Computing Willingness-to-pay in Random Utility Models

Welfare evaluation of a policy that alters the quality of a resource can often be cast as the problem of calculating mean Willingness to Pay (WTP) in a population of consumers with random utilities induced by varying tastes and budgets. This interpretation is particularly useful when some of the components of choice at the level of the individual are discrete. This paper reviews the theory of WTP measurement, and provides easily computed WTP bounds. It reviews generalized extreme value (GEV) random utility models, where analytic formulas for WTP result when indirect utility is linear in income. It shows that a representative consumer characterization of the random utility model, which yields exact WTP when indirect utility is linear in income, can give substantially biased estimates of WTP when indirect utility is nonlinear in income. Finally, it describes a monte carlo markov chain simulation method that can be used to obtain accurate approximation of mean WTP in GEV random utility models that are nonlinear in income. This procedure is of independent interest as a method for obtaining random draws from a GEV density. Acknowledgements: This research was supported by the E. Morris Cox endowment at the University of California, Berkeley, and by the Atlantic Richfield Company. The sponsors are not responsible for the conclusions I draw in this paper. In developing Section VI of the paper, I have benefited from discussions with John Geweke, Vassilis Hajivassiliou, Reed Johnson, Tony Lancaster, Peter Rossi, Kenneth Train, and Steve Waters.