Question

Growth Rate Calculations. U.S. GDP in 2018 was $20.9 trillion, and U.S. GDP/person in 2018 was about $62,500, while China’s GDP in 2019 is projected to be $14.2 trillion (converted to US$ at market exchange rates), and China’s GDP/person in 2019 is projected to be $19,520 (converted to US$ at PPP-adjusted exchange rates).

a) Suppose that U.S. real GDP continues to grow at its recent pace of 2.3%/yr. What will U.S. real GDP (in 2018$) be in 2028? (Recall that if a series y grows at a constant rate g, then yt = y0 egt, or equivalently, yt = ys eg(t-s).)

b) Suppose instead that U.S. real GDP grows at its longer-run historical rate of 3.25%/yr. What would U.S. real GDP (in 2018$) be in 2028 in that case?

c) Suppose that U.S. real GDP/person continues to grow at its recent pace of 1.6%/yr. What will U.S. real GDP/person (in 2018$) be in 2028?

d) Suppose instead that U.S. real GDP/person grows at its longer-run historical rate of 2.1%/yr. What would U.S. real GDP/person (in 2018$) be in 2028 in that case?

e) Suppose that China’s real GDP continues to grow at its historical average rate of 9.1%/yr. What will China’s real GDP (in 2019US$) be in 2029?

f) Suppose that China’s real GDP/person continues to grow at its historical average rate of 8.2%/yr. What will China’s real GDP/person (in PPP-adjusted 2019US$) be in 2029?

g) If the U.S. grows at the same rate as in part a, and China grows at the same rate as in part e, in how many years from now will China’s real GDP be equal to the U.S.’s real GDP? (Let’s ignore the difference between 2018US$ and 2019US$ and just assume they are the same.)

h) If the U.S grows at the same rate as in part c and China grows at the same rate as in part f, in what year will China’s standard of living be equal to the U.S.’s standard of living? (Again, ignore the difference between 2018US$ and 2019US$.)

Answer 1

To calculate effective future value of GDP or Per Person GDP which is growing at an effective yearly growth rate , we use the compounding method of time series to calculate future value

The formula is :-

Future Value = Present Value (1+ growth rate )ⁿ

Where :-

Present Value = Initial figure

Growth rate = % of growth per year

N = number of years

Answer a :-

U.S real gdp at growth rate of 2.3/year.

PV = 20,900,000,000,000

N =10 years

Growth rate = 2.3 % or 2.3/100=0.023

GDP at year 2028 =20,900,000,000,000(1+0.023)¹⁰

⁼26,236,302,116,000

Answer b :-

US real GDP at growth rate of 3.25/ year :-

PV = 20,900,000,000,000

N =10

r =3.25% or 0.0325

Future value of GDP at 2028 = 20,900,000,000,000(1+0.0325)¹⁰

= 28,777,090,951,000

Answer c :-

US real GDP per person at 1.6/year :-

PV =62500

N = 10

r = 1.6% or 0.016

Future value of GDP at 2028 =62500(1+0.016)¹⁰

=73251.596898

Answer d :-

U.S. real GDP per person at 2.1/year :-

PV =62500

N =10

r =2.1

Future per person GDP =62500(1+0.021)¹⁰

76931.763027

Answer e :-

China real GDP at 9.1/year :-

PV = 14,200,000,000,000

N =10

r =9.1% or 0.091

Future value of China GDP = 33,926,249,392,000

Answer f :-

China real per person GDP at 8.2 per year

PV = 19520

N =10

r =8.2 or 0.082

Future per person GDP =19520(1+0.082)¹⁰

=42929.163002

Answer g :-

The equation for calculation of how many years will it take for the GDP to became equal :-

20900000000000(1.023)ⁿ = 14200000000000000(1.082)ⁿ

Solving the problem we get

72.45 years

Answer h :-

Similarly to calculate standard of living we get

62500(1.016)ⁿ=19520(1.082)ⁿ

Solving the above equation we get

33.26 years