7.10: The Neoclassical Growth Model: Capital Deepening

Capital deepening happens when workers are given more tools, machines, or equipment to do their jobs. This means the amount of capital per worker increases. When this happens, each worker can produce more, and overall output rises. But this improvement doesn't continue at the same speed forever. As more capital is added, the extra output from each new machine or tool becomes smaller. This is called diminishing returns.

In the neoclassical growth model, output depends on both capital and labor. When we focus on output per worker, more capital per worker leads to more output per worker. But the increase happens at a decreasing rate. The first improvements bring strong results, but after a certain point, adding more capital doesn’t help as much.

Imagine a local furniture workshop. At first, workers use hand tools and take days to finish a single piece. Then the workshop brings in power tools, which make the process faster and raise output. Later, they buy advanced cutting machines. This helps, but not as much as before. Eventually, even with more machines, workers can’t go much faster. They already have what they need to be efficient. The extra equipment makes a small difference.

This shows the limit of capital deepening. It can raise productivity, but only up to a point. Once those gains slow down, simply adding more machines won’t lead to strong growth. To keep improving, something else has to change—like finding better methods or improving skills. Capital helps, but it’s not the full answer for long-term growth.

Capital deepening takes place when capital grows faster than the workforce, raising the amount of capital per worker.

For example, consider a farm—say, Agro Farm. Over time, it invests in more advanced machinery, such as replacing manual seeders with automated planters. As a result, each worker has more equipment to work with, raising productivity.

In the Solow model, output is described by an aggregate production function: Q = F(L,K), where the inputs, labor and capital, measure the level of output in the economy. When expressed in per-worker terms and holding technology constant, the function becomes Gw = f(Kw), where Gw represents output per worker and Kw represents capital per worker.

As Agro Farm increases capital per worker, output per worker rises, following a concave production curve, as the graph shows this relationship. The economy moves up along this curve, but at diminishing returns to capital. Each new unit of capital yields smaller gains resulting from diminishing returns.

Capital deepening alone cannot sustain long-term growth, as output gains diminish unless there is technological progress.