suppose we have 3 unimproved parcels
a12 – a11  p2 – p1
a23 – a22  p3 – p2
a31 – a33  p1 – p’3
Sum

a12 – a11  p2 – p1
a23 – a22  p3 – p2
a31 – a33  p1 – p3
Sum

New rents
0
Old rents
0
Benefits must equal 0!
Let’s improve a parcel (#1)
D = Benefits. Assume activity 1 moves to parcel 2, activity 2
to parcel 3, etc.
g -1
D   (a' jj 1 -a jj )  (a' g1 -agg )
1
With no improvement on first (g-1) parcels:
g -1
 (a'
1
g -1
jj 1
-a jj )   (a jj 1 - a jj )
1
From eq’m for jth firm
p ' j 1 - p ' j  a jj 1 - a jj  p j 1 - p j
Why they’re here now
Why they weren’t before
So, for g-1 firms:
g -1

g -1
g -1
1
1
p' j 1 - p' j   a jj1 - a jj   p j 1 - p j
1
g -1
We know:
 p'
j 1
- p ' j  p ' g - p '1
1
g -1
p
1
j 1
- p j  p g - p1
From eq’m for jth firm
p ' g - p '1  D - (a ' g1 -a gg )  p g - p1
(a ' g1 -a gg )  p ' g - p '1  D  p g - p1  (a ' g1 -a gg )
(a ' g1 -a gg ) - ( p '1 - p ' g )  D  (a' g1 -a gg ) - ( p1 - p g )
Increased profit at new prices
Increased profit at old prices
If we’re operating on the margin, we get equalities above:
p' j 1 - p' j  a jj 1 - a jj  p j 1 - p j
(a' g1 -a gg ) - ( p'1 - p' g )  D  (a' g1 -a gg ) - ( p1 - p g )
D  ( p'1 - p1 )
Earlier Problem
Activity is on polluted land p rather than unpolluted land u.
aip – pp aiu – pu
pu – pp aiu – aip
If pollution is eliminated, all land is same and net benefits are:
 (for half of parcels) (aiu – aip)
From above,
 (for half of parcels) (aiu – aip)  (n/2)(p2 – p1)
Here, with 200 parcels, 100 polluted, 100 not
 (for half of parcels) (aiu – aip)  100 (200 – 100) = 10000
Another example
Two types of land
Demand for unpolluted land: P = 250 – 0.5Q
Demand for polluted land: P = 110 –0.1Q
100 acres of each. Pu = 200; Pp = 100. Su = 2500; Sp = 500.
Total surplus = 3000.
If all land is now unpolluted, bidders will use first demand curve  Q = 200; P
= 150. Property values unchanged. New surplus = 10000
From (2.5)
(2.9) A - s  jp(j) - s j j ) + p  j - pj)
A -  7000 + 0
From above,  (for half of parcels) (aiu – aip)  10000