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## Relative Prices Matter: Why Cost-of-Living Indexes Don't Tell Us Much

Suppose you live and work in Indianapolis. Your employer informs you that it wants to transfer you to San Francisco. One of your first concerns is likely to be: “Hey, what about my salary? The cost of living is really high out there, isn’t it?” Anticipating such a reaction, your boss assures you that your salary will be bumped up based on the difference in your cost of living for the two cities. Should this allay your concern?

Subsequent coffee break, water fountain, and lunch hour conversation will assure you that it’ll be a break-even move as far as your salary-based living standard is concerned. Thus, it’ll all depend on your assessment of the non-monetary quality of life in the two cities. Sounds OK, doesn’t it? Nevertheless, it’s wrong, and at odds with the first principles of economics!

#### A Simple Numerical Example

The table below presents some evidence on the difference in the cost of living in the two cities. It comes from Sperling’s Best Places to Live website. Note the overall cost of living in San Francisco is slightly more than triple that of Indianapolis — what you get for \$60,000 annual income in Indianapolis requires \$180,929 in San Francisco. Also note that the bulk of this large difference is attributable to the cost of housing in the two cities. Housing is 8.162 (!) times more costly in San Francisco, while food, for example, is only 1.326 times more costly.

Cost of Living Comparison:
Indianapolis, Indiana — San Francisco, California

So, we assume: a salary of \$60,000 in Indianapolis, Indiana, should increase to \$180,929 in San Francisco, California.

#### Relative Prices Change

More important, and the crux of our argument, is that relative prices of the items change with a move to San Francisco. To see the importance of this, let’s confine discussion to two items in your budget — housing and food. While the example is straightforward, it contains some subtleties that might require putting on our “thinking caps.” A pencil and paper might help, too.

To keep the numbers simple, if the Indianapolis price of a unit of housing is \$5.00 per unit (square feet, for example), then its San Francisco price would be \$40.81 (\$5.00 x 8.162). Likewise for food: if the Indianapolis price is \$1.00 per unit, its San Francisco price would be \$1.32 (\$1.00 x 1.326).

Each time you purchase a unit of housing in Indianapolis (for \$5.00) you gave up the opportunity of having 5 units of food (\$1.00 each); and each time you purchased a unit of food you give up the opportunity of buying 0.20 units of housing.

These relative prices are different, big-time, in San Francisco. Now, each time you purchase a unit of housing you give up 30.9 units of food; and each time you purchase a unit of food you give up an opportunity of obtaining 0.03 units of housing. Housing is relatively more costly in San Francisco, 30.9 units of food vs. 5 units of food in Indianapolis. Food, on the other hand, is relatively cheaper in San Francisco, 0.03 units of housing vs. 0.20 units of housing.

A foundational principle of economics is that when relative prices change, people change their behavior. If not, school’s out and economics ceases to exist as a field of study. Accordingly, when you arrive in San Francisco, you can be expected to substitute away from housing (fewer square feet, for example) toward food (more expensive cuts of meat, for example). Not because you like housing less, mind you, but because it now costs more. Similarly, you buy more food, not because you like it more, but because it now costs less.

Since you have the opportunity to maintain your Indianapolis consumption pattern, but choose not to, we can say that your salary-related living standard in San Francisco must be — has to be — higher. Alternatively, your Indianapolis standard of living could be maintained in San Francisco with a smaller increase in your salary. That is, to less than \$180,929. Don’t tell your boss!

#### What if Others are Transferred?

What if some of your Indianapolis colleagues, with the same Indianapolis salary as yours, are also going to be transferred? Two types of consumption patterns stand out.

First, is the case of those whose Indianapolis consumption pattern has less housing and more food than you. Relative to you, a salary bump to \$180,929 will be more than enough for them to match their Indianapolis consumption bundle of food and housing. Moreover, like you, the change in relative prices will induce them to tilt their consumption pattern toward food and away from housing. They gain for two reasons. Like you, these folks should not tell their boss!

Second, those whose Indianapolis consumption pattern is skewed toward more housing compared to you, even with the salary bump to \$180,929 will leave them unable to buy what they bought for \$60,000 in Indianapolis. While they can also substitute away from housing toward food, the net effect on their living standard is uncertain. Anything can happen. That any would break even, as your “counselors” suggest, would be fortuitous at best.

#### Final Thought

The bottom line in all this is that uniformly adjusting salaries upward by the measured change in the cost of living in order to preserve pre-transfer living standards is virtually impossible. It’ll depend in pre-transfer consumption patterns and people’s willingness to substitute in response to relative price changes. Nevertheless, there is an aura of precision about it that makes it sound “scientific” to the ignorati.

Author:

Contact T. Norman Van Cott

T. Norman Van Cott, an adjunct scholar with the Indiana Policy Review Foundation, is professor of economics at Ball State University, Muncie, IN.

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