Taking Ein-Dor's recent reevaluation of Grosch's law one step further, the authors find evidence of different slopes for different classes of computers and the utility of an additional variable: the IBM or IBM-compatible factor. The analysis indicates that Grosch's law no longer applies to minicomputers. COMMENTS ON "GROSCH'S LAW RE REVISITED: CPU POWER AND THE COST OF COMPUTATION" YOUNG MOO KANG, ROBERT B. MILLER, and ROGER ALAN PICKAs hardware costs continue to decline and more attention is paid to the economics of software development and operation, hardware nonetheless remains a significant expense. In the face of decisions to be made about centralization versus decentralization of CPU resources, knowledge about economies of scale can help organizations narrow down the choice of alternatives to be seriously considered. For this reason, Ein-Dor's recent reevaluation of the applicability of Crosch's law [1] sparked our interest. Having looked into his analysis, we believe there is yet more information contained in the data Ein-Dor uses than his analysis reveals. Specifically, we find evidence of different slopes for different classes of computers, and the utility of an additional variable-the IBM or IBM-compatible factor. We hope the interest generated by the original article [2, 5] will maintain itself for this further analysis of the same data.

Based on microeconomics, computer hardware performance is analyzed using two methods. For the cost function analysis, both purchase and lease prices are used. The results show no economies of scale for the mainframes and superminis during the 1981-l 985 period. YOUNG MOO KANGThere has been significant interest in the economic analysis of computer performance because of its direct implications for corlputer resource management [l]. One of the most im:,ortant issues related to this subject has been the degrees of economies of scale (EOS) for computers. From early studies [ZO, 211 to recent ones [i'], there is empirical evidence for large EOS in computers However, this opinion has recently been challenged [la, 221. One of the 0bviot.s characteristics of past studies is that most empirical models are based on Grosch's statement: "I believe that there is a fundamental rule . . giving added economy only as the square root of the increase in speed-.hat is, to do a calculation ten times as cheaply, you must do it one hundred times as fast" [lo, p. 3101. Based on his remark, most studies have develo:ped models whereby computer cost is a function of computer perforniance.In this article, we examine problems with the models based on Grosch's slatement, introduce alternative approaches, and estimate the developed models. The proposed models are based on production and cost function approaches of microeconomics. These two approaches allow us tcm fully utilize all available information and to cross-chl!ck the validity of model specifications and estimation results.As we will discus!:, computer performance can be expressed as a function of computer characteristics for the production func ion approach, whereas computer cost can be expressed as a function of computer perfor--01989 ACM OOOl-0782/89/0500-0X% 51.50 mance and characteristic prices for the cost function approach. Therefore, we need to have price data on computer characteristics in order to estimate the cost function. However, the prices of certain computer characteristics are not available since there are no explicit markets for these characteristics. For example, there is no explicit price for millions of instructions per second (MIPS) or input/output (l/O) channels. In order to overcome the absence of price clata for certain computer characteristics, we develop a cost function expressed with computer characteristics and performance under the assumptions of minimizing cost and maximizing profit. For the price of a computer, we use both purchase and lease prices. The compatibility of results with the two different prices provides further support for the robustness of model specification and estimation results.The equations developed are estimated for mainframes and superminicomputers available during the years 1981-1985. We have found that the results from cost function approaches using purchase price and lease price, and from the production function approach are all compatible with each other. The estimates of EOS range from 0.934 to 0.848 depending on the models...

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