Labor Productivity

How come the increase in physical capital is more likely to increase labor productivity than an increase in the labor force participation rate?

Labor productivity is productivity per each worker. Upgrades in physical capital make each worker more efficient. Labor for participation rate is just the percent of those employed out of the total eligible population. It has nothing to do with the efficiency of the individual worker.

You have at least 2 factors of production: Labor (L) and Capital (K).

Labor force participation rate means the % of labor in total production factor (L+K).

Due diminishing returns of capital, diminishing marginal productivity of factors, you must reach an optimum ratio of labor and capital.

For example, you have 3 computers, so it is widely known that each pc is used by 1 person at any working day. Suppose each worker with one pc can issue 5 reports a day (15 total). What happens if you increase the labor participation rate? You hired a new worker but you still have 3 pcs, however, the total reports issued in a day increased to 16. The first thing you must note is that the extra worker has a marginal productivity of 1 report instead of 5 (the diminishing marginal productivity of a factor when you fix the other). If you add a new pc you can increase production to 20 reports, so capital is more likely to increase productivity than increasing labor participation.

In countries with low capital, this case turns to be 3 pcs and 10 workers, so here, adding capital is the best way to increase production, thus GDP. Advanced countries have 10 pcs and 10 workers (an optimum scenario), so they will necessarily increase both factors to expand economy, which is hard. Instead they rely in a third factor known as technology (A). Also, their Labor (L) is more educated to the extent they can make the best use of those new technologies.

Hope this helps.