Data Note
GDP per person changes with both aggregate output and population. Exact growth arithmetic distinguishes a larger economy from higher average output and identifies why population timing and matching price measures matter.
An economy can produce more in total while producing less per person. The outcome follows when population grows faster than output over a consistently defined period. It does not make aggregate GDP growth false; it changes the question from the scale of production to the average amount associated with each resident.
Statistics Canada's analysis of GDP per capita discusses that distinction and the limits of using a production average to assess broader well-being. Its historical observations are not treated here as current estimates. The purpose of this note is to make the arithmetic of a contemporary comparison explicit.
If is real GDP, population and , then:
Subtracting population growth from GDP growth provides an approximation, not the exact per-person change. The distinction becomes more material as the growth rates become larger.
Suppose, hypothetically, that real GDP rises from 2,000 to 2,040 and the corresponding population measure rises from 40 to 41. Aggregate output grows by 2 percent. Population grows by 2.5 percent. Output per person falls from 50 to approximately 49.756, a decline of about 0.488 percent.
The calculation does not establish that each resident's output, income or consumption fell by that amount. It divides aggregate production by a count of residents. Distribution across residents, the income accruing abroad and taxes or transfers can all affect the relationship with household resources.
A second hypothetical path illustrates a recovery requirement. After the per-person decline, restoring the original level of 50 with population remaining at 41 requires output of 2,050. That is roughly 0.49 percent above 2,040. Returning an average to an earlier level is a level comparison; the growth required depends on the population at the recovery date.
GDP measures production during an interval, whereas a population estimate can refer to a particular date or an average. A year-end population denominator may differ from the population present on average during the year. In periods of substantial demographic change, the choice can affect both the level and its growth.
An analytical series should retain the statistical agency's convention or identify the researcher's alternative clearly. Combining a quarterly GDP observation with a population estimate for a different quarter can manufacture a per-person movement. Population revisions also need to be reflected consistently across the historical comparison.
The output measure must match as well. Current-price GDP per person includes price changes; real GDP per person removes the price effects captured by the national-accounts volume measure. A dollar conversion at a changing market exchange rate introduces another source of variation. Those series should not be labeled interchangeably as domestic real growth.
Aggregate output can be relevant to the scale of infrastructure demand or a firm's potential market. Per-person output can be useful in assessing changes in average production capacity. Neither measure substitutes for the other when the population changes.
Even a per-person figure can conceal composition. An increase in the number of children, retirees, students or newly arrived workers can alter the connection between total population and current labor input. An assessment of productive capacity may therefore examine the employment rate, hours and capital available to workers alongside the population total.
The appropriate conclusion from the arithmetic is precise: total production and production per person need not move in the same direction. Reporting both, with matched periods and price measures, preserves that information. It avoids describing aggregate expansion as sufficient evidence of an improvement in every resident's economic position.