# Physical Capital and Diminishing Returns

… a core concept in Macroeconomic Policy

Click for MRU video

### Concept description

This deals with the concepts of diminishing returns and the marginal product of capital.

Alex Tabarrok (reference below and link to right) introduces his lesson video with:

“We’ll be digging into the K variable of our simplified Solow model: physical capital. To help with our discussion, we’ll be exploring two specific concepts. The first is the iron logic of diminishing returns which states that, for each new input of capital, there is less and less output produced. Your first input of capital will likely be the most productive, because you’ll allocate this first unit to the most important, value-adding tasks. The second concept we’ll cover is the marginal product of capital. This concept describes the output created by each new unit of invested capital.

“Can you already see how these two forces of capital help answer our question about Germany and Japan? For these two war-torn countries, the first few units of invested capital had a lot of bang for their buck. The first roads between destroyed cities, the first new steel mills, the first new businesses – these helped boost their growth rate tremendously. Even more so, remember that Germany and Japan were growing from a low economic base after the war. It’s easy to grow a lot when the base is small. But all else being equal, you’d rather have a larger base, and grow slower.”

Recall that in the simplified Solow Model output is a function of physical capital, human capital, and ideas – represented by Y = f (K, eL, A). If  human capital and ideas are held constant, Y = f (K). Because of the “iron logic of diminishing returns” output cannot increase linearly with capital, but by a lesser amount such square root of capital. In the following graph, output is assumed to increase with the square root of capital, represented by Y = √K.

###### Output increases with the square root of physical capital

From this second graph (also from the MRU video referenced below) it is clear that the marginal product of capital decreases with additional capital.

###### MRU practice questions

See http://www.mruniversity.com/node/330700, accessed 23 April 2016.

1. The following diagram appeared in the video; what does portion B represent?

Source

Alex Tabarrok, Physical Capital and Diminishing Returns, at http://www.mruniversity.com/courses/principles-economics-macroeconomics/law-diminishing-returns-marginal-product-capital, accessed 23 April 2016.

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