Economic Growth: Consider once again our very long-run global economic real GDP

Question

Economic Growth: Consider once again our very long-run global economic real GDP growth and prosperity table from lecture:

Assume that, going forward, world population peaks at 10 billion people in 2050 and then stabilizes. Assume that growth in world real GDP continues at its current 21st century pace.

a) The global well-off today—the top 10%—receive about 40% of global GDP as income. What is the average income of the global well-off? In what year will the average person on the globe be as well off as the typical member of the global well-off today?

b) The global rich today—the top 1%—receive about 15% of global GDP as income. What is the average income of the global rich? In what year will the average person on the globe be as well off as the typical member of the global rich today?

c) The global super-rich today—the top 0.01%, the top 740,000—receive about 3% of global income. What is the average income of the global super-rich? In what year will the average person on the globe be as well off as the typical member of the global super-rich today?

d) The global plutocracy today—the top 0.0001%, the top 7,400—receive about 1% of global income. What is the average income of the global plutocracy? In what year will the average person on the globe be as well off as the typical member of the global plutocracy today?

In the Shadow of Malthus Population (Millions) GDP per Capita ($2015) Total World GDP $2015 Billions) Year $750 $750 $750 $750 $1000 $2000 $7700 $10000 $4 38 $128 375 $750 $3000 $47740 74000 1000 1500 1800 1900 2000 2015 50 170 500 750 1500 7400

Explanation / Answer

(a)

(1) Top 10%

Population, top 10% = 7400 million x 10% = 740 million

GDP, top 10% = $74000 billion x 40% = $29600 billion

Average income = $29600 billion / 740 million = $40,000

(2) World GDP growth rate = ($74000 / $47740)1/15 - 1 = (1.55)1/15 - 1 = 1.0297 - 1 = 0.0297, or 2.97%

Current per capita GDP = $10000

So,

$10000 x (1.0297)N = $40000

(1.0297)N = 4

Taking natural logarithm,

N ln 1.0297 = ln 4

N x 0.0293 = 1.3863

N = 47.31

So, average person will be equally well-off (earning $40000 per capita) in (2015 + 47) = year 2062

(b) Global rich

(1)

Population, top 1% = 7400 million x 1% = 74 million

GDP, top 1% = $74000 billion x 15% = $11100 billion

Average income = $11100 billion / 74 million = $150,000

(2) World GDP growth rate = ($74000 / $47740)1/15 - 1 = (1.55)1/15 - 1 = 1.0297 - 1 = 0.0297, or 2.97%

Current per capita GDP = $10000

So,

$10000 x (1.0297)N = $150000

(1.0297)N = 15

Taking natural logarithm,

N ln 1.0297 = ln 15

N x 0.0293 = 2.708

N = 92.42

So, average person will be equally well-off (earning $150000 per capita) in (2015 + 92) = year 2107

(c) Global super-rich

(1)

Population, top 0.01% = 7400 million x 0.01% = 740000

GDP, top 0.01% = $74000 billion x 3% = $2220 billion

Average income = $2220 billion / 740000 = $3,000,000

(2) World GDP growth rate = ($74000 / $47740)1/15 - 1 = (1.55)1/15 - 1 = 1.0297 - 1 = 0.0297, or 2.97%

Current per capita GDP = $10000

So,

$10000 x (1.0297)N = $3,000,000

(1.0297)N = 300

Taking natural logarithm,

N ln 1.0297 = ln 300

N x 0.0293 = 5.7038

N = 195

So, average person will be equally well-off (earning $3,000,000 per capita) in (2015 + 195) = year 2210

(d) Global Plutocracy

(1)

Population, top 0.0001% = 7400

GDP, top 0.0001% = $74000 billion x 1% = $740 billion

Average income = $740 billion / 7400 = $1,000,000,000

(2) World GDP growth rate = ($74000 / $47740)1/15 - 1 = (1.55)1/15 - 1 = 1.0297 - 1 = 0.0297, or 2.97%

Current per capita GDP = $10000

So,

$10000 x (1.0297)N = $1,000,000,000

(1.0297)N = 100,000

Taking natural logarithm,

N ln 1.0297 = ln 100,000

N x 0.0293 = 11.5129

N = 393

So, average person will be equally well-off (earning $1,000,000,000 per capita) in (2015 + 392) = year 2408

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