Lind on Measuring Benefits © Allen C. Goodman, 2002

Suppose We have 2 types of land, half polluted (p), half not (u). P p = 100; P u = 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 a ij = maximum rent ind. i would pay for parcel j. Alternatively: a ij = Net earnings of firm i at parcel j exclusive of land cost. n activities, n parcels p j = rental value of parcel j. Activity locates at parcel j ONLY IF: (2.3) a ij  p j AND (2.4) a ij - p j  a ik - p k

Analysis Define consumer surplus (or profit) as s ij. s ij  a ij – p j. SO, the total benefit from land is (2.5)  a ij =  s ij +  p j Land is ENHANCED if there is some a ij > a ij for some parcels, and a ij =  ij for the rest. Let: A =  a jj (2.7) A  a j  (j) (2.8) A  a j  (j) - a j  j

Analysis (2.5)  a ij =  s ij +  p j Let: A =  a jj (2.7) A  a j  (j) (2.8) A  a j  (j) - a j  j From (2.5) (2.9) A  s j  (j) - s j  j ) +  p j - p j ) 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  in productivity = [a 12 – a 11 ] + [a 23 – a 22 ] + [a 31 – a 33 ] Since there is no improvement,  in productivity = [a 12 – a 11 ] + [a 23 – a 22 ] + [a 31 – a 33 ] From the equilibrium conditions: (2.3) a ij  p j AND (2.4) a ij - p j  a ik - p k [a jj+1 – a jj ]  p j+1 – p j AND [a g1 – p 1 ]  [a gg – p g ] New rents

Suppose we have 3 unimproved parcels [a jj+1 – a jj ]  p j+1 – p j AND [a g1 – p 1 ]  [a gg – p g ] ALSO [a jj+1 – a jj ]  p j+1 – p j AND [a g1 – p 1 ]  [a gg – p g ] New rents Old rents

Suppose we have 3 unimproved parcels a 12 – a 11  p 2 – p 1 a 23 – a 2 2  p 3 – p 2 a 31 – a 33  p 1 – p’ 3 Sum  0 New rents Old rents a 12 – a 11  p 2 – p 1 a 23 – a 22  p 3 – p 2 a 31 – a 33  p 1 – p 3 Sum  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. With no improvement on first (g-1) parcels:

From eq’m for jth firm Why they’re here nowWhy they weren’t before So, for g-1 firms: We know:

From eq’m for jth firm Increased profit at new pricesIncreased profit at old prices If we’re operating on the margin, we get equalities above:

Earlier Problem Activity is on polluted land p rather than unpolluted land u. a ip – p p  a iu – p u p u – p p  a iu – a ip If pollution is eliminated, all land is same and net benefits are:  (for half of parcels) (a iu – a ip ) From above,  (for half of parcels) (a iu – a ip )  (n/2)(p 2 – p 1 ) Here, with 200 parcels, 100 polluted, 100 not  (for half of parcels) (a iu – a ip )  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. P u = 200; P p = 100. S u = 2500; S p = 500. Total surplus = If all land is now unpolluted, bidders will use first demand curve  Q = 200; P = 150. Property values unchanged. New surplus = From (2.5) (2.9) A  s j  (j) - s j  j ) +  p j - p j ) A  +  From above,  (for half of parcels) (a iu – a ip )  10000