Cobb-Douglas Preferences Research Articles

A Note on the Preferences of Sports Fans: Partisanship Versus Uncertainty of Outcome

Since its inception, a core principle of sports economics has been the claim that fans desire balanced competition—the so-called Uncertainty of Outcome Hypothesis (UOH). While this idea has intuitive appeal, it runs counter to the equally obvious importance of partisanship in shaping fan interest in sporting contests. The absence of a well-accepted theoretical basis for the UOH, coupled with a lack of compelling empirical evidence in support of it, suggests important gaps in the literature. This paper takes a step toward addressing the former need by offering a contest utility function, based on standard Cobb-Douglas preferences, which embodies both partisanship and a demand for competitive balance. The model is used to derive a willingness-to-pay function for game tickets and an expression for aggregate attendance. Findings from the empirical literature are discussed in light of the analysis.

Endogenous timing and income inequality in the voluntary provision of public goods: Theory and experiment

AbstractThis study theoretically and experimentally investigates the effects of income inequality on donors' decisions regarding timing choices and contributions to public goods when contribution timing is endogenously chosen by contributors. To this end, we use the conventional voluntary provision models of Warr (1983) and Bergstrom, Blume and Varian (1986), with Cobb–Douglas preferences augmented with a two‐stage game of Hamilton and Slutsky (1990). The following results were obtained and experimentally confirmed. First, when the distribution of income is extremely unequal, donors are indifferent between the simultaneous and sequential moves in the contribution game. Second, as income inequality is decreased, the simultaneous‐move contribution game is likely to emerge because every donor prefers to act as a leader. Nevertheless, a higher‐income donor may also prefer to act as a follower without specific social preferences and uncertainty regarding the quality of public goods. Third, most theoretical predictions regarding timing decisions are supported in our laboratory experiment, provided that the participants had enough time to learn the consequences of their timing choices.

A New Characterization of Cobb-Douglas Preferences under Weber’s Law

A New Characterization of Cobb-Douglas Preferences under Weber’s Law

Distributional policy impacts, WTP-WTA disparities, and the Kaldor-Hicks tests in benefit-cost analysis

I examine how inequality in the distribution of income and a quasi-fixed good (e.g. environmental quality) can affect the disparity between aggregate willingness to accept (WTA) and willingness to pay (WTP) for policies that induce joint, nonmarginal and heterogeneous changes to income and the quasi-fixed good. These disparities can generate divergent conclusions from benefit-cost analysis (BCA). With Cobb-Douglas preferences, I show that greater inequality in policy impacts to the quasi-fixed good generally increases the range of conflicting conclusions from BCA using the Kaldor criterion (compensating variation) versus the Hicks criterion (equivalent variation). In two examples, I show that for any set of impacts to the quasi-fixed good there exists a degree of inequality in which the Kaldor-Hicks tests disagree. This disagreement arises because, with inequality, seemingly marginal policy changes can become nonmarginal when concentrated among marginalized or privileged groups, which can widen the gap between aggregate WTP and WTA. With CES preferences, when the goods are complements, WTA may be infinite, and when they are substitutes, budget constraints attenuate WTP: Both effects push the Kaldor-Hicks tests in opposing directions. I conclude that greater inequality increases the relevance of questioning whether to elicit WTP or WTA in nonmarket valuation for BCA.

Existence, uniqueness, and comparative statics of Nash equilibrium in a game of voluntary public good provision with two public goods

AbstractThis paper shows the uniqueness of a Nash equilibrium in the presence of many heterogeneous players with two public goods under Cobb–Douglas preferences. It provides a sufficient condition for a unique equilibrium including contributors providing both public goods, and shows that contributors providing both public goods appear frequently. This uniqueness property allows us to conduct a comparative statics analysis with a contributor and a free rider of both public goods, showing the role of the contributor providing both public goods.

Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market

Abstract In this paper, we investigate how pollution changes with preferences, focusing on a finite bilateral oligopoly model where agents have asymmetric Cobb-Douglas preferences. Producers are also consumers and the choice of heterogeneous preferences is related to the psychological foundations and identity aspects of group membership. We compare two strategic equilibria: the Stackelberg-Cournot equilibrium with pollution (SCEP) and the Cournot equilibrium with pollution (CEP). We show that considering the asymmetric preferences helps the public decision-maker to identify precisely the category of agents (consumer–producers or pure-consumers) for which a change in environmental preference parameters will most effectively reduce pollution. Furthermore, we find that firms’ emissions’ elasticity decreases with market power (when the market power increases) if their marginal cost is lower than their competitor. Finally, we show that when producers are also consumers, an action on pure-consumers’ preference parameters reduces more emissions than a similar action on consumer–producers, and this regardless of the timing of interaction.

Welfare targeting in networks

This paper investigates welfare targeting for public goods in networks. First, we show that a tax/subsidy scheme (not necessarily budget-balanced) affects each consumer only insofar as it affects his neighbourhood. Second, we show that either a Pareto-improving income redistribution can be found or there exist Negishi weights, which we relate to the network structure. Third, in the case of Cobb–Douglas preferences, we show that a Law of Welfare Targeting holds and links two well-known notions of the comparative statics of policy interventions: neutrality and welfare paradoxical effects. Collectively, our findings uncover the importance of the −1 eigenvalue to economic and social policy: it is an indication of how consumers absorb the impact of income redistribution.

Cournot Duopoly Games: Models and Investigations

This paper analyzes Cournot duopoly games that are constructed based on Cobb–Douglas preferences. We introduce here two models whose dynamic adjustments depend on bounded rationality, dynamic adjustment, and tit-for-tat mechanism. In the first model, we have two firms with limited information and due to that they adopt the bounded rationality mechanism. They update their productions based on the changing occurred in the marginal profit. For this model, its fixed point is obtained and its stability condition is calculated. In addition, we provide conditions by which this fixed point loses its stability due to flip and Neimark–Sacker bifurcations. Furthermore, numerical simulation shows that this model possesses some chaotic behaviors which are recovered due to corridor stability. In the second model, we handle two different mechanisms of cooperation. These mechanisms are dynamic adjustment process and tit-for-tat strategy. The players who use the dynamic adjustment increase their productions based on the cooperative output while, in tit-for-tat mechanism, they increase the productions based on the cooperative profit. The local stability analysis shows that adopting tit-for-tat makes the model unstable and then the system becomes chaotic for any values of the system’s parameters. The obtained results show that the dynamic adjustment makes the system’s fixed point stable for a certain interval of the adjustment parameter.

Advantageous leadership in public good provision: the case of an endogenous contribution technology

From the perspective of standard public good theory the total amount of greenhouse gas mitigation (or public good supply in general) will be lower in a leader–follower (Stackelberg) game than in a simultaneous Nash game so that strategic leadership is disadvantageous for climate policy. We show that this needs no longer be true when the leading country has the option to employ a technology by which it can reduce its abatement costs and thus improve the productivity of its contribution technology. Then both countries also are better off in the Stackelberg game than in the Nash game. Our general result is illustrated by an example with Cobb–Douglas preferences and, finally, an empirical application to global climate policy is briefly discussed.

Sticker Shocks: Using VAT Changes to Estimate Upper-Level Elasticities of Substitution

We estimate the upper-level elasticity of substitution between goods and services of a nested aggregate CES preference specification. We show how this elasticity can be derived from the long-run response of the relative price of a good to a change in its VAT rate. We estimate this elasticity using new data on changes in VAT rates across 74 goods and services for 25 European Union countries from 1996 through 2015. Depending on the level of aggregation, we find a VAT pass-through rate between 0.4 and 0.7. This implies an upper-level elasticity of 3, at the lowest level of aggregation with 74 categories, and 1 (Cobb–Douglas preferences) at a high level of aggregation that distinguishes 10 categories of goods and services.

Endogenous Timing and Income Inequality in the Voluntary Provision of Public Goods: Theory and Experiment

This paper investigates how the heterogenous incomes and preferences of potential donors affect the timing of contribution decisions when it is endogenously determined by contributors themselves. More specifically, we use a simple setting with two donors, Cobb-Douglas preferences, and complete information to investigate how income inequality affects the endogenous choices of contribution timing and the level of the voluntary supplied public goods. This paper obtains the following results. First, when income is extremely unequal, potential contributors are indifferent between the timing choices of simultaneous and sequential moves, even if they have different preferences towards a public good. Second, as income inequality decreases, the simultaneous move-game is increasingly likely to emerge, because all potential contributors prefer to act as a leader. Third, in the presence of multiple public goods, contributors with higher valuations for one public good tend to be first contributors to that one. Fourth, these theoretical predictions regarding the timing decisions of individuals are not supported by the laboratory experiment, although those regarding individuals’ contribution decisions are consistent with the experimental results.

Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games: Replacement Function Approach

This study shows the uniqueness of Nash equilibrium in the model of multiple voluntarily supplied public goods with potential contributors possessing different Cobb-Douglas preferences. This study provides a sufficient condition for uniqueness using graph theory. This sufficient condition allows us to use the replacement function approach of Cornes and Hartley (2007) not only to develop an algorithm for identifying free riders, but also to provide an alternative proof for the uniqueness of a Nash equilibrium in multiple public goods models.

Sticker shocks: using VAT changes to estimate upper-level elasticities of substitution

We estimate the upper-level elasticity of substitution between goods and services of a nested aggregate CES preference specification. We show how this elasticity can be derived from the long-run response of the relative price of a good to a change in its VAT rate. We estimate this elasticity using new data on changes in VAT rates across 74 goods and services for 25 E.U. countries from 1996 through 2015. Depending on the level of aggregation, we find a VAT pass-through rate between 0.4 and 0.7. This implies an upper-level elasticity of 3, at the lowest level of aggregation with 74 categories, and 1 (Cobb-Douglas preferences) at a high level of aggregation that distinguishes 10 categories of goods and services.

Psychophysical foundations of the Cobb–Douglas utility function

Relying on a literal interpretation of Weber’s law in psychophysics, we show that a simple condition of independence across good categories implies the Cobb–Douglas preferences.

Pairwise Normalization: A Neuroeconomic Theory of Multi-Attribute Choice

We present a theory of multi-attribute choice founded in the neuroscience of perception. According to our theory, valuation is formed through a series of pairwise, attribute-level comparisons implemented by (divisive) normalization — a normatively-grounded form of relative value coding observed across sensory modalities and in species ranging from honeybees to humans. As we demonstrate, “pairwise normalization” captures a broad range of behavioral regularities, including the compromise and asymmetric dominance effects, the diversification bias in allocation decisions, and majority-rule preference cycles (among several others). The model also offers a potential neurobiological foundation for Cobb-Douglas preferences and other classic microeconomic preference representations.

Advantageous Leadership in Public Good Provision: The Case of an Endogenous Contribution Technology

From the perspective of standard public good theory the total amount of greenhouse gas mitigation (or public good supply in general) will be lower in a leader-follower game than in a simultaneous Nash game so that strategic leadership is disadvantageous for climate policy. We show that this need no longer be true when the leading country has the option to employ a technology by which it can reduce its abatement costs and thus improve the productivity of its contribution technology. Our general result is illustrated by an example with Cobb-Douglas preferences and, finally, an empirical application to global climate policy is briefly discussed.

Psychophysical Foundations of the Cobb-Douglas Utility Function

Relying on a literal interpretation of Weber's law in psychophysics, we show that a simple condition of independence across good categories implies the Cobb-Douglas preferences.

Growth in Illyria: The role of meritocracy in the accumulation of human capital

In this paper we present a dynamic model of cooperative production with human capital accumulation. We assume CES preferences on consumption and leisure in each period. When agents do not care about future generations, sustained growth occurs iff the elasticity of substitution between consumption and leisure is larger or equal than one. Meritocracy always has a positive effect on output, but when the elasticity of substitution is less than one, is only a level effect. When agents care about future generations, under Cobb–Douglas preferences in each period and some extra conditions, there is constant growth at a rate that is larger than the one when future generations do not count. For any discount rate between generations, there is a unique level of meritocracy for which efficiency is achieved.

Growth in Illyria: The Role of Meritocracy in the Accumulation of Human Capital

In this paper we present a dynamic model of cooperative production with human capital accumulation. We assume CES preferences on consumption and leisure in each period. When agents do not care about future generations, sustained growth occurs if the elasticity of substitution between consumption and leisure is larger or equal than one. Meritocracy always has a positive effect on output, but when the elasticity of substitution is less than one, is only a level effect. When agents care about future generations, under Cobb-Douglas preferences in each period and some extra conditions, there is constant growth at a rate that is larger than the one when future generations do not count. For any discount rate between generations, there is a unique level of meritocracy for which efficiency is achieved.

Discrete dynamics in a two-country model with a durable good

In this paper, we extend Doi et al. (2007) in the sense that households in both countries consume a durable good. Although this generalization makes the model much complicate, it will be shown that under the standard Cobb–Douglas preferences, the model has a unique steady state and saddle-point stability.