Capital Deepening
What is Capital Deepening?
Capital deepening is an increase in the stock of physical capital per worker, which raises labor productivity and output per worker.
Capital deepening happens when the capital stock grows faster than the workforce, so each worker has more machines, tools, vehicles and structures to work with and can produce more per hour. It has to be paid for out of saving, since resources used to build capital are resources not consumed, and the saving can come from domestic households, firms and government or from foreigners lending through a capital inflow. The process runs into diminishing marginal returns: the second machine per worker adds less than the first, while depreciation grows with the size of the capital stock, so growth from deepening slows and eventually stops at a steady state where investment only replaces worn-out capital. That is the main prediction of the Solow model, and it is why capital deepening explains why some countries are richer than others and why poor countries can grow fast while catching up, but not why the frontier economies keep getting richer decade after decade. Permanent growth in output per worker has to come from better technology and better human capital, not from stacking up more of the same machines.
Capital Deepening: a worked example
A country has a capital stock of $2 trillion and 50 million workers, so capital per worker is $2 trillion / 50 million = $40,000. Suppose output per worker follows y = 200 x the square root of k. Then y = 200 x the square root of $40,000 = 200 x 200 = $40,000 per worker. Now investment raises the capital stock to $8 trillion while the workforce is unchanged, so capital per worker quadruples to $160,000 and output per worker becomes 200 x 400 = $80,000. Capital per worker rose fourfold but output per worker only doubled, which is diminishing returns in one line. Compare the alternative: if the workforce had also quadrupled to 200 million, capital per worker would be back at $40,000, output per worker would sit at its original $40,000, and total output would have quadrupled with no gain in living standards at all.
The mistake students make with capital deepening
Students treat any rise in investment or in the total capital stock as capital deepening. The measure that matters is capital per worker, so when capital and the labor force grow at the same rate the result is capital widening, which raises total output while leaving output per worker and wages flat. A second error is expecting capital deepening to deliver permanent growth in living standards. Diminishing returns mean it raises the level of output per worker and then fades out, so sustained growth per person depends on technological progress.
Capital Deepening questions
What is the difference between capital deepening and capital widening?
Capital deepening raises capital per worker, while capital widening adds capital in step with new workers so that capital per worker is unchanged. Widening lets a growing population keep working at the same productivity, which raises total output but not output per person. Only deepening, or better technology, raises average living standards, which is why a country with rapid labor force growth has to invest heavily just to avoid going backwards on capital per worker.
Why does capital deepening eventually stop raising growth?
Because the marginal product of capital falls as capital per worker rises, so each addition contributes less output than the one before, while required replacement investment rises with the size of the stock. Eventually gross investment only covers depreciation and the growth of the workforce, capital per worker stops rising, and the economy sits at its steady state. Poorer countries have little capital and therefore a high marginal product, which is the reasoning behind the convergence prediction that they should grow faster while catching up.
How is capital deepening financed?
Out of saving, because resources devoted to building capital cannot simultaneously be consumed. The saving can be domestic, from households, retained corporate earnings or a government surplus, or foreign, in which case the capital inflow shows up as a current account deficit. A country with a very low saving rate and little access to foreign capital struggles to raise capital per worker, which is one reason development policy pays so much attention to financial systems and to attracting investment.
Formula / Example
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