Fullerton, Herbert H.

Keith, John E.

Meale, Eric R.

English

Research Papers in Economics

A  Comparison  of the Economic Rent and
Consumer  Surplus  Methods  of
Valuing  Recreation  Boating  Sites
Eric R.  Meale,  John E.  Keith  and Herbert H. Fullerton
Allocating  public  monies  among  competing
uses  is  among  the  most  difficult  problems  facing
government  agencies  concerned  with  natural
resources.  In  the  public  sector,  recreation  is  often
provided  at  a  nominal  cost and therefore the price
mechanism  does  not  provide  a  meaningful  guide
to  consumer  preference  and  willingness  to  pay.
Consequently,  a  satisfactory  measure  of benefits
(and  opportunity  costs)  is  lacking.  However,  it is
these benefits  which are  relevant to the investment
decision  in  the  public sector. To overcome  this de-
ficiency, indirect  valuation methods have been pro-
posed  for  imputing  values  to  recreation  resources
to  assist  in  the  allocation  of scarce  public  invest-
ment funds among alternative recreation  sites.
Economists  have  devised  various  models  de-
signed  to  measure  recreation  benefits  of  values
such  as  consumer  surplus  (Hotelling;  Wennergren
1964),  non-discriminating  monopolist  [Clawson;
Brown],  consumer  survey  [Davis],  and  economic
rent  [Trice;  Wennergren  1972].  However,  due  to
differences  in assumptions,  the  models yield varia-
tions  in  value  of  a  recreational  site  which  creates
the  problem  of which  valuation  estimate  is most
appropriate  and  under  which  circumstances  are
models  comparable  [Beardsley;  Carey;  Seckler].
Most  of these models  have  been  developed  within
the  conceptual  context  of  consumer  demand
theory. Economic  rent has been less widely used as
a  measure  of  value,  even  though  the  conceptual
equivalence of the economic rent measure and that
of consumer  surplus  as  indicators  of changes  in
social  well-being  has  been  argued  [Mishan].  The
objective  of this paper is to determine  the compar-
ability  of  consumer-surplus  and  economic  rent
methodologies  of recreation resource valuation.
Eric  R.  Meale  is an economist with  the Idaho Department
of Water  Resources  and former graduate assistant  at Utah
State  University;  John  E.  Keith  is  an assistant  professor
of  economics  and  Herbert  H.  Fullerton  is  an  associate
professor of economics at Utah State  University.
The  concept of consumer surplus applies  to the
values  that  possessors  of  a  commodity  receive  in
excess  of  the  pruchase  price.  With  respect  to
recreation,  individual  site  demand  estimates  are
based  on  the concept that a recreationist is subject
to  costs  and,  consequently,  to implicit prices  in-
curred  in  the  consumption  of  the  recreational
experience,  which  regulate  his  consumption  and
reflect the value  of the experience to the consumer,
thus,  providing  a  useful  approach  to  estimating
recreational  demand.  The  concept  of  economic
rent  defines  economic  rent  as  the  difference  be-
tween  selling  price  and  unit  production  costs
expended  in  using  the  most  productive  resource.
The  application  of  economic  rent  to  recreation
valuation  is  based  upon  the  concept  that  points
of  origin  are  spatially  related  to  the  site; those
origins  most  closely  located  extract  an  economic
rent  relative  to  that 'origin  most  distant  or  dis-
advantageously  located  with  respect  to  the  site.
The  two  models  of  recreation  valuation  incor-
porate  the  relationship  existing  between  the
variable  use  costs  associated  with  various  origins,
sites, and units of activity.
Data were collected  from a total 9,491  question-
naires  mailed  to  a  sample  of Utah  boaters  drawn
randomly  from  a  master  list  of  approximately
31,500  registered  boats in  1973.  A total  of 1,408
questionnaires  (14.8  percent)  were  returned  and
used in  the  study. Information  was obtained from
the  questionnaires  with  respect to boater's  origin,
boating  sites  visited,  number  of trips  taken  to a
site  and  trip  expenses.  Using  this  information,
together  with  standardized  distances  and  an
assumed  variable  cost  of  travel,  estimates  of con-
sumer  surplus  and  economic  rent  were  made  for
twenty-four boating sites in Utah.
To  facilitate the  comparison of the two method-
ologies,  both  estimates  of  resource  value  were
based  upon  the  same  set  of  observed  activity.
252Valuing Recreation Boating Sites
Consumer surplus estimates were  made using linear
demand  functions  and  curvilinear  demand  func-
tions.  The  consumer  surplus  was  calculated  rela-
tive to the highest cost user to alleviate the problem
of  high  surplus  values  due  to  inelastic  demand
functions and  to put economic  rent and consumer
surplus  estimates  on  an  equivalent  basis. The  cal-
culations  of  economic  rent  are  consistent  with
the  methodology  advanced  by  Wennergren  and
Fullerton  [1972].  The  consumer  surplus  esti-
mates  are  consistent  with  the  methodology
developed  by Hotelling.
The  comparison  and  anlysis  of economic  rent
and  consumer  surplus  was  developed  through  the
use  of  a  common  mathematical  model.  The
common  mathematical  model  incorporated  the
logic  and  notation  of both the economic  rent and
consumer  surplus  models.  An  empirical  compari-
son  was  utilized  to  aid  in  the  understanding  of
the  conclusions  arrived  at  in  the  mathematical
model  and  to  evaluate  the  conclusions  through
empirical  observation.  The  mathematical  defini-
tions  of  consumer  surplus  and  economic  rent
used  in  the  study  and  the notation  are presented
below.  The  consumer  surplus  definition  below  is
based upon the use of linear demand functions.1
n
Z  Bi
n  i=l
TERj=  Z  (Pnj-Pij)Tij  n
i= 1  Z  Ri
i= 1
n
TCSj =  z
i=l
Pnj
[ f  (-  P+aj)dP]Bi
Pij  bj
n  (Pnj - Pij)  Tij  Tnj
=  [  - - (-+  n ) ] Bi
i=l  2  Ri  n
where:
TERj  =  The total economic  rent for site j.
TCSj  = The total consumer  surplus for site j.
Pij  = The  travel  costs from  origin  i to site j.
Pnj  =  The  travel  costs  from  the  most  dis-
tant origin (n) to site j.
Tij = The  number  of  trips  from  origin  i to
site j.
The  use  of linear  demand  functions  is  not essential
to the  analysis  although  it does  facilitate  the comparison
by  simplifying  the presentation  and interpretation  of the
results.
Tnj  =  The  number  of  trips  from  the  most
distant origin (n) to site j.
Ri =  The  size  of  the  sample  of  registered
boaters from origin i.
Bi =  The  total  number  of registered  boat-
ers in origin i.
bj  =  The  travel  costs  (price)  intercept  of
the demand  function for site j.
aj  =  The  trips  per  capita  (quantity)  inter-
cept of  the demand function for site j.
i  =  A typical origin (1,..., n).
j  = A typical site (1,..., m).
Three  stages,  or  levels  in  the  calculation  pro-
cedure  were  considered  in  the  comparison  and
analysis  of  the  two  methodologies.  The  first
stage  compared the  basic  economic  rent  and basic
consumer  surplus  values  per  origin  visiting  a  site.
The  second  stage  took  into  consideration  the
effects  of  the  respective  projection  factors  upon
the basic resource values in calculating the projected
economic  rent  and  consumer  surplus  values  for
an  origin  traveling  to  a  recreational  site.2 The
third  stage  analyzed  the relationship  between the
total  economic  rent  and  the  total  consumer  sur-
plus  values  for  the  site in light of the  findings  of
stage one and two.
In  stage  one,  it  was  found  that  the  basic
economic  rent value  will exceed the basic  consumer
surplus  value  for  all  origins  visiting  a  recreation
site.  The  reason  for  this relationship  is  the  eco-
nomic  rent  model  utilizes  the  number  of trips
taken  from  an  origin  to  the  site,  while  the  con-
sumer surplus  model uses  the  number of trips  per
capita in calculating  the resource values.  The num-
ber  of trips will  always  equal  or  exceed  the num-
ber  of  trips  per  capita.  By  using  the  number  of
trips from  an  origin  to a  site in the economic rent
model,  the  rent  values  are  influenced  by  large
population  centers,  whereas  in  the  consumer
surplus  model,  this  influence  is  reduced  by using
the  number  of  trips per capita,  thereby  standard-
izing  large  and  small  population  centers  and  re-
flecting a more accurate  activity  rate among origins
visiting  a  site.  A second  reason  for  the  difference
in  resource  values  is  the  assumption  that  the
economic  rent  is  constant  for  each  trip  taken,
2The  projection factors determine the total number  of
trips  that  would  be  expected  from  the  total  boating
population  of an  origin  visiting  a  boating recreation  site
based upon  the size of the sample.
253
Meale, Keith, and F~ullertonWestern J. Agr. Econ.
whereas  the marginal value in the consumer surplus
model  declines  as  additional  trips  from  an  origin
are  consumed.  Since  the  basic  economic  rent
exceeds  the  basic  consumer  surplus,  the rent can
be  expressed  as  a  multiple  of  the  surplus.  The
magnitude  of the  multiple  will  vary among origins
visiting  a  site  and  among  the  sites  visited  by  an
origin  because  the  number  of  trips  and  trips  per
capita  varies  among  the  origins visiting  a  site,  and
the  elasticity of the demand function  varies among
the  sites.  The  range  of the multiple  is from  one to
a factor of two times the sample size per origin.
In  stage  two,  no  consistant  relationship  was
found  between  the projection factor for economic
rent and  the similar projection factor for consumer
surplus.  The  projection  factor  for  economic  rent
may  be  greater  than,  equal  to,  or  less  than  the
similar  projection  factor  for  consumer  surplus
depending  upon  the  relevant  data.  Since  the
projection  factors  determine  the  total  expected
number  of  trips  that  would  be  taken  from  an
origin,  the  inconsistent  relationship  between  the
projection  factors creates  an analogous relationship
between  the  economic  rent  values  and  the  con-
sumer surplus values.  Depending upon the  relation-
ship  between  the  relevant  projection  factors,  the
projected economic  rent value  for an origin  visiting
a  site  could  be  greater  than, equal  to,  or  less than
the projected consumer surplus value for the origin.
The  main  reason  for  the  difference  between  pro-
jection factors is that the economic rent projection
factor  is  an  aggregation  of  the  population  and
sample  size,  whereas  the  consumer  surplus  projec-
tion  factor  is  on  a  per-origin  basis,  thereby  yield-
relationshiping  the  greater  than,  equal  to,  or less
than relationship.
In  stage  three,  again  no  consistent relationship
between  the  total  economic  rent  and  total
consumer surplus  values  for  a  site  was  found. The
total  site  value  is the  summation  of the  projected
origin  values  for  those  origins  visiting  the  site.  In
the process of determining the total  resource values
for a site, each  stage  in the  process  contributes  to
the  lack  of  a  unique  relationship  between  the
economic  rent  and  consumer  surplus  valuation
methodologies.  The  basic  economic  rent  exceeds
the  basic  consumer  surplus  for  all  origins  visiting
a  site  due  to  the  difference  in  assumptions  con-
cerning  the  use  of  trips  and  trips  per  capita  and
the  concept  of  constant  economic  rent  per  trip.
The  projection  factors  further  complicate  the
relationship  as  discussed  above.  Since the relation-
ship  between  the  projected  origin values  is  incon-
sistent,  the  summation  of  these  values  to  arrive
at total site values will  also be inconsistent depend-
ing upon the net effect of stages one and two.
The empirical  comparison of the  total economic
rent  and total consumer surplus values for twenty-
four  boating  sites in  Utah  is presented  in table  1.
The  empirical  comparison  reflected  the  variations
in  the  use  of data,  in  the  calculation  procedure,
and  in the  assumptions  between the  two method-
ologies.  The use of regression  analysis  to determine
the  demand  functions  in  the  consumer  surplus
model  did  reflect  a  difference  in  the  trips  per
capita  from  an  origin  than  was  actually  observed
thereby  generating  some  bias  in  the  empirical
values  for  the  consumer  surplus model  compared
to  the  economic  rent  model,  which  utilized  the
actual  data,  but this did not affect the conclusions
arrived  at  in  the  mathematical  comparison.  The
conclusions  of  stages  one,  two,  and  three  of  the
Table  1. Total  economic  rent  and  total  consumer
surplus values for 24 boating sites in  Utah,
1973
Total
Total  Consumer
Total  Consumer  Surplus
Economic  Surplus  (Curvi-
Boating  Site  Rent  (Linear)  linear)
---------  - dollars ----------
Bear  Lake  222528  113781  129577
Big Sands  Wash  4947  65275  12196
East  Canyon  Lake  9329  9003  7126
Fish  Lake  13883  28567  16238
Flaming  Gorge  303049  192471  213212
Huntington  Lake  4119  3641  930
Hyrum State  Park  6865  3436  2269
Joe's  Valley  3858  4137  2233
Johnson  2660  1605  1035
Koosharem  5253  3972  1894
Mantua  1111  1447  466
Navajo  11353  6791  1759
Otter Creek  22578  16495  8533
Palisades  State  Park  3661  3230  1016
Panquitch  2528  1782  1556
Pineview  49778  33412  23147
Rockport  78869  92726  38716
Scofield  24997  60354  31073
Starvation  69868  179568  96154
Strawberry  101947  151166  69677
Willard  Bay  55112  45557  40280
Yuba State  Park  7409  3615  3113
Twin  Lakes,  Idaho  1940  1963  631
Pelican  1765  1774  1477
254
June 1977Valuing Recreation Boating Sites
mathematical  comparison  were  substantiated
through empirical  observations.
An  additional  empirical  comparison  of  the
two  methodologies  involved  the  calculation  of
the  quality  and location  values  based on  the  con-
sumer  surplus  estimates.  Estimates could  be  made
for  only  eleven  of the  twenty-four  sites in Utah,
since  insufficient  data  were  available  to  generate
consumer  surplus  location  estimates.  This  is con-
sidered  significant,  since  it  illustrates  the  greater
data  needs  of  the  consumer  surplus  methology.
Although  the  economic  rent  model  has  definite
time  and  cost  advantages  in  the  collection  and
analysis  of  data,  it  does  have  shortcomings  in
that  the  differences,  as  pointed out in stages one,
two,  and  three  of  the  mathematical  comparison,
restrain  its comparability  to the  consumer  surplus
methodology.
In  conclusion,  the identification  of variations in
the  methodologies  and  their  influence  upon  the
resource  values  will  assist  in  understanding  the
differences  and  problems  of recreational  resource
valuation  techniques.  A broader  understanding  of
these  differences  may lead to improved uniformity
in  the  valuation  propedures  and  to  a better under-
standing of the interpretation  of the results.
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A COMPARISON OF THE ECONOMIC RENT AND CONSUMER SURPLUS METHODS OF VALUING RECREATION BOATING SITES

A COMPARISON OF THE ECONOMIC RENT AND CONSUMER SURPLUS METHODS OF VALUING RECREATION BOATING SITES

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