The price or the rate of exchange of one good in terms of another is the amount of the other good divided by the amount of the first good. In the money economy, price will be the amount of money divided by the amount of the first good.

Suppose two transactions were conducted. In the first transaction, one TV set is exchanged for $1,000. In the second transaction one shirt is exchanged for $40. The price or the rate of exchange in the first transaction is $1,000 per TV set. The price in the second transaction is $40 per shirt. Could we then establish the average price paid in these two transactions?

In order to calculate the average price, we must add these two ratios and divide them by two. However, $1,000 per TV set cannot be added to $40 per shirt, implying that it is not possible to establish the average price. Murray Rothbard wrote,

Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate. Even pounds of sugar and pounds of butter cannot be added together, because they are two different goods and their valuation is completely different.

#### Fixed-Weight Price Index Belongs to the World of Robots, Not Humans

The use of a fixed-weight price index seems to offer a solution to the calculation of an average price. The index, it is held, can establish changes in the overall purchasing power of money, which permits us to ascertain changes in real output.

For instance, in the first period, Tom bought one hundred hamburgers for $2 each. He also bought five shirts at $20 each. His total outlay in period one stood at

($2 × 100) + ($20 × 5) = $300.

Observe that hamburgers carry a weight of 0.67 in the total outlays while shirts have a weight of 0.33.

In period two, hamburgers are exchanged for $2.20, an increase of 10 percent. Shirts are exchanged in period two for $21, an increase of 5 percent. By applying unchanged weights, (unchanged pattern of consumption), we can establish that Tom’s monetary expenditure in period two stood at

($2.20 × 100) + ($21 × 5) = $325.

Note again that Tom’s monetary expenditure in period two was $325 against $300 in period one (i.e., an increase of 8.3 percent). We can then establish that the purchasing power of Tom’s monetary expenditure fell by 8.3 percent:

(10% × 0.67) + (5% × 0.33) = 8.3%.

If we were to assume that Tom’s pattern of consumption represents an average consumer, then we could say that the overall purchasing power in the economy fell by 8.3 percent. Consequently, if it was established that the overall monetary expenditures in period two increased by 8 percent, then we could ascertain that in real terms expenditure declined by 0.3 percent.

Periodically, government statisticians conduct extensive surveys to establish a pattern of spending of an “average” consumer. The obtained weights in turn serve to establish changes in the average price and hence in the purchasing power of money. Once changes in the purchasing power of money are established, one could make an estimate of changes in total real output.

The assumption that weights remain constant is, however, questionable. This portrays an individual with frozen preferences (i.e., a robot).

#### Variable-Weight Price Index Cannot Help to Establish the Purchasing Power of Money

The view that a variable-weight price index could bring more realism and, hence, permit the estimate of the purchasing power of money also misses the point. In the world of a fixed-weight price index, the change in prices is entirely attributed to changes in the purchasing power of money. This is not so with respect to the variable-weight index.

For example, in period two, say Tom’s pattern of consumption changes and he consumes one hundred twenty hamburgers rather than one hundred and still buys five shirts. His overall monetary expenditure in period two is

($2.20 × 120) + ($21 × 5) = $369.

This means that Tom’s expenditure has increased by 23 percent from period one. We cannot, however, attribute this increase to the decline in the purchasing power of money while ignoring the increase in quantity of hamburgers bought. There could be many reasons why Tom has increased his expenditure on hamburgers in the second period. One can only infer that changes in the variable-weight price index are driven by monetary and nonmonetary factors. The influence of these factors on prices is intertwined and cannot be separated.

Consequently, it is not possible to isolate changes in the purchasing power of money from changes in the price index. According to Rothbard,

All sorts of index numbers have been spawned in a vain attempt to surmount these difficulties: quantity weights have been chosen that vary for each year covered; arithmetical, geometrical, and harmonic averages have been taken at variable and fixed weights; “ideal” formulas have been explored—all with no realization of the futility of these endeavors. No such index number, no attempt to separate and measure prices and quantities, can be valid.

Also, according to Ludwig von Mises,

In the field of praxeology and economics no sense can be given to the notion of measurement. In the hypothetical state of rigid conditions there are no changes to be measured. In the actual world of change there are no fixed points, dimensions, or relations which could serve as a standard.

Moreover, Rothbard wrote,

There are only individual buyers, and each buyer has bought a different proportion and type of goods. If one person purchases a TV set, and another goes to the movies, each activity is the result of different value scales, and each has different effects on the various commodities. There is no “average person” who goes partly to the movies and buys part of a TV set. There is therefore no “average housewife” buying some given proportion of a totality of goods. Goods are not bought in their totality against money, but only by individuals in individual transactions, and therefore there can be no scientific method of combining them.

#### The Total Purchasing Power of Money Cannot Be Established Conceptually

We suggest that the total purchasing power of money cannot be established, even conceptually. Thus, when $1 is exchanged for one loaf of bread, all we can say is that the purchasing power of $1 is one loaf of bread. If $1 is exchanged for two tomatoes then this also means that the purchasing power of $1 is two tomatoes.

It is not possible, however, to establish the total purchasing power of money since we cannot add up tomatoes to bread. We can only establish the purchasing power of money with respect to a particular good in a transaction at a given point in time and at a given place. Hence, if something cannot be established conceptually it is obvious that any attempt to quantify it is futile.

#### Conclusion

Any concept of average price level involves adding or multiplying quantities of completely different units of goods and is therefore meaningless. According to Mises, in economics no sense can be given to the notion of measurement. In the hypothetical state of rigid conditions there are no changes to be measured. In the actual world of change there are no fixed points, dimensions, or relations which could serve as a standard.