Knowledge that Transforms

The economy of massed reserves, first mentioned by E. A. G. Robinson (1958, pp. 26-27), is now firmly established in industrial organization literature as an example of a potential plant-level scale economy. The massing of reserves results in a savings in proportion of required reserves to expected output as scale of a facility increases. Examples of such reserves are bank tellers, specialized tools and equipment, repairmen, inventories, spare parts, and checkout lines. The potential economies from massing reserves are dependent on underlying stochastic processes governing supply and/or demand of service provided. Theoretical justification for economies of massed reserves has usually been based on an appeal to law of large numbers. For example, Donald Hay and Derek Morris wrote the law of large numbers makes number of breakdowns more predictable in a plant using a large number of machines, so that number of stand-by maintenance staff need not be increased in proportion to size (1979, p. 44). This paper demonstrates that law of large numbers does not provide a theoretical explanation of massed-reserves scale economies. Instead, it is shown that expected economies of massed reserves can be calculated from steady-state properties of well-known queuing models. Queuing models apply to any case where a servicing input is held in reserve to cope with stochastic nature of market or production process. In addition, a method for quantifying expected economies of queuing processes is developed. The magnitude of these expected economies is shown to be significant and calculable. For example, expected economies inherent in a widely applied queuing model are shown to exceed 23 percent in some cases. Section I establishes irrelevance of law of large numbers as a theory of scale economies. Section II provides a formal method for determining scale economies inherent in most often mentioned massed-reserves example: machine repair. Section III shows that same method can be used to calculate scale economies for remaining massed-reserves examples: specialized repair tools and equipment; checkout counter clerks, bank tellers, and other service personnel; capacity; and inventories and spare parts. In addition, it is demonstrated that same method can be used to calculate scale economies for some multiproduct operations.

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Let V(X) be any direct utility function characterizing consumer preferences that are reflexive, transitive, and complete, and whose parameters are fixed relative to the usual linear budget constraint p X = M. Here X designates the vector (X1,.. ., X,) and is confined to the positive n-orthant; Xi designates quantity of the ith commodity; p is the vector (P,, ...,pn) of positive commodity prices; and M designates total expenditure. Let X(p, M) designate the system of demand functions derived from V(X) subject to pX = M, which possess the properties of zero degree homogeneity, symmetry, and semidefinite negativity. Let W( X; 0) designate a direct utility function with (a) parameter vector 0 dependent on the price vector p that appears in the budget constraint and (b) that rationalizes the same system of demand functions as V(X), namely, X(p, M). Probably, many economists who have considered price-dependent preferences' would conjecture that every such price-dependent utility function W(X; p) satisfying (a) and (b) is of the rather restricted form

Sebastian Edwards uses a new, money variable-based on the addition of the contemporaneous fiscal deficit to my autoregressive money growth equations -to argue that 1) in Brazil and Chile there is no significant relationship between unexpected money growth and output growth, 2) unexpected money growth has different estimated effects on output in Colombia, Peru, and Mexico, and these effects substantially exceed those estimated in Brazil and Chile, and 3) thus my 10 percent rule for the effect of unexpected money growth on output growth does not hold. In addition, Edwards incorporates the terms of trade in his output equations and finds they are important in the case of Chile and Mexico.' Finally, Edwards takes issue with my use of lagged inflation to explain output. Edwards and I use somewhat different data, not only in terms of sources, but also Edwards often uses M2 rather than Ml in reporting his best results. However, Edwards' and my basic results are broadly similar (compare his Table 1 and my original Tables 1 and 4). This is encouraging, and in general makes it seem not worth quibbling over the differences in data. However, there is one difference which affects the results that I will discuss later. The inclusion of the fiscal deficit in the money growth equation is a key difference in our work. As I pointed out in my earlier article, fiscal and monetary policy often are closely related in Latin America. Thus it is not surprising that Edwards finds the deficit (divided by lagged money) is a significant factor in explaining money growth. However, the point is not to explain money growth, but to estimate a relationship which the public could have been using to predict how much money, and thus nominal aggregate demand, has grown since the last observation on the money stock.2 It strains credulity to assume that, in Latin America, the budget deficit could be used by the public to estimate money growth contemporaneously. Data on the cash deficit usually are available publicly only with a long lag. Moreover, many alternative versions of a deficit, involving creative accounting methods, are reported. For example, for many years in Colombia, the reported deficit, which is available with about a one-quarter lag, treated both the unspent portion of the budget and the accounting profits from the revaluation of the local currency value of exchange reserves as income; procedures which caused great confusion inside as well as outside the government. Despite such problems, the cash deficit still might be useful as a monetary growth predictor; for example, it may be correlated with some other easily available contemporaneous indicator of money growth. However, its usefulness can best be judged from a comparison of the results when the deficit is used only as the money growth predictor to determine unexpected money (a constrained equation) with those obtained when it is used as an additional independent variable (an unconstrained equation), a test Robert Barro has suggested in another context. *World Bank. The views and interpretations expressed in this article are my own and should not be attributed to the World Bank, its affiliated organizations, or to any individual acting in their behalf. 'Edwards also uses the seemingly unrelated regression technique to take into account possible interrelationships in the error terms across countries. Judging from the reported t-statistics, this procedure did not improve the fits greatly. 2Surprisingly, the deficit is not significant in explaining domestic credit in Mexico. This result and the estimated negative relationship between Edwards' domestic credit series and output suggest a problem in the domestic credit variable.

Rather than start directly on the sensitive issue of the economic role of unemployment, I would like to spend some time first on a parallel question of rather less social importance, and then draw some analogies to the problem of unemployment. The phenomenon I will examine is the time people spend idle at airports. Ultimately, I will compare the analysis of idle airport time with the analysis of idle time in the labor market. In any airport at any time, numerous people are waiting for something to happen. These people are not doing anything particularly constructive with their time-they are waiting because they arrived early, because their planes have been delayed, or because they are in a queue for the next available flight. An observer who knew nothing about the purpose of an airport would be puzzled by the chronic idleness of most of the people there. The observer might gather data on airport idleness along the following lines. At any given time, 0.2 percent of the population is idle at the airport. The idle population turns over frequentlythe median duration of a spell at the airport is 35 minutes. But long spells account for the bulk of idleness-half of all idleness occurs in the course of spells which will last 5 hours or more. Airport idleness is highly concentrated in the population. In a given year, three-quarters of the population are never idle at the airport; 5 percent of the population incurs half of all idleness. A predictable seasonal pattern is apparent-idleness reaches sharp peaks at Thanksgiving, Christmas, and Easter, plus a broad peak in the summer. Were it quantitatively more significant, airport idleness would be a social issue. The airport idle are not usually engaged in useful activities. Few of them spend time trying to locate earlier flights, nor do many of them try to accelerate their movement by offering to pay a higher fare. A surprisingly large fraction do nothing more than sit. The opportunity cost of time spend idle at the airport is essentially zero, it would appear.