Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Measuring the Welfare Gain from Personal Computers: A Macroeconomic Approach

Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Measuring the Welfare Gain from Personal Computers: A Macroeconomic Approach

Article excerpt

Working Paper 2011-05 March 2011

Abstract: The welfare gain to consumers from the introduction of personal computers is estimated here. A simple model of consumer demand is formulated that uses a slightly modified version of standard preferences. The modification permits marginal utility, and hence total utility, to be finite when the consumption of computers is zero, implying that the good won't be consumed at a high enough price. It also bounds the consumer surplus derived from the product. The model is calibrated and estimated using standard national income and product account data. The welfare gain from the introduction of personal computers is in the range of 2 percent to 3 percent of consumption expenditure.

JEL classification: E01, E21, 033, 047

Key words: compensating variation, computers, electricity, equivalent variation, technological progress, Tornqvist price index, welfare gain

1 Introduction

What is the welfare gain to consumers from the development of and improvements in personal computers (PC's)? This is the question addressed here. The answered offered is that welfare increased by somewhere between 2 and 3 percent, 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 CPI, some 15 years after their debut, results in a bias of up to 2 percent per year in the telecommunications--services price index. To do this, Hausman (1999) effectively integrates back the estimated demand curve for cellular telephones to obtain the indirect utility function for consumers. This function can be inverted to obtain the expenditure function, from which welfare measures can be obtained. The procedure was developed earlier in 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. …

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