Question

Suppose that country A initially has a lower income-per-head than country B. Then for several years country A saves and invests more of its income. Explain and illustrate the effect of this change over time.

Answer 1

Before answering your question we have to understand the concept of per head income.
Per head income or par capita income is the average income of citizens of a country.
It is calculated by dividing net national income by total population.

Basic formula for calculating net national income is
C + I + G + NX + NFF - IT - D = net national income.
Where, C is Consumption, I is Investments, G is Government expenditures, NX = Net exports (export-imports), NFF is Net foreign factor income, IT is Indirect taxes, D is Depreciation.
As it is clear that investment plays very important role in size of national income, thus increasing investment will lead to growth of national income as whole.
and there's direct relationship between investment and savings.
Investment are considered to be important intermediary forms of savings as it produces value.
For example if a person is saving 40% of it's income, he would definitely be investing it in stocks, bonds, govt. Securities, real estate etc rather than keeping the money at home.

So if country A saves and invest more of it's income in agriculture, machinery, transport vehicles, construction and other sectors then it would increase its national income, and eventually per head income would increase.

Good luck.