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Note that even when the probability of the maximum reward is high, say 0.95, some will prefer the cash of $500 (those who are highly loss-averse). This shows the failure of expected value theory and demonstrates the need for a theory that explains such a behavior. For instance, if some individuals are to choose between a cash money of $500 or a probable payoff of (−$1000 or $5000) both of equal chances, many will choose the sure amount of $500 while the expected value of the second option is $2000. Therefore, the satisfaction of a surplus made by some trade/business is not necessarily well assessed by the expected value rather, the utility is the rational valuation of the surplus from the decision makers’ perspective. The “utility” is an economic term referring to the total satisfaction attained from consuming a good or a service. Risk attitudes are modeled by the utility functions. It intensely influences ordering, pricing and other marketing decisions in business environments. Risk-averse behavior of the decision makers affects their future choices and decisions, a matter which has been acknowledged by a good deal of the literature. While profit maximization/cost minimization served as a milestone objective for so long, in economics, the default assumption is that the decision makers are usually risk-averse, meaning that the individuals have a positive and diminishing marginal utility of money. The management of stochastic inventories is a critical issue for the success of modern business, particularly in retail industry. The presented formulas are advantageous in finding the optimal order quantities and risk premiums of a stochastic short-shelf life inventory when the loss is a key factor in the decision-making process. Higher standard deviations, on the other hand, mean lower utility-optimal quantities and higher risk premiums. Similar conclusion holds when the overage/underage costs increase. In addition, we show that high loss aversion entails higher risk premiums. The results show that when an exponential loss aversion exists, the classical newsvendor optimal quantity serves as a lower bound when the overage costs are high and as an upper bound when the underage costs are high. New formulas are introduced to find the utility-optimal order quantity of the normal distribution. In contrast, this paper deals with the utility maximization of the newsvendor using a class of bounded utility functions to study the effect of loss aversion on the newsvendor certainty equivalents and risk premiums. Moreover, the use of unbounded utility to model risk attitudes fails to explain some decision-making paradoxes. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. The bold part.Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. My question is why are we multiplying by 2 and subtracting 1 from the equation. Thus, as buying X yields a higher expected utility, the investor ought to buy it.Ĭertainty Equivalent = (10.03987576)^2 = 100.7991 If, however, they do not buy X, then their expected (and certain) utility is: If Investor B buys X, then they will enjoy an expected utility of:Ġ.5 + 2(sqrt(92) -1)] = 18.08 Will the Investor B choose to buy Investment X? (i) Suppose that Investor B has an initial wealth of 100 and is offered the opportunity to buy Investment X for 100, which offers an equal chance of a payout of 110 or 92. Suppose Investor A has a power utility function with y = 1, whilst Investor B has a power utility function with y = 0.5.