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Growth in Output per Capita

24 April, 2015 - 17:03

Of course, it is not just how fast potential output grows that determines how fast the average person’s material standard of living rises. For that purpose, we examine economic growth on a per capita basis.

An economy’s output per capita equals real GDP per person. If we let N equal population, then

EQUATION 23.1

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In the United States in the third quarter of 2008, for example, real GDP was $11,720 billion (annual rate). The U.S. population was 305.7 million. Real U.S. output per capita thus equaled $38,338.

We use output per capita as a gauge of an economy’s material standard of living. If the economy’s population is growing, then output must rise as rapidly as the population if output per capita is to remain unchanged. If, for example, population increases by 2%, then real GDP would have to rise by 2% to maintain the current level of output per capita. If real GDP rises by less than 2%, output per capita will fall. If real GDP rises by more than 2%, output per capita will rise. More generally, we can write:

EQUATION 23.2

% rate of growth of output per capita ≅ % rate of growth of output − % rate of growth of population

For economic growth to translate into a higher standard of living on average, economic growth must exceed population growth. From 1970 to 2004, for example, Sierra Leone’s population grew at an annual rate of 2.1% per year, while its real GDP grew at an annual rate of 1.4%; its output per capita thus fell at a rate of 0.7% per year. Over the same period,Singapore’s population grew at an annual rate of 2.1% per year, while its real GDP grew 7.4% per year. The resultant 5.3% annual growth in output per capita transformed Singapore from a relatively poor country to a country with the one of the highest per capita incomes in the world.

KEY TAKEAWAYS

  • Economic growth is the process through which an economy’s production possibilities curve shifts outward. We measure it as the rate at which the economy’s potential level of output increases.
  • Measuring economic growth as the rate of increase of the actual level of real GDP can lead to misleading results due to the business cycle.
  • Growth of a quantity at a particular percentage rate implies exponential growth. When something grows exponentially, it doubles over fixed intervals of time; these intervals may be computed using the rule of 72.
  • Small differences in rates of economic growth can lead to large differences in levels of potential output over long periods of time.
  • To assess changes in average standards of living, we subtract the percentage rate of growth of population from the percentage rate of growth of output to get the percentage rate of growth of output per capita.

TRY IT!

Suppose an economy’s potential output and real GDP is $5 million in 2000 and its rate of economic growth is 3% per year. Also suppose that its population is 5,000 in 2000, and that its population grows at a rate of 1% per year. Compute GDP per capita in 2000. Now estimate GDP and GDP per capita in 2072, using the rule of 72. At what rate does GDP per capita grow? What is its doubling time? Is this result consistent with your findings for GDP per capita in 2000 and in 2072?

Case in Point: Presidents and Economic Growth

President

Annual increase in Real GDP (%)

Growth Rate (%)

Truman 1949–1952

5.4

4.4

Eisenhower 1953–1960

2.4

3.4

Kennedy-Johnson 1961–1968

5.1

4.3

Nixon-Ford 1969–1976

2.7

3.4

Carter 1977–1980

3.2

3.1

Reagan 1981–1988

3.5

3.1

G. H. W. Bush 1989–1992

2.4

2.7

Clinton 1992–2000

3.6

3.2

G. W. Bush 2001–2008 (Q3)

2.1

2.7

 


Presidents are often judged by the rate at which the economy grew while they were in office. This test is unfair on two counts. First, a president has little to do with the forces that determine growth. And second, such test simply compute the annual rate of growth in real GDP over the course of a presidential term, which we know can be affected by cyclical factors. A president who takes office when the economy is down and goes out with the economy up will look like an economic star; a president with the bad luck to have reverse circumstances will seem like a dud. Here are annual rates of change in real GDP for each of the postwar presidents, together with rates of economic growth, measured as the annual rate of change in potential output.

The presidents’ economic records are clearly affected by luck. Presidents Truman, Kennedy, Reagan, and Clinton, for example, began their terms when the economy had a recessionary gap and ended them with an inflationary gap or at about potential output. Real GDP thus rose faster than potential output during their presidencies. The Eisenhower, Nixon-Ford, H. W. Bush, and G. W. Bush administrations each started with an inflationary gap or at about potential and ended with a recessionary gap, thus recording rates of real GDP increase below the rate of gain in potential. Only Jimmy Carter, who came to office and left it with recessionary gaps, presided over a relatively equivalent rate of increase in actual GDP versus potential output.

ANSWER TO TRY IT! PROBLEM

GDP per capita in 2000 equals $1,000 ($5,000,000/5,000). If GDP rises 3% per year, it doubles every 24 years (=72/3). Thus, GDP will be $10,000,000 in 2024, $20,000,000 in 2048, and $40,000,000 in 2072. Growing at a rate of 1% per year, population will have doubled once by 2072 to 10,000. GDP per capita will thus be $4,000 (=$40,000,000/10,000). Notice that GDP rises by eight times its original level, while the increase in GDP per capita is fourfold. The latter value represents a growth rate in output per capita of 2% per year, which implies a doubling time of 36 years. That gives two doublings in GDP per capita between 2000 and 2072 and confirms a fourfold increase.