Ski-Lift Pricing with Applications to Labor and Other Markets: Comment

by Tyler Cowen, Amihai Glazer
Ski-Lift Pricing with Applications to Labor and Other Markets: Comment
Tyler Cowen, Amihai Glazer
The American Economic Review
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Ski-Lift Pricing with Applications to Labor and Other Markets: Comment

In a recent article for this Review, Robert Barro and Paul Romer (1987) argue that nominal price stickiness can be compatible with the optimal provision and utilization of excludable goods. The paradigmatic case examined by Barro and Romer is the ski lift: instead of charging for each ride, a comparable equilibrium can be attained by charging a single price for access to the ski lift and using a quantity constraint to limit an individual's number of rides.

In particular, the more people show up to ski, the fewer rides each person can get, so that the real price of a single run down the slope increases. Crowding costs thus serve as a substitute for the flexibility of nominal prices by automatically changing the real prices individuals face.

Although Barro and Romer develop some imaginative applications of their analysis, they do not indicate that the basic model is a rediscovery of the theory of clubs (James Buchanan, 1965; Richard Cornes and Todd Sandler, 1986; Suzanne Scotchmer, 1985). In fact, Scotchmer (1985) explicitly mentions ski lifts as an example of clubs. Barro and Romer cite Frank Knight (19241, whose article was a forerunner of the theory of clubs, but do not mention that many of their primary results are well known in the pub- lic-economics literature.

The theory of clubs is concerned with the optimal size of a congestible facility, the

*Cowen: Department of Economics, George Mason University; Glazer: Department of Economics, Univer- sity of California, Irvine, CA 92717. We thank Suzanne Scotchmer, Esko Niskanen, and an anonymous referee for their comments, and members of the Transporta- tion Economics Study Group at U.C. Irvine for stimu- lating discussions,

optimal intensity of its use, and pricing methods that lead to profit maximization and to social optimality. These questions correspond to the issues in Barro and Romer which involve the optimal number of skiers and the optimal price for a ski-lift ticket. Membership fees for clubs are analogous to ticket prices for the ski lift. The number of rides that skiers obtain is analogous to con- gestion in club theory; congestion reduces each user's utility as the number of people who visit the facility increases.

In an undergraduate text, Robin Boad- way and David Wildasin (1984 p. 97) note that the optimal number of users of a club is reached when the per-person price equals the marginal congestion cost imposed by a single club member. In the context of the ski-lift example, the price of a lift ticket must equal the value of the rides that other skiers are deprived of. Romer and Barro (1987 pp. 878-9, 886) obtain an analogous result.

Many of the conclusions Barro and Romer obtain by making stringent assumptions about the effect of increased congestion (each skier obtains proportionally fewer rides) are derived by the theory of clubs from more general assumptions about the effect of congestion. Boadway and Wildasin (1984 p. 98) present the following summary of the results of club theory for the case in which intensity of use is fixed:

If exclusion is possible without cost

and if the costs of providing the good

are constant, the competitive market

mechanism can be relied upon to pro-

vide an of many

with the correct size of facility and the

correct number of members, and,

therefore, the correct number of such

facilities for the entire population.


Similar conclusions are reached under yet more general assumptions by Scotchmer (1985).

Other results in Barro and Romer corre- spond to results in club theory: markets attain the optimum even if different ski areas vary in quality, that is, even if clubs congest at different rates. Also, the compet- itive solution is socially optimal when con- sumers have heterogeneous preferences if separate ski-lift areas serve consumers with different preferences (see Cornes and Sandler, 1986 Ch. 11).

Though there is no novelty in the prob- lems Barro and Romer treat and no novelty in the conclusion that competitive markets can efficiently provide congestible goods, Barro and Romer do extend the theory of clubs in two important directions. First, they show that, under some conditions, efficiency can be attained by an entry fee alone; the effect of increased congestion on demand can obviate the need for imposing a price on each ride. (In contrast, Eitan Berglas [I9761 and Scotchmer [1985, 19871 demon- strate that, in general, efficiency requires imposing a price for each ride.) Second, Barro and Romer offer the interesting pos- sibility that, in some cases, both profit-max- imization and efficiency imply constant prices following changes in demand.


Barro, Robert J. and Romer, Paul M., "Ski-Lift Pricing, with Applications to Labor and Other Markets," American Economic Re- view, December 1987, 77, 875-90.

Berglas, Eitan, "On the Theory of Clubs," American Economic Review, May 1976, 66, 116-21.

Boadway, Robin W. and Wildasin, David E., Public Sector Economics, Boston: Little, Brown, 1984.

Buchanan, James M., "An Economic Theory of Clubs," Economica, February 1965, 32, 1-14.

Cornes, Richard and Sandler, Todd, The The- ory of Externalities, Public Goods, and Club Goods, Cambridge, U.K.: Cambridge University Press, 1986.

Knight, Frank H., "Some Fallacies in the Interpretation of Social Cost," Quarterly Journal of Economics, August 1924, 38, 582-606.

Scotchmer, Suzanne, "Two-Tier Pricing of Shared Facilities in a Free-Entry Equilib- rium," Rand Journal of Economics, Win- ter 1985, 16, 456-72.

-, "Competitive Equilibrium and the Core in Club Economiew With Anony- mous Crowding" Journal of Public Eco- nomics, 1987, 24, 159-73.

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