Measuring the Welfare Gain from Personal Computers

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What is the welfare gain to consumers from the development of and improvements in personal computers (PCs)? This is the question addressed here. The answer offered is that welfare increased by somewhere between 2% and 3%, measured in terms of total personal consumption expenditure, due to the introduction of the PC and its subsequent price decline. This finding is obtained by employing a model of consumer behavior, based upon more-or-less standard preferences, which is fit to aggregate national income and product account data using a direct and simple calibration/estimation strategy.

To estimate the welfare gain from the introduction of a new product one must know what utility is in the absence of the good. A conventional isoelastic utility function has two problems. First, at zero consumption the utility function returns a value of minus infinity, whenever the elasticity of substitution is less than one. In this case the welfare gain from the introduction of the new good is infinitely large. Second, marginal utility at zero consumption is infinite, so long as the elasticity of substitution is finite. Therefore, consumers will always purchase some of the good in question, no matter how high the price is, albeit perhaps in infinitesimal quantities. To avoid these problems a form for preferences will be adopted that gives a finite level for marginal utility, and hence one for total utility, at zero consumption. With this utility function, high prices may result in the consumer optimally choosing to buy none of the new good. In addition, the consumer's surplus associated with the introduction of a new good is generally finite.

This paper contributes to the growing literature on measuring the welfare gains from new goods. A classic example is the work by Hausman (1999), who studies the introduction of cellular telephones. He finds that their tardy inclusion in the Consumer Price Index (CPI), some 15 years after their debut, results in a bias of up to 2% per year in the telecommunications-services price index. To obtain this estimate, Hausman (1999) effectively integrates back the estimated demand curve for cellular telephones to recover the indirect utility function for consumers. This function can be inverted to obtain the expenditure function, from which welfare measures can be calculated. The procedure was developed earlier in work by Hausman (1981). Analytical solutions for the expenditure function can be obtained when the demand equation is (ln) linear. When the demand equation is not linear the indirect utility function may have to be recovered by numerically solving a differential equation. This procedure is dual to the one presented here, which focuses on the consumer maximization problem. Some utility functions, such as the one employed in the current work, may not lead to a linear demand equation of the form that is conventionally estimated.

Hausman (1999) also suggests an approximate measure of welfare based on a linear demand curve. While he states explicitly that this measure of welfare is a lower bound, this caveat is often forgotten in applied work. It may work well in the cell phone example that he studies. As illustrated in the PC example studied here, however, this approximate demand curve method can lead to a serious underestimate of the welfare gains arising from the introduction of a new product.

Similarly, the use of conventional price indices, such as the Fisher Ideal and Tornqvist price indices, may lead to inaccurate estimates of the consumer surplus that arises from the introduction of a new good and/or the good's subsequent price decline. The accuracy of such methods will depend on how fast the marginal utility for a new good rises as the quantity consumed goes to zero. Figuring this out is part and parcel of the new goods problem. That is, what utility function or demand equation should be used for estimating the welfare associated with the introduction of a new good? …