Calculating rate of growth of per capita income?

Question

Given this question:National income is increasing by 1.5% a year and population by 2.5% a year. What is the rate of growth of per capita income?Attempt: Since per capita income is GDP/ population. I divided 1.5 by 2.5 and got 0.6. Is this right?Thanks.

Answer 1

let Y_t = current national income and

N_t = current population we are looking for

((Y_t+1/N_t+1)-(Y_t/N_t)l/(Y_t/N_t)

We can we can multiply through get the percent change in per capita income as

(Y_t+1/Y_t)/(N_t+1/N_{t -1}

now Define n such that (1+n)=N_t+1/N_t

and y such that (1+y)= Y_t+1/Y_t

so, change in per capita income is (1+y)/(1+n)-1

In in this example that becomes

1.015/1.025 -1

this is close to minus 1%.

The population is growing 1% faster than income so income per person is shrinking by about 1% although not exactly.

If you have any questions in macroeconomics please feel free to reach out I know this stuff cold

Answer 2

Yt/Yt-1 = 1.015 POPt/POPt-1 = 1.025

Yt/POPt / Yt-1/POPt-1 =(Yt/Yt-1)/(POPt/POPt-1) = 1.015/1.025 = .9902 which is approximately -1%.