The Economics of Superstars, Sherwin Rosen
In certain kinds of eco activity there is concentration of output among few individuals. For ex:
1) The capacity for television to produce high incomes, comedians earn much more than before and it cannot be said that there’s been an increase in the demand of comic relief.
2) The first rank classical performers have substantial difference income with those in second rank, even when consumers would have difficult detecting the difference.
In these and other examples there are 2 common elements: there is a close connection btwn personal reward and the size of one’s own market and second, a strong tendency for market size and reward to be skewed toward the most talented people in the activity. Recognition that one’s personal market is important has a long history, but the idea has not been developed extensively. The analytical framework used is a special type of assignment problem (the marriage of buyers to sellers). The distribution of talent is assumed to be fized in the population of potential sellers and costlessly observable, if m is the size of market and p the price, the overall market equilibrium is a pair of functions p(q) and m (q) indicating price and market size of sellers of every observable talent and a domain of q such that all sellers max profit and cannot earn larger amounts in other activities and all buyers max utility and cannot improve themselves by purchasing from another seller.
Sellers max net revenue functions R (q) is convex. Since it is the transformation that takes the distribution of talent to the distribution of rewards, it implies that the income distribution is stretched out in its right had tail (compared to the distribution of talent). Convexity means that small diff in talent become magnified in larger earning diff, with great magnification of the earnings talent gradient increases sharply near the top of the scale. Convexity of returns can be sustained by imperfect substitution among diff sellers. However there is a second feature, best explained by tech rather than tastes. Joint consumption implies that the cost of production do not rise in proportion to the size of a sellers’ market (same effort if 1 of 1000 read one book). The key diff btwn this a public good is that property rights are legally assigned (customers are excluded).
STRUCTURE OF DEMAND: Imperfect substitution among quality differentiated goods arises from indivisibilities in the tech of consumption. My solution is to adopt a smooth quantity quality substitution tech and introduce the indivisibility through a fixed cost of consumption per unit of quantity. Consumers attempts to min consumption costs give a competitive advantage to higher quality sellers. A cardinal measure of quality of talent must rely on measurement of actual outcomes. The cost of one unit of a given quality is its price plus a fixed cost. So there is a balance btwn greater talent and greater quantity.
STRUCTURE OF SUPPLY: The eco activities under consideration involve direct contact of buyers with the seller. The seller’s choice of market size amounts to determining the number of contacts to make with buyers. Though, this tech is subject to congestion (external diseconomies of scale-> degradation of services a seller supplies to each of his customer as the contacts expand-> 2 reasons: if duplication is possible, market expansion requires using inferior techniques to render the service and the analysis should apply to cases of one-on one buyer seller contact and the negative effects of personal market scale are caused by limitations on the sellers time). This market is competitive even though a seller affects the unit price charged by choosing m, because each seller is closely constrained by other sellers offering similar services, the extent of substitution decreases with distance.
MARKET EQUILIBRIUM: There is a rising supply price in the service market and there is a falling demand price.
Internal diseconomies: the cross section structure of the market equilibrium is most easily established in the case where there are no effects of a seller’s market size on service quality. The tendency toward skewed rewards arising from convexity of revenues holds under general circumstances: individuals who can sell their services for higher prices have incentives to produce more. The increase in price and quantity with quality implies that talent has a multiplicative effect of reward.
Pure Joint Consumption: Even if there is one seller, potential entry maintains a competitive market, and an equilibrium can be reached.
External diseconomies: they support a non degenerate eq distribution of sellers. With only internal diseconomies the multiplicative effect of both positive price and quantity gradients with respect to quality implies convexity of the return function R(q). There are strong forces working toward convexity.
Heterogenous consumers: if there consumer differences intensity of demand for services are unrestricted, there no longer is a single equilibrium, diff imply restrictions on market outcomes that strengthen the qualitative results.
Demand shifts: an increase in the number of consumers or in the intensity of their demands, increases the market demand of services. Market eq price rise. Since R(q) increases, less talented people enter, existing sellers expand their scales of operations. Though average quality or sellers falls, previous entrants earn larger rents than before and the largest increase accrue to the most talented persons. Therefore the distribution of reward becomes more skewed than before. It is advantageous to operate in a larger overall market.
Supply shifts: Lesser diseconomies increase the market supply of services, reduce the equilibrium value and make consumers better off. The effect of the distribution of talents depends on the elasticity of the demand. If it is elastic, then cost reducing effects swamp the decline in unit prices and rents of sellers increase. If demand is inelastic the number of sellers decleines and the average remaining talent rises. The practical importance of all this is related to tech changes. These changes in communications and transportation have expanded the potential market for all kinds of professionals, with elastic demands there is a tendency for increasing concentration of income at the top as well as greater rents for all sellers as these changes proceed over time.
Interactions: A change in S shifts the supply of services, al though is a consumer parameter. It reduces market process and market supply. Therefore the equilibrium service price increases and the rent distribution is altered in favor of the more talented.