Something about Pc

[De4thzone]

A century of innovation

The iPhone is just one of a myriad of new goods that, thanks to technological innovation, have emerged over the past century. Markets that have seen some of the largest increases in the number of goods include automobiles, packaged and processed food, consumer electronics, and health care. For example, in 1908 one of the few cars available was Ford’s Model T, sold in a single colour – black. By the early 1970s there were 140 different vehicle models on the market in the US. By the late 1990s, the number of models had increased to 260.2 Automobiles have benefited from vast improvements in quality. Over time, adjustable steering columns, airbags, air conditioning, anti-lock brakes, cruise control, power locks, remote control keys, and remote controlled side view mirrors have all become standard features.

One of the most significant new goods in the twentieth century was the personal computer (PC). The first successfully mass-produced PC was the Apple II. Released in 1977, it consisted of a 1 megahertz microprocessor, 4 kilobytes of random-access memory (RAM), no hard disk, and an audio cassette interface for program loading and data storage. The computer retailed at approximately US $1,200. Rapid technological progress led to consistent improvement in the Apple II following its release. For example, in 1978 the floppy disk drive peripheral, far superior to cassettes, became available.

Rapid technological progress has since fueled continual quality improvements and declining costs of production. Today’s computers are often equipped with multi-core processors running at over 3,000 megahertz, gigabytes of RAM, and hard drives capable of storing hundreds of gigabytes of data.

Quality improvements in computers and computer production have resulted in an enormous fall in quality-adjusted PC prices. In fact, prices have dropped at an astounding rate of 25% per year. Thus, a PC today is more than 700 times less expensive than one in 1977. Starting from virtually zero demand for personal computers prior to 1977, the fall in prices throughout the last thirty years has been synonymous with a rapid rise in demand, as shown in Figure 1. As the demand for personal computers rose, so did their share of total expenditure, climbing from zero in 1977 to more than 0.6% in 2004, as shown in Figure 2.

Source: U.S. National Income and Product Accounts, Tables 2.4.4 and 2.4.5

Source: U.S. National Income and Product Accounts, Tables 2.4.4 and 2.4.5

When constructing price and quantity indices, it is vital to adjust for the improvements in product quality that have occurred over time. When calculating the price of a computer, an economist must take into account that an amount spent today will buy much more than it would have yesteryear. In light of this tremendous improvement in quality, economists at the Bureau of Economic Analysis (BEA) try hard to produce price and quantity indices for an idealised standardised computer. One way they do this is by estimating hedonic price regressions, in which the price of a computer is estimated as a function of its characteristics - say hard drive size, memory, processor speed, etc., and time. The coefficient on time measures the decline in the price of a standardised computer, so to speak, after controlling for characteristics. For the period 2001 to 2005, Wasshausen and Mouten (2006, Table 3) report that quality adjustment accounts for 11.5 percentage points of the 16.4% decline in the BEA's price index for computers.
What’s a PC worth?

How much have consumers benefited from the invention of PCs and the fall in their quality-adjusted price since 1977? One measure of a welfare gain is called the compensating variation. The compensating variation is the amount of income a consumer would have to give up to attain the level of utility he or she would have realised if computers had never been invented or sold at some ridiculously high unaffordable price.

A growing number of studies have dealt with how to measure the welfare gain from a new good such as the PC.3 While some techniques are quite involved, Jerry Hausman (1999) proposes an easy way to estimate the welfare gain from a new product based on a linear approximation to the demand function for that good. His formula for the welfare gain is to simply approximate the compensating variation as one half of the new good’s share of expenditure divided by its price elasticity of demand. When applied to PCs, this formula yields a welfare gain of 0.16% of 2004 expenditure. Is this number reasonable? Using an alternative technique, Hausman (1996) estimates the welfare gain to consumers from the introduction of Apple-Cinnamon Cheerios in 1989, a minor product innovation, to be 0.002% of 1992 consumption expenditure. Could the welfare gain from PCs in 2004 be only 80 times the welfare gain from Apple-Cinnamon Cheerios in 1992?

The linear demand approximation may not work well for major innovations, where the first few units of a good yield a lot of extra utility. For example, electricity was 1.5% of personal consumption expenditure in 2001. If one uses Reiss and White’s (2002, p. 26) price elasticity of demand for electricity of 0.39, then the welfare gain from the introduction of electricity would be about 1.9% of personal consumption expenditure. Electricity reached a high of 2.4% of personal consumption expenditure in 1984.4 If one now supposes that the price elasticity of electricity is 0.15, a very low estimate, then a very liberally computed welfare gain is about 8 percent.5 Surely, this formula underestimates the welfare gain from the introduction of electricity. It might be best to view it as a lower bound, as Hausman (1999) himself suggested.

Greenwood and Kopecky (2008) suggest an alternative technique that uses a simple model of consumer demand and aggregate quality-adjusted price and quantity data to calculate the welfare gain directly. Computing the compensating variation requires defining a representative consumer’s utility function. Economists most commonly use isoelastic utility functions. However, these utility functions are problematic for measuring the welfare gain from new goods. The problems arise because computing the welfare gain requires calculating the utility of the consumer when his computer consumption is zero. At zero consumption, the utility function returns a value of minus infinity for some parameterisations. This is illustrated in Figure 3. The dashed red line is the standard utility function. Notice that as computer consumption goes to zero the function goes to minus infinity. In this case the welfare gain from the introduction of the new good is infinitely large. In addition, regardless of the parameterisation, the marginal utility at zero consumption is infinite. This is also illustrated in Figure 3 by the green dashed line. Infinite marginal utility at zero consumption means the consumer will never choose this point regardless of the price since he will always want to consume at least a small amount of the good.

These problems can be avoided by shifting the utility function to the left, using the constant ν. This yields a utility function similar to the solid red line and a marginal utility function similar to the solid green line in Figure 3. Notice that the new utility function gives finite levels for marginal and total utilities at zero consumption. Thus, high prices may result in the consumer optimally choosing to purchase zero computers. Greenwood and Kopecky (2008) calibrate/estimate such a utility function using quality-adjusted national income and product account data to calculate the welfare gain from the introduction of PCs.

What is your PC worth to you? About 4% of your total expenditure on consumption, according to the simple approach discussed here. That number is 25 times larger than the one found using Hausman’s approach and 2,000 times larger than the welfare gain from Apple-Cinnamon Cheerios.



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