### What Is Its Relative Value in UK Pounds: Methods, Sources, and Examples

#### I. Method of Calculation

The user makes three entries: (1) a "first-year" monetary amount, expressed either in pounds, shillings, and pence (prior to 1971) or in decimalized pounds (from 1971 onward), (2) a "second year," and (3) a comparison measure. The calculator yields a corresponding amount ("relative value" of the first-year amount) in the second year. The years may be anywhere between 1270 and the present. It is permissible for the "second year" either to follow or precede the "first year." The "relative value" in the second year is obtained by multiplying the first-year amount by the ratio of the comparison measure in the second year to the comparison measure in the first year. This calculator, for U.K.-pound ("pound-sterling," in the parlance of economic historians) monetary amounts, is modeled after, and meant to complement, What is its Relative Value in US Dollars?

#### II. Definition and Appropriateness of Comparison Measures

Retail Price Index:The retail price index (RPI) measures the cost in a given period of the goods and services purchased by a typical household or consumer in a base period. The relative value resulting from this measure can be interpreted as the hypothetical second-period price of the first-period commodity on the assumption that the price of the commodity changed between the two periods by the same percent as the consumer price index. The more standardized, homogeneous, and stable in quality is the commodity, the more meaningful is the relative value provided by the consumer price index. Therefore the RPI is a measure best used for ordinary commodities, such as tea, milk, bread, haircuts, bicycles, and gasoline. It is less appropriate for goods subject to rapid technological change, such as personal computers and cell-phone service.

Also, for the monetary amount constituting earnings, wages, or wealth, the relative value via the RPI is the usual formula to generate "real" wage or wealth, that projects to the second year the purchasing power (over consumer goods and services) of the first-year's flow (wages or earnings) or stock (wealth or asset-value) amount.

For the United Kingdom, the retail price index is distinguished from the consumer price index (CPI). The RPI is the traditional measure of inflation as it affects consumers; the CPI is a more recently developed measure. The RPI covers a population representative of the typical household, whereas the CPI encompasses a broader population.

GDP Deflator: The GDP (gross-domestic-product) deflator is an index that incorporates all domestic production of goods and services — not only commodities purchased by households but also investment (machinery, equipment, and construction) as well as government expenditure. Also unlike the consumer price index, the GDP deflator is current-weighted rather than base-weighted. So the GDP deflator is suitable as a comparison measure for virtually any produced or purchased commodity. Similar to the consumer price index, use of the GDP deflator yields the hypothetical second-year price of the first-year commodity.

For wages, earnings, and wealth, the GDP deflator yields second-year buying power over all produced goods and services that is equal to that in the first year. Except for high-income and high-wealth individuals, the CPI is logically the superior measure; for the typical household or consumer would not generally purchase items outside those represented by the CPI.

Average earnings: Average earnings are the average over all workers of weekly wages, non-cash (in-kind) payments, bonuses, commissions, and piece-rate payments. Not an index number, this series allows for changes in the occupational and industrial structure of the employed population. In this respect, it is comparable to the GDP deflator rather than to the CPI. As a comparison measure, average earnings provide the second-year amount that maintains in the second year the first-year ratio of the specified amount to average earnings. This measure makes good sense to obtain relative value for income or wealth.

Average earnings may also be useful to measure relative value of commodities or expenditures in terms of labor, that is, the second-year value of the specified amount holding fixed the amount of first-period "work" to obtain it. By "work" is meant the first-year ratio of the commodity or expenditure amount to average earnings. It must be remembered that average earnings, because current-weighted, is a shifting standard. Depending on one's perspective, that property of the measure may or may not be advantageous compared to the unskilled-worker wage rate in Williamson's U.S.-dollar calculator.

Per-capita GDP: This measure is a more-comprehensive indicator of average income than is average earnings, because not only wages but also other sources of income (interest, dividends, rents, etc.) are included. That seems an advantage, but not all GDP goes directly to persons. Per-capita GDP might be better understood as U.K. total output per person. As a comparison measure, per-capita GDP involves maintaining in the second period the first-period ratio of the specified amount to per-capita GDP. The measure appears most suitable for wage and other income flows, as well as stock magnitudes such as wealth and assets.

Gross domestic product (GDP) is the most comprehensive comparison measure. GDP is the total output of the economy. GDP as a measure yields the second-period value that retains the first-period share of GDP accounted for by the specified amount. In that respect, GDP is a measure that is logically applicable to monetary amounts of all types – commodities, income, wealth, expenditures, etc. It is true that some first-period amounts constitute an insignificant share of GDP; but no matter. The point is that the share, whether small or large, is maintained in the second period, whence relative value is generated. It is true, though, that GDP as a measure may be most interesting for expenditures that indeed are substantial proportions of total output.

#### III. Data Sources for Comparison Measures

Retail Price Index and Average Earnngs, see: The Annual RPI and Average Earnings for Britain, 1209 to 2010 (New Series).

The source for GDP, Population, and GDP Deflator from 1820 to the present is the Bank of England's "Three Centuries of Macro Data."

Observations before 1830 are from British Economic Growth, 1270-1870: An Output -based Approach, by Stephen Broadberry, Bruce Campbell, Alexander Klein, Mark Overton and Bas van Leeuwen (Cambridge university Press, 2015). and are used with their permission. Download the database underlining this work here.

The data are merged between their 1270 to 1700 and the 1700 to 1870 data sets and that series is merged with the Bank of England series at 1870.

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