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Observed choices between risky lotteries are difficult to reconcile with expected utility maximization, both because subjects appear to be too risk averse with regard to small gambles for this to be explained by diminishing marginal utility of wealth, as stressed by Rabin (2000), and because subjects’ responses involve a random element. We propose a unified explanation for both anomalies, similar to the explanation given for related phenomena in the case of perceptual judgments: they result from judgments based on imprecise (and noisy) mental representations of the decision situation. In this model, risk aversion results from a sort of perceptual bias—but one that represents an optimal decision rule, given the limitations of the mental representation of the situation. We propose a quantitative model of the noisy mental representation of simple lotteries, based on other evidence regarding numerical cognition, and test its ability to explain the choice frequencies that we observe in a laboratory experiment.

To capture the risk-aversion intuition, the standard approach in economics has been to utilize the model of expected utility, in which risk aversion derives from diminishing marginal utility for wealth (or diminishing marginal utility for aggregate consumption). The expected utility model for risk aversion has been used to derive many important insights. But over the years, economists and psychologists have identified various problematic issues with expected utility as a descriptive model of choice. In this article, we urge economists to take seriously the research agenda of developing and assessing different ways to model risk aversion. We proceed in three main steps. First, we highlight that the basic intuition of risk aversion that drives many results in economics is not intimately tied to expected utility. Second, we describe a few alternative models that can also capture the basic intuition of risk aversion. Finally, we discuss that, while expected utility and the alternative models might all capture the basic intuition of risk aversion, the alternative models can generate additional, more nuanced implications not shared with expected utility, that in some cases seem to be borne out by data. We emphasize that these alternative models also are not perfect, and further research is needed to identify even better approaches.

Auctions often involve the sale of many related goods: Treasury, spectrum, and electricity auctions are examples. In multi-unit auctions, bids for marginal units may affect payments for inframarginal units, giving rise to \"demand reduction\" and furthermore to incentives for shading bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings of the two formats are ambiguous. However, in settings with symmetric bidders, the pay-as-bid auction often outperforms. In particular, with diminishing marginal utility, symmetric information and linearity, it yields greater expected revenues. We explain the rankings through multi-unit effects, which have no counterparts in auctions with unit demands. We attribute the new incentives separately to multi-unit (but constant) marginal utility and to diminishing marginal utility. We also provide comparisons with the Vickrey auction.

We use data on insurance deductible choices to estimate a structural model of risky choice that incorporates \"standard\" risk aversion (diminishing marginal utility for wealth) and probability distortions. We find that probability distortions—characterized by substantial overweighting of small probabilities and only mild insensitivity to probability changes—play an important role in explaining the aversion to risk manifested in deductible choices. This finding is robust to allowing for observed and unobserved heterogeneity in preferences. We demonstrate that neither Kőszegi-Rabin loss aversion alone nor Gul disappointment aversion alone can explain our estimated probability distortions, signifying a key role for probability weighting.

Harry Markowitz is widely recognized to be the father of portfolio theory. But, for unknown reasons, his substantial contributions to utility theory are less well-known. Daniel Bernoulli is widely renowned for explaining the Saint Petersburg paradox. Most people recognize Adam Smith as being the father of capitalism. Some people are aware that Carl Menger (1840–1921) was one of the first to discuss (in German) diminishing marginal utility. Jules Dupuit (1804–1866) distinguished between total utility and marginal utility and, in the process, he went on to discover the consumers’ surplus. Although it is not widely recognized, Herman Heinrich Gossen (1810–1858) was the first economists to explain that the fundamental principle of marginal utility theory is that a person maximizes his utility when he distributes his available money among the various goods so that he obtains the same amount of satisfaction from the last unit of money spent on each different commodity. After explaining the Saint Petersburg paradox earlier in his career comma, Daniel Bernoulli later brought many utility suggestions together into one tidy package, and even went on to suggest that decision-maker’s decisions can probably be best represented by the logarithmic utility function. Each one of the previous contributions to utility theory constitutes a significant improvement in the previous theory. But in 1952 Harry Markowitz published several suggestions that each represented a significant advancement to the existing utility theory. The value of Markowitz’s suggestions was acknowledged in 1979 and 1992 by two psychologists named Daniel Kahneman and Amos Tversky when they introduced their prospect theory. These co-authors list and discuss several of Markowitz’s contributions to expected utility theory in their 1979 prospect theory paper.

We develop an approach to analyzing the sustainability of competitive advantage that emphasizes demand-side factors. We extend the added-value approach to business strategy by introducing an explicit treatment of how firms create value for consumers. This allows us to characterize how consumer heterogeneity and marginal utility from performance improvements on the demand side interact with resource heterogeneity and improving technologies on the supply side. Using this approach, we address a variety of questions including whether technology substitutions will be permanent or transitory; the sequence in which new technologies attack different market segments; how rents from different types of resources change over time; whether decreasing marginal utility and imitation give rise to similar rent profiles; the extent of synergies within a firm's resource portfolio; the emergence of new generic strategies; and the conditions that support strategic diversity in a market. Our focus on consumer utility and value creation complements the traditional focus in the strategy literature on competition and value capture.

This paper provides novel empirical evidence on the value of the elasticity of marginal utility, \\[ \\eta \\], for the United Kingdom. \\[ \\eta \\] is a crucial component of the social discount rate (SDR), which determines the inter-temporal trade-offs that are acceptable to society. Using contemporaneous and historical data, new estimates are obtained using four revealed-preference techniques: the equal-sacrifice income tax approach, the Euler-equation approach, the Frisch additive-preferences approach and risk aversion in insurance markets. A meta-analysis indicates parameter homogeneity across approaches, and a central estimate of 1.5 for \\[ \\eta \\]. The confidence interval excludes unity, the value used in official guidance by the UK government. The term structure of the SDR is then estimated. The result is a short-run SDR of 4.5% declining to 4.2% in the very long-run. This is higher and flatter than the UK official guidance. The difference stems from incorrect calibration of social welfare and estimation of the diffusion of growth. Other things equal, the results suggest that current UK guidance might need to be updated.

The author blends historical narrative with a topical approach and discusses such aspects of the theory as measurement, total value, and imputation. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Diminishing marginal utility (DMU) is a basic tenet of economic and psychological models of judgment and choice, but its determinants are little understood. In the research reported here, we tested whether insensitivities in valuations of dollar amounts (e.g., $40, $100) may be due to inexact mappings of symbolic numbers (i.e., \"40,\" \"100\") onto mental magnitudes. In three studies, we demonstrated that inexact mappings appear to guide valuation and mediate numeracy's relations with riskless valuations (Studies 1 and 1a) and risky choices (Study 2). The results highlight the fundamental notion that individuals' valuations of $100 depend critically on how individuals perceive and map the symbolic quantity \"100.\" This notion has implications for conceptualizations of value, risk aversion, intertemporal choice, and dual-process theories of decision making. Normative implications are also briefly discussed.

Estimates of the elasticity of the marginal utility of income are necessary for determining distributional weights to correct for diminishing marginal utility of income, which is particularly important in light of increasing concern about accounting for distributional impacts in regulatory review. The elasticity is also necessary for computing the social discount rate using the Ramsey formula. Despite many attempts to estimate the elasticity of the marginal utility of income, considerable uncertainty exists about the magnitude of this key parameter. In this paper, we use meta-analysis of estimates of the elasticity from the US and UK to shed light on the appropriate elasticity values to use for both distributional weighting and discounting. Relying on our findings, we tentatively conclude that it is reasonable to base the social discount rate and distributional weights on an elasticity of 1.6, with lower- and upper-bound sensitivity testing at 1.2 and 2.0. This estimate results in distributional weights which appear plausible, and which we believe can contribute to a consensus on how to conduct distributional weighting. Moreover, the resulting social discount rate is within the range typically recommended when the Ramsey formula is used.