17
Once the demand function has been estimated, the consumer surplus provides an
approximation of the welfare associated with visiting the site. Formally, based on
equation (4), the consumer surplus is equal to:
(5) CS ( p о, qо) = - 1r r„
β2
where ro is r* in equation (4) for the initial levels of quality (here, q=0) and price:
r0 = exp( βo + β1 w + β2 P 0).
The surplus change brought by a quality improvement is:
(6) ΔCS = CS(P1,ql) - CS(p0,q0) = -ɪ[r -r⅛],
β2
where r1 = exp(βo + β1w + β2P1 + β3), where P1 is the new price level. In our
questionnaire, p1 = p 0 in the first contingent behavior question, and p1 = 1.2 ∙ p 0 in the
second.
C. Econometric Model.
Given the relatively few annual trips to our sites, a count data model is the
appropriate model for the number of trips Y. We specify a Poisson model with
individual-specific λij:
(7)
Pr(Yij = yij ) =
e ^ λjλlyij
yj !
where λ>0 is the parameter of the Poisson distribution (which is equal to both the
expected value and the variance of Ylj ), λlj = exp(xljβ1 + pljβ2 + qjβ3) , x is a vector of
determinants of visits to the cultural heritage site (including income), plj is the price per