Tag Archives: marginal product of capital

Economic History Part V: Factors of Production, The Black Death

Gross Domestic Product, or GDP, is one of the most reliable—or at least most popular—measures for how well an economy is doing. GDP is the total market value of all final goods and services provided in a country in a given year, equal to total consumer, investment, government spending, and net exports (Source A).

Y = C + I + G + NX

But what determines the total production of goods and services? To answer this question, we turn to the factors of production and the subsequent production function. Factors of production are the inputs used to produce goods and services, the most important of which are capital and labor (Source B). This is not a very difficult concept to grasp, as capital is the set of tools that workers use—trucks, drills, buildings, etc.—and labor is quite simply the time people spend working. Capital is denoted by K and labor is denoted by L.

The relationship between the two inputs is expressed through the production function, which states how output is a function of labor and capital:

Y = F(K,L)

Another critical piece of knowledge for anyone interested in GDP is that the total output of an economy is equivalent to its total income, both of which are essentially considered the same thing by economists. And since the factors of production and the production function together determine the total output of goods and services, they also essentially determine national income (Source B).

The distribution of national income is determined by factor prices, which are the amounts paid to the factors of production which, for our purposes, are capital and labor. To put it in perspective, we are talking about the wages that laborers earn and the rent which owners of capital collect.

So what is the relationship between factor prices and factor quantities?

Well I would argue that the best way to find out is through real-life examples. Let’s take a look at 14th century Europe, or more specifically, the 1348 outbreak of the bubonic plague. “The Black Death visited unprecedented mortality rates on Europe, realigning relative values of factors of production, and in consequence the costs and benefits of defining and enforcing property rights…overall one-quarter to one-third of the continent’s population perished in half a decade, although in extreme instances some locales were utterly depopulated…” (Source C).

Due to the massive depopulation taking place in these countries at this time, the marginal product of labor, or MPL, rose significantly. Marginal product of labor is the extra amount of output gained from one extra unit of labor, holding the amount of capital fixed. The economy became unbalanced as feudal society adapted very poorly to the rapid changes taking place; many medieval institutions were destroyed (Source C).

The Black Death left most land and physical capital unscathed, and the effects on the animal population were not so significant, but the human casualties, again, were astounding. Naturally, this led to an increase in the marginal product of labor because the amount of labor fell—the sharp increase in real wages support this fact (Source C). The reduction in the labor force resulted, in fact, in the doubling of real wages (Source B).

The severe drop in the labor force reduced the marginal product of capital as well. As fewer people were available to farm the land, adding more land and other physical capital would not necessarily have increased their output, so land rents fell (Source C).

Essentially, the production function measures technology and not economic behavior. Click here if you’d like an alternate explanation with a practice problem!

  1. Source A:
  2. Source B: Macroeconomics, by Gregory Mankiw.
  3. Source C:
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Posted by on April 7, 2011 in Economic History


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