Analogy to dig trenches: digging with bare hands is hard and slow; with a shovel you dig faster; with a backhoe you’re even more productive. The same idea applies to nations: more capital increases productivity.
The more capital available to workers, the more productive a nation will be.
Higher productivity leads to higher wages and standards of living.
Having more capital is desirable, but capital wears out and needs replacement.
The problem with capital is that it wears out over time and must be replaced to maintain or grow the stock.
Gross investment, depreciation, and net investment
Gross investment measures how much capital is being created.
Gross investment alone does not tell us whether the total capital stock is growing or shrinking.
Depreciation is the amount of capital that wears out or is used up during a year.
Net investment tells us how the stock of capital changes over a period.
Net investment is defined as the difference between gross investment and depreciation.
Key equations
Net investment equation:
\text{Net investment} = \text{Gross investment} - \text{Depreciation}
or equivalently
NI = GI - D
If net investment is positive, the total capital stock of a country is growing.
If net investment is negative, capital is depreciating faster than it is being replaced, so the overall capital stock will fall.
In the real world, investment is measured in dollars, but the same principle applies to physical capital as well.
Example: a quick calculation
Starting conditions (at the beginning of the year):
Capital stock: 5 backhoes
Workers: 6
Five workers are very productive and one is not (note: describes individual productivity distribution but not required for the core calculation).
Events during the year:
One backhoe wears out (depreciation): D = 1 backhoe
Two new backhoes are purchased (gross investment): GI = 2 backhoes
Net investment for the year:
NI = GI - D = 2 - 1 = 1 backhoe
Interpretation:
Net investment is positive, so the capital stock increases: new end-of-year stock = 5 - 1 + 2 = 6 backhoes.
With more capital, all workers have access to capital and are more productive than before.
Practical note:
In the real world, the numbers are measured in dollars or other monetary units rather than backhoes, but the principle remains the same.
Implications for productivity and living standards
Positive net investment implies a growing capital stock, which tends to raise worker productivity over time.
Higher productivity tends to raise wages and standards of living.
Negative net investment implies the capital stock is shrinking, which can reduce productivity and potentially wages and living standards over time.
Recap of core ideas
Capital enhances productivity: more capital per worker leads to higher output per worker.
Gross investment vs depreciation:
Gross investment adds to the capital stock.
Depreciation reduces the capital stock by wearing out capital.
Net investment determines the change in the capital stock: NI = GI - D.
Positive NI ⇒ increasing capital stock; negative NI ⇒ decreasing capital stock.
Real-world application: the same math applies when investment is measured in dollars; the underlying concept is about changes in the capital stock over time.