Labor Productivity

Labor productivity, output per worker, is important because many economists agree that it explains the large variation in living standards among countries – countries enjoying higher labor productivity levels have higher living standards than those with lower productivity. Paul Krugman, a recipient of the Nobel Memorial Prize in Economic Sciences in 2008, in his book The Age of Diminishing Expectations (1994), claimed,

Productivity isn’t everything, but in the long run it is almost everything. A country’s ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker.

The formal definition of the term labor productivity is quantity of goods and services produced by a worker in one hour. In a formula form,

labor productivity = quantity of goods and servicestotal hours worked

Labor Productivity example :

Let’s turn back to our beloved economy, Dateland. However, this time, to make things clearer we are going to assume that Dateland produces only Ajwa dates.

Figure 1 depicts a simplified production process (or you can say a production function) for Ajwa dates.

Inputs in this production function are date palms, labor, ladders to climb palm trees to pick dates, and land, whereas the output (sometimes, it is called throughput) is Ajwa dates.

More precisely, according to the production function depicted in Figure 1, the combination of 20 date palms, 5 laborers, 2 ladders and 1,000 square meters land produces 1,000 kgs Ajwa dates.

using the following formula

From the second input box in Figure 1, we deduce that those five workers (laborers) work 8,000 hours annually [=5 workers x 8 hours per day x 200 days]. Thus, 8,000 workerhours produce 1,000 kgs Ajwa dates. If we apply our labor productivity formula given above,

labor productivity =
1,000 kgs Ajwa dates8,000 workerhours = 0.125 kgs Ajwa dates per workerhour

In its simplest form, labor productivity tells us, in Dateland, 0.125 kgs Ajwa dates are produced by a Dateland worker in one hour.

quantity of goods and services(realGDP)=total income=total expenditure=labor productivity×total hoursworked

What happens when the Labor productivity changes:

Imagine that with a move of a magician’s wand we increase the labor productivity of Dateland’s workers to 2 kgs of Ajwa dates per worker-hour.

This means with the same amounts of other inputs, Dateland would be able to produce 16,000 kgs of Ajwa dates [ 8,000 workerhours × 2 Ajwa dates per workerhour].

In aggregate, with the productivity level of 2 Ajwa dates per workerhour, Dateland’s citizens real income would increase 16 times relative to the productivity level of 0.125 Ajwa dates per workerhour.

By the way, we will soon learn that we do not need a magician’s wand to increase productivity.

There are factors that affect productivity positively. However, before delving in these factors, we will introduce another concept, total factor productivity, or multifactor productivity, which is widely used by economists and statisticians. 

Multifactor Productivity (Total Factor Productivity):

Multifactor productivity (or total factor productivity) is a more comprehensive economic performance measure than that of labor productivity, because multifactor productivity takes all inputs (production factors) used in the production process into account. 

Multifactor productivity = total factor productivity = quantity of goods and servicescombined inputs

However, there are two challenges in combining inputs under “combined inputs”. The first challenge is that inputs are different in the sense that their units are different – land is measured by using meter square or square foot whereas workerhours by hours.

Thus, adding them up without converting their amounts into a common unit leads to the apple and orange problem. In our case, for example, we cannot add 20 date palms to 2 ladders.

The second challenge is that some inputs have longer horizon in their usage than other inputs. In our case, for example, a date palm has, on average, a 100-year useful life whereas a ladder has, on average, a useful life of 20 years.

Since productivity is usually measured annually, we cannot load the entire cost of a date palm, which will generate dates for 100 years, into “combined inputs,” - the denominator of multifactor productivity formula.

Thus, we should convert inputs into a common unit. The common unit is, in our case, SAR. Then, we should calculate the annual cost of each input in the production process. And finally, we should add these annual costs together to estimate “combined inputs.”

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We have 20 date palms priced at 1,500 SAR per tree having a useful life of 100 years each (from Figure1).

Assuming that after 100 years, the palm tree has zero market value, and the usage is uniform in each year for 100 years, then the annual cost (depreciation) of 300 SAR per year for using date palms is estimated based on the formula below:

20 date trees × 1,500 SAR100 years = 300 SAR/year