Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Willingness-to-pay estimation function

w(preferences) = WTP

Maps stated or modelled preferences for a change in health or health care to a sum of money: the marginal value of an attribute from the coefficients of a discrete choice model, or the mean of individual valuations from a contingent valuation survey, scaled to the affected population. Aggregate WTP is the monetary benefit that cost-benefit analysis sets against the present value of costs.

  • Marginal willingness to pay from a discrete choice experiment

    MWTP_k = -beta_k / beta_c

    Divides the utility coefficient of an attribute, or the difference in coefficients between two of its levels, by the negative of the coefficient on the cost attribute. The cost coefficient measures the marginal utility of money, so the ratio is the payment that leaves utility unchanged when the attribute improves by one unit or moves between the two levels.

  • Mean willingness to pay and aggregate benefit from a survey sample

    WTP_mean = sum_(i=1)^n [w_i] / n; B = N_pop * sum_(i=1)^n [w_i] / n

    Averages the stated values of the n respondents in the analysis sample to give mean WTP, and multiplies the mean by the number of people in the population to give aggregate WTP, the monetary benefit used in cost-benefit analysis. Mean WTP multiplied by the population equals the sum of individual values; median WTP describes the typical respondent and is reported alongside, but it is not a welfare total.