Cobb-Douglas Preferences Research Articles

Wage and Labor Supply: A Simple Model to Explain Some Empirical Findings

Research about labor supply with flexible hours generates some conflicted findings and raises debate — which model is better, intertemporal neoclassical or reference-dependent preferences? This paper provides the third solution — static neoclassical. Specifically, a simple model with Cobb-Douglas preferences, incorporating fixed cost and narrow bracketing of decisions, is provided. This model is able to explain the seemingly conflicted results in several renowned papers.

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With the democratization of cloud and datacenter computing, users increasingly share large hardware platforms. In this setting, architects encounter two challenges: sharing fairly and sharing multiple resources. Drawing on economic game-theory, we rethink fairness in computer architecture. A fair allocation must provide sharing incentives (SI), envy-freeness (EF), and Pareto efficiency (PE). We show that Cobb-Douglas utility functions are well suited to modeling user preferences for cache capacity and memory bandwidth. And we present an allocation mechanism that uses Cobb-Douglas preferences to determine each user's fair share of the hardware. This mechanism provably guarantees SI, EF, and PE, as well as strategy-proofness in the large (SPL). And it does so with modest performance penalties, less than 10\% throughput loss, relative to an unfair mechanism.

REF

With the democratization of cloud and datacenter computing, users increasingly share large hardware platforms. In this setting, architects encounter two challenges: sharing fairly and sharing multiple resources. Drawing on economic game-theory, we rethink fairness in computer architecture. A fair allocation must provide sharing incentives (SI), envy-freeness (EF), and Pareto efficiency (PE). We show that Cobb-Douglas utility functions are well suited to modeling user preferences for cache capacity and memory bandwidth. And we present an allocation mechanism that uses Cobb-Douglas preferences to determine each user's fair share of the hardware. This mechanism provably guarantees SI, EF, and PE, as well as strategy-proofness in the large (SPL). And it does so with modest performance penalties, less than 10\% throughput loss, relative to an unfair mechanism.

On Cobb-Douglas Preferences in Bilateral Oligopoly

Les préférences de type Cobb-Douglas en oligopole bilatéral L’oligopole bilatéral est une structure de marché dans laquelle un nombre fini de vendeurs cherchent à échanger les biens qu’ils possèdent contre de la monnaie détenue par un nombre fini d’acheteurs. Lorsque les échanges sont organisés dans le contexte d’un jeu stratégique de marché, l’oligopole bilatéral peut être analysé comme un jeu de marché divisé en deux sous-jeux liés. Fixons d’abord la quantité des stratégies agrégées des acheteurs à B ; dans le premier jeu partiel la quantité offerte agrégée à l’équilibre est alors donnée par . Fixons ensuite la quantité offerte agrégée à X ; dans le deuxième jeu partiel, la stratégie d’achat agrégée est donc donnée par . Ces deux jeux partiels prennent en considération, dans chaque cas, les interactions au sein d’un même côté du marché. Or, le marché d’oligopole bilatéral met aussi en évidence des interactions entre les deux côtés de ce marché, et l’équilibre requiert notamment . Lorsque tous les agents ont des préférences représentées par des fonctions d’utilité de type Cobb-Douglas, ne dépend pas de B et ne dépend pas de X ; il n’y a donc pas d’interdépendance stratégique entre les agents appartenant aux deux côtés du marché. Le cas d’une économie Cobb-Douglas fournit un cadre d’analyse utile pour étudier l’échange stratégique mais ne peut rendre compte de toutes les propriétés de l’échange en oligopole bilatéral. Certaines de ces propriétés sont étudiées dans l’article. Classification JEL : C72; D43; D50.1.

On Cobb-Douglas Preferences in Bilateral Oligopoly

SummaryBilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two “partial games”. First, fix the aggregate bid at B; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is (B). Next, fix the aggregate supply at X; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is (X). The analysis of these two partial games takes into account competition within each side of the market. Equilibrium in bilateral oligopoly must take into account competition between sellers and buyers and requires, for example, ((B)) = B. When all traders have Cobb-Douglas preferences (B) does not depend on B and (X) does not depend on X: whilst there is competition within each side of the market there is no strategic interdependence between the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated.

Cobb-Douglas preferences under uncertainty

This paper axiomatizes Cobb-Douglas preferences under uncertainty. First, we extend the original Trockel (Econ Lett 30:7–10, 1989)’s axiomatic foundation to a general state space framework based on the Strong Homotheticity Axiom, obtaining also the incomplete case a la Bewley (Decis Econ Financ 25:79–110, 2002). We show that this key axiom for the Cobb-Douglas expected utility specification is refuted by Ellsberg’s uncertainty aversion behavioral pattern. Our main result provides a set of meaningful axioms characterizing Cobb-Douglas min-expected utility preferences, an important class of uncertainty averse preferences for studying the consequences of ambiguity in finance and other fields. Finally, we present briefly how to obtain more general representations like the variational case.

Wealth effects and countercyclical net exports

Two-country, one-good business cycle models with Cobb–Douglas preferences predict procyclical net exports. The opposite is observed in the data. We show that introduction of preferences that eliminate wealth effects on labour supply remedies this discrepancy. It also improves the model's ability in matching cross-country correlations.

The DM and the Ossi Consumer: Price Indexes During Transition

Family budget data for East and West Germany over the past decade are analyzed in the light of the convergence of relative price structures and the elimination of quantity constraints in the East during the process of eastern economic reconstruction. Exact cost-of-living indexes for generalized Cobb-Douglas preferences are calculated for the missing (index) link between the end of the old German Democratic Republic and the beginning of German economic unification. Exact deflators are provided for the period 1989 through 1998 for low to high income family budgets.

Immiserizing Growth and the Metzler Paradox in the Ricardian Model

Conditions for the occurrence of immiserizing growth and the Metzler paradox are analysed in the Ricardian model when consumers in the foreign country have Leontief preferences while consumers in the home country have Cobb-Douglas preferences. By using specific functional forms, the conditions for the occurrence of the two paradoxes are defined in terms of the exogenous parameters of the model rather than endogenous variables such as the foreign import demand elasticity in the conditions of Bhagwati (1958) and Metzler (1949a, b). It is shown that the simultaneous occurrence of both paradoxical results is possible for some parameter values.

Labor, Output and Consumption in Business Cycle Models of Emerging Economies

Motivated by the fact that, over the business cycle, labor dynamics in emerging economies differ in nontrivial ways from those observed in developed economies, we assess the relative importance of trend shocks in emerging economies in the business cycle model of Aguiar and Gopinath (2007) when labor data is explicitly taken into account. We study Mexico and Canada as representatives of emerging and developed economies, respectively. We find for Mexico that, in the benchmark case with Cobb-Douglas preferences, the income effect on consumption of trend shocks is too strong, delivering countercyclical and counterfactual fluctuations in employment. The model faces a trade-off between, on the one hand, having sizeable growth shocks, thereby having a good match in terms of relatively high consumption volatility, and, on the other, having procyclical employment dynamics. This is remedied when both quasilinear preferences are assumed and the econometric identification strategy explicitly takes into consideration labor dynamics. In this case trend shocks continue to be relatively stronger in emerging economies. Additionally, we find that differences in labor dynamics across emerging and developing economies are associated with the relatively large informal labor sector in emerging economies. It is in this dimension, when trying to match the dynamics of formal employment, that we find less evidence supporting an important role of trend shocks as being the main driving force of business cycles in emerging economies.

Note on social choice allocation in exchange economies with Cobb–Douglas preferences

We show that in a pure exchange economy with two agents and a finite number of goods, there exists no strategy-proof, Pareto-efficient, and non-dictatorial social choice allocation function on any local Cobb–Douglas preference domain. This is a slight extension of a result proved by Hashimoto (2008).

Household expenditures, wages, rents

New evidence from the 1980, 1990, and 2000 Decennial Census of Housing indicates that expenditure shares on housing are constant over time and across US metropolitan statistical areas (MSA). Consistent with this observation, we consider a model in which identical households with Cobb–Douglas preferences for housing and non-housing consumption choose a location and locations differ with respect to income earned by their residents. The model predicts that the relative price of housing of any two MSAs disproportionately reflects differences in incomes of those MSAs and is independent of housing supply in each MSA. According to the predictions of our calibrated model, the dispersion of rental prices across low- and high-wage MSAs should be larger than we observe: High-wage MSAs like San Francisco are puzzlingly inexpensive relative to low-wage MSAs like Pittsburgh.

Intergenerational Risk Sharing and Labour Supply in Collective Funded Pension Schemes with Defined Benefits

In many countries, collective funded pension schemes with defined benefits (DB) are being replaced by individual schemes with defined contributions. Collective funded DB pensions may indeed reduce social welfare. This will be the case when the schemes feature income-related contributions that distort the labour-leisure decision. However, these schemes also share risks between generations. This adds to welfare if these risks cannot be traded on capital markets. This paper compares the welfare gains from intergenerational risk sharing with the welfare losses that are due to labour market distortions. We adopt a two-period overlapping-generations model for a small open economy with risky returns to equity holdings. We derive analytically that the gains dominate the losses for the case of Cobb-Douglas preferences between labour and leisure. Numerical simulations for the more general CES case confirm these findings which also withstand a number of other model modifications, like the introduction of a short-sale constraint for households and the inclusion of a labour income tax. These results suggest that collective funded schemes with well-organized risk sharing are preferable over individual schemes, even if labour market distortions are taken into account.

Ecological discounting

Which rates should we use to discount costs and benefits of different natures at different time horizons? We answer this question by considering a representative agent consuming two goods whose availability evolves over time in a stochastic way. We extend the Ramsey rule by taking into account the degree of substitutability between the two goods and of the uncertainty surrounding the economic and environmental growths. The rate at which environmental impacts should be discounted is in general different from the one at which monetary benefits should be discounted. We provide arguments in favor of an ecological discount rate smaller than the economic discount rate. In particular, we show that, under certainty and Cobb–Douglas preferences, the difference between the economic and the ecological discount rates equals the difference between the economic and the ecological growth rates. Using data about the link between biodiversity and economic development, I estimate that the rate at which changes in biodiversity should be discounted is 1.5%, whereas changes in consumption should be discounted at 3.2%.

Strategy-proofness versus efficiency on the Cobb-Douglas domain of exchange economies

In this paper we prove that in pure exchange economies with two agents and a finite number of goods, a social choice function on the Cobb-Douglas preference domain is strategy-proof and Pareto-efficient if and only if it is dictatorial. Indeed, we can establish substantially stronger results that are the impossibilities on any arbitrarily small 1-dimensional intervals of Cobb-Douglas preferences.

Skills Distribution, Migration and Wage Differences in Pure Service-Exchange Economy

This paper considers an economy with skilled agents exchanging their services. Using Cobb-Douglas preferences, the paper shows that there exists an optimal (average welfare maximizing) skills' distribution. This optimal distribution is independent of productivity and is welfare equalizing. If the skill-distribution is not optimal, then some agents are better-off than others. In such a scenario, migration in some sectors is average-welfare improving while inviting skilled-agents in others reduces average welfare. Productivity increase of worse-o sector without changing the overall skills' composition of economy increases the wage gap.

On the role of public debt in an OLG model with endogenous labor supply

This paper argues that some propositions reported in a recent paper by [Fanti., L., Spataro, L., 2006. Endogenous labor supply in Diamond’s (1965) OLG model: A reconsideration of the debt role. Journal of Macroeconomics 28, 28–438] are not warranted. They claim that including an endogenous labor supply in an overlapping generations model may change the conclusions concerning the capital accumulation and welfare effects of (internal) public debt issue. We show that their results are not the consequence of the Cobb–Douglas preferences they posit, but of a rather incomplete development of their model. When this incompleteness is corrected, and under general assumptions on preferences and technology, the propositions arrived at originally by [Diamond, P.A., 1965. National debt in a neoclassical growth model. American Economic Review 55, 1126–1150] in a model that does not take the labor–leisure decision into account continue to hold. In particular, no matter whether the starting point is a dynamically efficient or inefficient steady state, an increase in the stock of public debt per taxpayer unambiguously depresses the capital–labor ratio and raises the interest rate. Moreover, the welfare level will increase (decrease) when the starting point is a dynamically inefficient (efficient) steady state.

Sudden Stops and Output Drops: Can Theory Link the Two?

Empirical literature overwhelmingly suggest that sudden stops lead to output drops. Can general equilibrium theory predict this link or is it theoretically impossible for sudden stops to generate output drops by themselves as other studies suggest? In this paper we contend that the answer depends on the response of labor to a sudden stop which in turn depends on the type of preference specification used. To this end, we use a small open economy model where agents face a constraint on foreign borrowing and a sudden stop occurs due to an abrupt tightening of the borrowing constraint. We find that under Cobb-Douglas preferences, the dominant wealth e¤ect of a sudden stop leads to labor increases which in turn generates an output increase as opposed to a drop! In contrast, under GHH preferences that by construction eliminate the wealth effect, a sudden stop leads to declines in future capital and labor supply leading to drops in output. We find empirical support of our conclusion in data from a sample of emerging economies where labor declined significantly in the aftermath of a sudden stop.

Engel’s What? A Response to Gan and Vernon

Previous articleNext article No AccessCommentsEngel’s What? A Response to Gan and VernonAngus Deaton and Christina PaxsonAngus DeatonPrinceton University Search for more articles by this author and Christina PaxsonPrinceton University Search for more articles by this author Princeton UniversityPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Journal of Political Economy Volume 111, Number 6December 2003 Article DOIhttps://doi.org/10.1086/378535 Views: 105Total views on this site Citations: 17Citations are reported from Crossref © 2003 by The University of Chicago. All rights reserved. PDF download Crossref reports the following articles citing this article:K. V. Kuznetsov Monitoring of The Consumption Level for Sustainable Development Goals, Statistics and Economics 19, no.11 (Mar 2022): 18–27.https://doi.org/10.21686/2500-3925-2022-1-18-27John Gibson, Bonggeun Kim Economies of scale, bulk discounts, and liquidity constraints: comparing unit value and transaction level evidence in a poor country, Review of Economics of the Household 16, no.11 (Sep 2017): 21–39.https://doi.org/10.1007/s11150-017-9388-7Thomas F. Crossley, Yuqian Lu Returns to scale in food preparation and the Deaton–Paxson puzzle, Review of Economics of the Household 16, no.11 (Dec 2017): 5–19.https://doi.org/10.1007/s11150-017-9399-4Federico Gutierrez A Sharing Model of the Household: Explaining the Deaton-Paxson Paradox and Computing Household Indifference Scales, SSRN Electronic Journal (Jan 2018).https://doi.org/10.2139/ssrn.3098290Eve Colson-Sihra, Clement Bellet The Conspicuous Consumption of the Poor: Forgoing Calories for Aspirational Goods, SSRN Electronic Journal (Jan 2018).https://doi.org/10.2139/ssrn.3270814Maneka Jayasinghe, Andreas Chai, Shyama Ratnasiri, Christine Smith The power of the vegetable patch: How home-grown food helps large rural households achieve economies of scale & escape poverty, Food Policy 73 (Dec 2017): 62–74.https://doi.org/10.1016/j.foodpol.2017.09.005Donald F. Vitaliano A note on the ‘food paradox’: some contradictory evidence, Review of Economics of the Household 13, no.44 (Jun 2013): 1043–1053.https://doi.org/10.1007/s11150-013-9206-9José Heleno Faro Cobb-Douglas preferences under uncertainty, Economic Theory 54, no.22 (Jan 2013): 273–285.https://doi.org/10.1007/s00199-012-0738-7Alejandrina Salcedo, Todd Schoellman, Michèle Tertilt Families as roommates: Changes in U.S. household size from 1850 to 2000, Quantitative Economics 3, no.11 (Mar 2012): 133–175.https://doi.org/10.3982/QE76TREVON D. LOGAN ECONOMIES OF SCALE IN THE HOUSEHOLD: PUZZLES AND PATTERNS FROM THE AMERICAN PAST, Economic Inquiry 49, no.44 (Mar 2010): 1008–1028.https://doi.org/10.1111/j.1465-7295.2009.00240.xR. Godoy, E. A. Undurraga, D. Wilkie, V. Reyes-García, T. Huanca, W. R. Leonard, T. McDade, S. Tanner, V. Vadez, The effect of wealth and real income on wildlife consumption among native Amazonians in Bolivia: estimates of annual trends with longitudinal household data (2002-2006), Animal Conservation 13, no.33 (Nov 2010): 265–274.https://doi.org/10.1111/j.1469-1795.2009.00330.xDavid Jacobson, Petroula M. Mavrikiou, Christos Minas Household size, income and expenditure on food: The case of Cyprus, The Journal of Socio-Economics 39, no.22 (Apr 2010): 319–328.https://doi.org/10.1016/j.socec.2009.12.009Timothy J. Halliday Mismeasured Household Size and its Implications for the Identification of Economies of Scale, Oxford Bulletin of Economics and Statistics 72, no.22 (Apr 2010): 246–262.https://doi.org/10.1111/j.1468-0084.2009.00570.xPeter Lanjouw, Rinku Murgai Poverty decline, agricultural wages, and nonfarm employment in rural India: 1983-2004, Agricultural Economics 40, no.22 (Mar 2009): 243–263.https://doi.org/10.1111/j.1574-0862.2009.00373.xSanae Tashiro Differences in Food Preparation by Race and Ethnicity: Evidence from the American Time Use Survey, The Review of Black Political Economy 36, no.3-43-4 (Jan 2009): 161–180.https://doi.org/10.1007/s12114-009-9045-3Federico Perali The second Engel law: Is it a paradox?, European Economic Review 52, no.88 (Nov 2008): 1353–1377.https://doi.org/10.1016/j.euroecorev.2008.01.005John Gibson, Bonggeun Kim Measurement Error in Recall Surveys and the Relationship between Household Size and Food Demand, American Journal of Agricultural Economics 89, no.22 (May 2007): 473–489.https://doi.org/10.1111/j.1467-8276.2007.00978.x

Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting

The purpose of this paper is to show how conjectural variations can be derived as a reduced form in an infinitely repeated game of private provision of public goods. We obtain explicit closed forms of conjectural variations associated with maximal sustainable equilibria in which the sum of the utilities of all of a community's members is maximized for both quadratic and Cobb–Douglas preferences, provided that the resulting sequence of contributions can be sustained as a Nash (or subgame perfect) equilibrium in the underlying repeated game. We also show that positive conjectural variations will emerge as long as people place positive weight on the future, and that those conjectures are positively related to the discount factor.