Luxury Prices: an Expository Note*

Economists generally associate the redistribution of resources with the apparatus of taxes and transfer payments. Such redistributions are done by the power of the authorities. However, resources are redistributed by other means as well. People give away income in a variety of ways, deliberate and unintentional. In this paper, agents transfer consumption goods in return for a good which lacks material qualities and affects their preferences because it has “value”. An example of a real life commodity without intrinsic value is diamonds. The standard consumption value of a diamond is low, especially as artificial diamonds look the same as real ones to the naked eye. Many luxury goods such as art pieces have similar characteristics. Owning a house in a “rich” area could have extra benefits in consumption and, yet, one important motivation is simply to live in an expensive neighborhood. By holding such a good an agent refrains from acquiring resources that he could consume and, thus, frees resources for other agents. Our thinking on this issue originates from a naive question. Why are wealthy people striving to be wealthier? It is quite absurd to think that rich people wish to increase the consumption of standard goods as assumed in the classical consumer model. Indeed, by acquiring an expensive diamond or an original piece of art, a consumer demonstrates his avoidance of consumption. We construct and analyse an elementary competitive equilibrium model in which the value of “useless” jewels enter the preferences of consumers. We show that if jewels are scarce, they can trade at a positive price despite having no intrinsic utility. Under fairly natural assumptions, a positive price equilibrium redistributes consumption from the rich to the poor. Thus, the model demonstrates the common wisdom that the existence of luxury goods can have a positive effect on income distribution. This paper is mainly expository. The idea of consumption goods lacking intrinsic value and of prices entering directly the utility functions is not original. Veblen (1899) pointed out that some goods are consumed by some people for reasons not connected with their intrinsic values. Veblen referred to consumption intended to impress and to signal wealth as conspicuous consumption. Arrow and Hahn (1971) (see also Kalman, 1968) discussed a general equilibrium model in which agents care not only about the consumption but also about the price vector. Under standard assumptions, they proved existence of competitive equilibrium. In our