Willingness-to-pay
In economics, willingness to accept (WTA) is the minimum amount of money that а person is willing to accept to abandon a good or to put up with something negative, such as pollution. It is equivalent to the minimum monetary amount required for sale of a good or acquisition of something undesirable to be accepted by an individual. Conversely, willingness to pay (WTP) is the maximum amount an individual is willing to sacrifice to procure a good or avoid something undesirable. The price of any goods transaction will thus be any point between a buyer's willingness to pay and a seller's willingness to accept. The net difference between WTP and WTA is the social surplus created by the trading of goods.
Several methods have been developed to measure consumer willingness to pay or accept payment. These methods can be differentiated whether they measure consumers' hypothetical or actual willingness to pay or accept and whether they measure consumer willingness to pay or accept directly or indirectly.
Choice modelling techniques may be used to estimate the value of the WTP or WTA through a choice experiment.
Unlike WTP, WTA is not constrained by an individual's wealth. For example, the willingness to pay to stop the ending of one's own life can only be as high as one's wealth, while the willingness to accept compensation to accept the loss of one's life would be an extremely high number (or maybe infinite, meaning that there would be no finite acceptable payment amount).
Let u(w, x) be an individual's utility function, where w is the person's wealth and x is a dummy variable that takes the value one in the presence of an undesired feature and takes the value zero in the absence of that feature. The utility function is assumed to be increasing in wealth and decreasing in x. Also, define w0 as the person's initial wealth. Then the "willingness to accept" is defined by
That is, the willingness to accept payment in order to put up with the adverse change equates the pre-change utility (on the right side) with the post-change utility including compensation.
In contrast, the willingness to pay is defined by
That is, the willingness to pay to avoid the adverse change equates the post-change utility, diminished by the presence of the adverse change (on the right side), with utility without the adverse change but with payment having been made to avoid it.
The concept extends readily to a context of uncertain outcomes, in which case the utility function above is replaced by the expected value of a von Neumann-Morgenstern utility function.
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