Invisible hand at consumption-leisure production possibility frontier: the allocation of time between goods and services under wage and price dispersions.

Malakhov, Sergey (2020): Invisible hand at consumption-leisure production possibility frontier: the allocation of time between goods and services under wage and price dispersions. Published in: 68th AFCE Congress No. Lille (8 June 2021)

Abstract

If the equilibrium price is equal to the lowest willingness to pay of consumers with zero search costs, it accumulates under price dispersion the willingness to sell of consumers with positive search costs. The satisficing searcher buys at a low price, which unintentionally equalizes marginal costs of his search with its marginal benefit and maximizes his consumption-leisure utility with regard to the equilibrium price. Labor and search costs are unit elastic with respect to the quantity demanded. Suboptimal choices reproduce initial corner solutions; satisficing purchases become optimal; consumers either buy optimally or quit the market. The producer’s knowledge is limited by the quantity demanded, but he meets the consumer with a price, like he knows in advance his willingness to pay and the time spent on search. The consumption-leisure production possibility frontier optimally allocates his time between production and delivery; it determines not only the price for the quantity demanded, but also the meeting point, where the producer stops consumer’s search and sells him goods with leisure. Being unaware of how much the consumer has spent on labor and search, the producer unintentionally optimizes his consumption-leisure choice. The transformation of producer’s time into consumer’s leisure time discovers the rate of their mutual interest or their gravitation, where its force is directly proportional to the product of quantity supplied and quantity demanded, and inversely proportional to the product of times the parties to the transaction have spent on it.

• Item Type: MPRA Paper
• Language: English
• Keywords: invisible hand, consumption-leisure choice, production possibility frontier, search, price dispersion, gravitation
• Subjects: D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

References

Arrow, K. (1985) ‘The Potentials and Limits to the Market in Resource Allocation’, 107-124. In Issues in Contemporary Economics, George R.Feiwel (eds.), Springer, 510 p.

Aguiar M., Hurst E. (2007a) ‘Measuring Trends in Leisure: The Allocation of Time over Five Decades’, Quarterly Journal of Economics, 122(3), 969-1006.

Aguiar M., Hurst E. (2007b) 'Life-Cycle Prices and Production, American Economic Review, 97,5,1533-1559.

Baye,M., Morgan,J., Sholten, P. (2006) ‘Information, Search, and Price Dispersion’ In: Economics and Information Systems, Vol.1, T.Hendershott (Eds.).Amstersdam: Elsevier, 323-376.

Berninghaus, S., Güth, W., Levati, V., Qiu, J. (2011) ‘Satisficing search versus aspiration adaptation in sales competition: experimental evidence.’ International Journal of Game Theory, 40, 179-198.

Chade, H., Eeckhout,J., Smith, L. (2017) ‘Sorting through Search
and Matching Models in Economics.’ Journal of Economic Literature, LV (June), 493-544.

Diamond, P. (1987) ‘Consumer Differences and Prices in a Search Model’, Quarterly Journal of Economics, 102,429-436.

Lancaster, K.J. (1966) ‘A New Approach to Consumer Theory.’ Journal of Political Economy, 74, April, 132-157.

Kunst, A. (2019) 'Grocery shopping: U.S. households' frequency by income 2017', Statista, Sep. 3.

Lester, B., Visschers, L., Wolthoff, R. (2015). ‘Meeting Technologies and Optimal Trading Mechanisms in Competitive Search Markets.’ Journal of Economic Theory 155, 1–15.

Macfie, A.L. (2003). 'The Individual in Society: Papers on Adam Smith.' London: Routledge, 168 p.

Malakhov, S. (2016) ‘Law of One Price Under Equilibrium Price Dispersion: arbitrage and optimization of search’, Journal of Institutional Studies, 8 (1),85-99.

Malakhov, S. (2018). 'Self-organization of Imperfect Markets under Equilibrium Price Dispersion: invisible hand against conspicious consumption.' Journal of Institutional Studies, 10 (2), 6-25.

Malakhov, S. (2019) 'Willingness to Take Care of Good Cars: from the theorem of lemons to the Coase theorem.' Paper presented at the 68th AFSE Congress, Orléans 2019, June 17-19.

Malakhov, S. (2020a) 'Consumers' Diligence as a Natural Way to Cope with Externalities: from the Coase theorem to the invisible hand.' Journal of Institutional Studies, 12(1), 38-65.

Malakhov, S. (2020b). ‘Proof of the Invisible Hand: Why the satisficing purchase becomes optimal?’ Terra Economicus, 18(2), 70–94.

McCall, B., McCall, J. (2007) ‘The Economics of Search.’ London and NY: Routledge, 576 p.

Oslington, P. (2011) ‘God and the Market: Adam Smith’s Invisible Hand.’ Journal of Business Ethics 108, 4, 429-438.

Qingmin, L., Mailath, G., Postlewaite, A., Samuelson, L. (2014). ‘Stable Matching with Incomplete Information.’Econometrica 82 (2), 541–87.


Sen, A. (2009) ‘Introduction. The Theory of Moral Sentiments. By Adam Smith. 6th ed. 1790.’ New York: Penguin, 2009, vii–xxix.

Shlefer, J. (2012) 'There Is No Invisible Hand.' Harvard Business Review, April 10.\

Slutsky, E. (2010) ‘Slutckij E. Ekonomicheskie i statisticheskie proizvedeniya.’ Moscow: Eksmo, 1152 p.

Smith, A. . (1976). ‘An inquiry into the nature and causes of the wealth of nations’ (R. H. Campbell, A. S. Skinner, & W. B. Todd, Eds.). Oxford: Oxford University Press.

Stahl, D. O. (1989) ‘Oligopolistic Pricing with Sequential Consumer Search.’ American Economic Review, 79(4),700–712.

Stigler, G. (1961) ‘The Economics of Information.’ Journal of Political Economy, 69(3), 213-225.

Stiglitz, J. E. (2002). ‘There is no invisible hand.’ The Guardian, Friday 20 December.