Abstract
In this paper I show that within expected utility large buying and selling price gap is possible and Rabin (2000) paradox may be resolved if only initial wealth is allowed to be small. It implies giving up the doctrine of consequentialism which may be reduced to requiring initial wealth to be total lifetime wealth of the decision maker. Still, even when initial wealth is allowed to be small and interpreted narrowly as gambling wealth, classic preference reversal is not possible within expected utility. I show that only another kind of reversal which I call preference reversal B is possible within expected utility. Preference reversal B occurs when buying price for one lottery is higher than for another, but the latter lottery is chosen in a direct choice. I demonstrate that classic preference reversal is susceptible to arbitrage whereas preference reversal B is not which suggests that the latter reversal is more rational.
Highlights
Willingness to accept (WTA) or selling price for a lottery is a minimal sure amount of money which a person is willing to accept to forego the right to play the lottery
Along the lines of Rubinstein (2006) I will argue that the source of this belief lies in associating expected utility theory with the doctrine of consequentialism, according to which “the decision maker makes all decisions having in mind a preference relation over the same set of final consequences”
If initial wealth is allowed to be small, I will show that expected utility is consistent with large buying/selling price spreads, i.e. that within expected utility for levels of risk aversion consistent with experimental evidence, one can obtain a buying/selling price spread of the magnitude observed in experiments
Summary
I start with basic assumptions and definitions. Assumption 1 Preferences obey expected utility axioms. Definition 2 I define selling price and buying price for a lottery x at wealth W as functions of wealth W denoted, respectively, S(W, x) and B(W, x) Provided that they exist, values of these functions will be determined by the following equations: EU [W + x] = U [W + S(W, x)]. If utility function is defined over the whole real line as is the case for constant absolute risk aversion, buying and selling price as functions of wealth exists for any wealth level by Assumption 1. Definition 3 Given two lotteries x and y and some wealth level W , define buying/selling price reversal as: S(W, y) > S(W, x) and B(W, x) > B(W, y) This kind of preference pattern may be interpreted as follows. On the other hand, he does have the right to play the lottery initially, he would prefer to sell x than y
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