Theory suggests that WTA(y) = WTP(y +

WTA(y)) where y is income. This insight provides an opportunity to test the validity of the contingent valuation method. For example, Hammack and Brown (1974) surveyed the WTP of hunters to preserve duck populations estimating the following equation:

ln(WTP) = 2.48 + 0.466 ln(y)

Suppose that individual preferences are given by the following indirect utility function:

V(P, y, z)

where P is prices and z is environmental quality.

(a) Use the indirect utility function to write down an expression for WTP for an increase in environmental quality from z

0 to z 1

.

(b) Now use the same function to write down an expression for an individual’s WTA for a reduction in environmental quality from z

1 to z 0

.

(c) Write down the expression for WTP for an increase in environmental quality from z

0 to z 1 when the consumer’s income is y + WTA(y). Comparing this expression to the one given in 2, demonstrate that WTA(y) = WTP(y + WTA(y)) must indeed be the case.

(d) In Hammack and Brown’s paper, what is the WTP of a hunter with an income of

$12 100? Hammack and Brown predict a WTA of $1044. Does such a high value for WTA refute or confirm the theory underlying contingent valuation?