# Willingness to accept

Willingness to accept (WTA) is the amount that а person is willing to accept to abandon a good or to put up with something negative, such as pollution. It is the minimum monetary amount required for sale of a good or acquisition of something undesirable to be accepted by an individual. This term stands in contrast to willingness to pay (WTP), which 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.

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.

## Formal definition

Let u(w, x) be an individual's utility function, where w is the person's wealth and x is a 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", denoted WTA, is defined by

$u(w_0 + WTA , 1) = u(w_0 , 0).$ [1]

Thus WTA is the amount of compensation which, combined with the presence of the undesired feature, gives the person the same level of utility as would occur if there were no compensation and no undesired feature.

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.

## Standard theory versus experimental results

The standard assumptions of economic theory imply that when income effects are small, the gap between WTP and WTA should be negligible. Thus indifference curves are drawn without reference to current endowments. This leads to the wide acceptance of the Coase theorem assertion that, subject to income effects, the allocation of resources will be independent of the assignment of property rights when costless trades are possible. This is to say, the allocation of property rights does not influence the way externalities are internalized by the market. However, an experiment by Daniel Kahneman, Jack L. Knetsch and Richard Thaler showed that measures of WTA greatly exceed measures of WTP.[2] One explanation is that the endowment effect makes people value a good or service more if they possess it.

## Applications

WTP and WTA are important factors for public policy. Many economic decisions are based upon the implicit assignment of property rights. When looking at a lake which is being polluted by a nearby factory, the WTA and WTP for treatment of an effluent treatment plant may have different consequences based upon how property rights are politically assigned. If lakeside residents have no property right to an effluent-free lake, then their willingness to pay to treat the lake's water supply would be considered. Conversely, if the lakeside residents are found to have a property right to a clean lake, then their willingness to accept compensation for a polluted lake would be considered.