KHZ is defined in terms of the WTP and WTA. The KHZ test is passed when the aggregation of gains and losses as measured by the WTP and WTA are positive. When this occurs, I shall say that there are net benefits from the project. This test meets the essential requirement: any one person who has net benefits over a set of projects, can be said unequivocally to have gained. Incidentally, it also meets two other requirements that were thought to be important for KH: it meets a potential compensation test, and is subject to neither Scitovsky reversals nor status quo bias.
The essential test that positive net benefits exist over a set of projects for an individual is met whether or not there is path dependence. The path dependence issue is the following: suppose an individual, over a set of two projects, loses $9 on the first and gains $10 on the second. Is this the same result as if the individual gained $10 on the first and lost $9 on the second so that in either case there is a gain of $1 over all. When the order makes no difference, then there is said to be path independence. When there is no path dependence, then many projects can be treated as one so that the overall net benefit KHZ test gives the correct answer. When there is path dependence, KHZ will also give the right answer by following the correct path.
In modern economics, the measure of welfare change is normally the expenditure function. The function M*(puU0) is the minimum cost or expenditure of achieving utility level U0 at price pL. M* represents the expenditure level that is the solution to the problem of minimizing cost or expenditure. Changes in the value of the expenditure function show the change in expenditures to attend a given utility level as prices change.
Consider a price change from p0 to pL. Let U0 represent the psychological reference point before the change. Then the difference in expenditures Mc occasioned by the price change is
This measure of welfare change is path independent so that all projects affecting a particular individual may be treated as one project for that individual.
The literature on the psychological nature of gains and losses, however, suggests that gains and losses are in fact path dependent. In general, KHZ notes that the correct measure of gains and losses must take into account the psychological underpinnings or value. Thus the recognition of path dependence does not affect the fact that an individual with net gains over a set of separate projects can be said to be better off. Rather, KHZ corrects for the measure of gain and loss to determine net benefits.
Suppose, for example, that the government proposes a project that will raise the price of electricity to consumer A but that to undertake it they also need to buy land from consumer A and the income from the sale of the land will more than offset the higher electricity cost. Consider two ways to value this project. It could be regarded as two different projects, one involving the sale of land and the other an increase in electricity prices, or as one project. When it is evaluated as two separate projects, this assumes that the consumer values the higher price as a loss to be measured by the WTA. If the consumer were to regard the project as just one project with a gain, the KHZ measure would be the WTP and the measure of gain for the overall project would be larger than when valued as two separate projects. Thaler (1985) reports an experiment in which the following questions were asked. Who should be happier: A who wins $100 in the state lottery but the same day drops a bottle of ink and does $80 worth of damage to his living room rug; or B, who wins $20 in the lottery? Of a large sample of subjects 70 percent responded B, 25 percent said A, and 5 percent said the two should be equally happy. Since KHZ recognizes the psychological nature of gains and losses, it recognizes this path dependence. Thus, KHZ in general would not treat the $20 net gain from the lottery as the same as the $100 gain with the $80 loss.
In its emphasis on WTP and WTA measuring gains and losses, KHZ differs from the KH criteria. The KH criteria are potential compensation tests. KHZ is defined rather in terms of aggregate WTP and WTA. The usual measure of welfare changes through the EV and CV are not quite the same as potential compensation tests (Boadway and Bruce 1984). The KHZ measure is consistent with the practice, roughly derived from KH, of expressing benefit-cost analysis in terms of WTP and WTA.
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