### Computing 'Real Value' Over Time with a Conversion between U.K. Pounds and U.S. Dollars, 1791 to Present

This comparator will compute a "real value" of a price or a cost measured in British Pounds or U.S. Dollars in
an *initial* year and "valued" in the other currency in a *desired* year. For example, you can ask
what is the value in dollars in the year 2000 (desired year) of something that was valued at five pounds in
1950 (initial year). The comparator must take into consideration the rate of price change, or inflation, in the two
countries when making the calculations. Therefore the value of the five pounds will increase at the rate of inflation in
Britain from 1950 to the year the conversion takes place, and at the inflation rate in the United States for that
year up to 2000.

Note that there is no single "correct" measure of value over time, and economic historians use one or more different series depending on the context of the question. This comparator uses price series; however, if you go to the relative worth comparators for the United States and the United Kingdom, you will find others.

This comparator gives more than one answer. In fact, you can observe answers equal to twice the number of years between the initial and desired years. The reason for this is that it uses two measures, the CPI (or RPI) and the GDP deflator, to measure price changes in the two countries, and it uses the exchange rate for each sequential year. Thus, it starts with the idea that the year the value is converted is the initial year, then that the conversion takes place the second year, and so on until the desired year. Since the inflation rate in the two countries has not been the same, the CPI (or RPI) is better index if the subject is a consumer good or something else of interest to an individual. The GDP deflator is the better index if the subject is a capital investment or government expenditure.

The theory of purchasing power parity (PPP) predicts that all the answers will be the same. PPP says that prices (expressed in a common currency) should be the same in both counties, thus if prices rise faster in one currency than the other, then the exchange rate should adjust to keep prices the same. Therefore, in theory, the exchange rate should change at the rate of change in the ratio of the inflation rates of the two currencies. This has not been true, since exchange rates are determined by many other factors besides relative inflation rates. Thus the year that the conversion takes place can make a big difference in the results.

In the example above, five pounds in 1950 is "worth" anywhere from $85 to $194 in 2000 U.S. dollars, depending on which price index is used and which year the conversion takes place. What is presented here is the average of all the answers for the two indices. You can also see the table of all the answers as well.

#### Citation

Lawrence H. Officer and Samuel H. Williamson, "Computing 'Real Value' Over Time with a Conversion between U.K. Pounds and U.S.
Dollars, 1791 to Present", MeasuringWorth,
.

Please let us know if and how this discussion has assisted you in using our comparators.