Question

From 2009 to 2010, per capita real gross domestic product (GDP) in the United States grew by 2.8 percent. Given that prices increased by 1.5 percent and the population grew by 1 percent. Assume that the US nominal GDP growth rate is constant, how long will it take for the nominal GDP to double?

Answer 1

Per capita real GDP = Real GDP / Population = (Nominal GDP / Price level) / Population

= Nominal GDP / (Price level x Population)

So,

% Growth in Per capita real GDP = % Growth in Nominal GDP - % Growth in Price level - % Growth in Population

2.8% = % Growth in Nominal GDP - 1.5% - 1%

2.8% = % Growth in Nominal GDP - 2.5%

% Growth in Nominal GDP = 4.3%

If doubling period be N years, then

Nominal GDP x (1.043)^N = 2 x Nominal GDP

(1.043)^N = 2

Taking natural log,

N x ln 1.043 = ln 2

N x 0.0421 = 0.6931

N = 16.46 years