Functions & Formulae

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

Equivalent variation function for health and income changes measured at the status quo

v(p_0, q_0, Y + EV) = v(p_1, q_1, Y); EV = Y * (exp(b * Delta_h) - 1); EV_k = Y_k * exp(b * Delta_h_k) - Y_0

Maps a change from the status quo to the equivalent variation: the change in income, without the change, that would leave the person as well off as the change would. For a gain it is the least the person would accept to forgo the gain, and for a loss the most the person would pay to avoid it. Because every option is valued at the same status quo prices and quantities, equivalent variation ranks several options in the same order as the person's utility. The general expenditure-function definition is given on the Welfare Economics formula page; these records give the closed forms under a log-income utility function, and the log-sum formula of a logit model, HE-FM-CVAR-002, gives both Hicksian measures at once. The records follow the notation of the Equivalent Variation article.

  • Equivalent variation for a health change under log-income utility

    EV = Y * (exp(b * Delta_h) - 1)

    With utility equal to the natural log of income plus b times a health index h, the equivalent variation solves ln(Y plus EV) plus b times h_0 equals ln Y plus b times h_1. For a gain it exceeds both the linear value Y times b times Delta_h and the compensating variation of the same gain; for a loss of the same size it equals minus the compensating variation of the gain, so the two measures swap values between a gain and a loss. HM Treasury's wellbeing guidance gives the same form for the equivalent surplus of a large change in life satisfaction and notes that, under its ln(income) formulae, the equivalent surplus always exceeds the compensating surplus for a gain.

  • Equivalent variation of an option that changes both health and income under log-income utility

    EV_k = Y_k * exp(b * Delta_h_k) - Y_0

    Values an option that moves both the health index and the person's income, for example a treatment with a copayment, from the same status quo income Y_0 and health. Solving ln(Y_0 plus EV_k) plus b times h_0 equals ln Y_k plus b times h_k gives the formula. Because each option is valued at the same status quo, the option with the larger equivalent variation gives the higher utility, the ranking property that compensating variation lacks when there are income effects. With Y_k equal to Y_0 the formula reduces to HE-FM-EVAR-001.

Equivalent Variation — Functions & Formulae | HealthEconomics.wiki