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,
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,
In its simplest form, labor productivity tells us, in Dateland, 0.125 kgs Ajwa dates are produced by a Dateland worker in one hour.
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 (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.
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.”
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:
the same formula does apply to ladders costing 750 SAR each, assuming
uniformity in usage and zero market value after 20 years. Thus, the annual cost (depreciation) of
75 SAR per year for using ladders is estimated based on the formula below:
In other words, it is assumed that land has an infinite useful life.
Therefore, formula used above does not apply to land. The cost of land used in date production is estimated by the rental rate of the land.
It is assumed that this rate is 2 SAR per square meter per year. Hence, the annual rental cost of 1,000 square meters of land, 2,000 SAR, is estimated based on the formula below:
1,000 square meters × 2 SAR per square meter per year = 2,000 SAR/year
We have 5 workers working 200 days in a year, and each day each works 8 hours. Hourly wage is 15 SAR. Hence, the annual labor cost of 5 workers, 120,000 SAR/year, is estimated based on the formula below:
5 workers x 200 days x 8 hours per day x 15 SAR per hour = 120,000 SAR/year
As a result, the annual cost of combined inputs, i.e., combined units for short, is 122,375 SAR
[=300 SAR/year for date palms + 75 SAR/year for ladders + 2,000 SAR/year for land + 120,000 SAR/year for labor].
We have now all the ingredients for the formula to calculate multifactor productivity (or total factor productivity). We plug them in the formula to get 0.0082 kgs Ajwa dates per one unit SAR.
In other words, we find that the total factor productivity is 0.0082 kgs, or 8.2 grams Ajwa dates per one unit SAR. As you remember, we have, based on this hypothetical data, found that productivity 0.125 kgs Ajwa dates per workerhours
Most of the data sources provide us with multifactor productivity series for countries.
However, even with an economy producing only one type of product, as shown above, it’s extremely a tedious task to estimate multifactor productivity directly.
In real world, countries produce millions of different products and services. Thus, to estimate multifactor productivity through a direct method shown above becomes an impossible task. Still, there are methods to estimate multifactor productivity indirectly.
One of the most famous one among indirect measurements of multifactor (total) productivity is called Solow Residual, which we will not explain because for our purpose to understand the meaning of multifactor (total) productivity is sufficient.
(or simply capital) is one of them. Plant, property, and equipment (PPE) are in
the category of physical capital. The better tools available to workers of a date farm, the higher
the productivity might be. For example, workers equipped with shaking machines will harvest
more dates in one hour than those of workers using simple ladders for harvesting.
is another factor that can improve productivity. Human capital refers to the knowledge and skills acquired by workers through education, training, and experience.
For example, date farmers trained for proper harvesting and cultivating of date palms will not reduce the palm trees capacity of producing dates in the next harvest.
Natural resources are inputs provided by nature, which are used in the production of goods and services. These inputs include land, rivers, mineral deposits, air and so on. For example, sandy loamy soils are best for date palms. Moreover, these trees need plenty of water during flowering and fruiting stages.
Technological knowledge refers to society’s knowledge of how to do something effectively and efficiently.
This knowledge, in the case of date farming, have been accumulated for thousands of years because there is archeological evidence that dates were cultivated in the Fertile Crescent, a region bordered by the Tigris and Euphrates Rivers, as early as 4000 B.C.
Even though it seems that technological knowledge and human capital are intently related, there is still a significant difference between them.
For example, a society having substantial amount of technological knowledge on how to produce dates but failing to transmit this knowledge to its date farmers would experience poor human capital.
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