## What is Capital Deepening?

Capital deepening refers to an increase in the capital-labor ratio. The capital-labor ratio can go higher either due to an increase in the capital stock or through a decrease in the number of workers. Capital deepening increases the marginal product of labor and decreases the marginal product of capital, i.e., it makes labor more productive (because there are now more units of capital per worker) and capital less productive (because there are now fewer workers per unit of capital).

### Capital Deepening and Standard Economic Growth Theory

Popular theories of growth such as the Solow Growth Model assume that capital and labor are complementary in the production process. It is a very strict assumption because it rules out cases where labor and capital act as substitutes in the production process – for example, robots and manual labor can serve as substitutes in the production of cars. Modern theories of growth tend to distinguish between skilled labor and unskilled labor.

However, within the framework of the Solow Growth Model, capital and labor need to be combined together to produce output. The inputs in the production process (capital and labor) and the output are linked through the production function: **Y = f(K,L)**, where Y is output, K is capital, and L is labor.

The production function exhibits diminishing returns for each individual factor of production and constant returns for all factors of production combined, i.e., the production function is directly replicable, meaning it satisfies the following properties.

- The marginal increase in output due to a one unit increase in capital decreases with the overall capital stock.
- The marginal increase in output due to a one unit increase in labor decreases with the total number of workers.
- The marginal increase in output due to a one unit increase in capital increases with the total number of workers.
- The marginal increase in output due to a one unit increase in labor increases with the overall capital stock.
- Doubling both the level of capital stock and the total number of workers exactly doubles the level of output in the economy.

Capital deepening and its consequences on the productivity of workers are a direct result of the fourth property above. As the capital-labor ratio increases, the marginal product of labor, i.e., the amount of product that can be produced by supplying one more unit of labor, increases.

### Illustrative Example

Consider a farm that uses labor (farmers) and capital (tractors and harvesting machines) to produce output (wheat). Suppose the farm uses 100 farmers and 10 tractors to produce 2,000 tons of wheat per year. If we assume that the farm’s production function satisfies the standard assumptions, then adding one more tractor would make the farmers more productive.

An intuitive way to understand the fact is to think of overcrowding. Increasing the number of tractors means that each farmer (unit of labor) gains more room to work with on a tractor. Thus, each farmer is now more productive.

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