The Solow Model 1 – Introduction
The Solow Model is a workhorse model of economic growth. Many subsequent papers in growth theory (and in business cycle theory) build on this model. A model of growth helps us to structure our thinking. Why is it, for example, that China is growing faster than the United States despite having much poorer institutions such as the rule of law? Surprisingly, even a simple version of the Solow model offers some useful predictions and ways to interpet aspects of the growth data. The four videos in this section will be especially useful for people who will see the Solow model in other classes and for anyone who wants to read more of the primary literature on growth theory or the empirics of growth (such as can be found, for example, in Barro and Sala-i-Martin's Economic Growth or David Weil's excellent textbook Economic Growth). We think these videos will be useful, however, even if you don't want to study the theory in more depth. We also offer a briefer treatment in our video The Solow Model (Brief, no math).
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I wonder about your tractor example - if we think of cash crops, every tractor harvests the same amount of land, there would be no productivity decrease as long as you don´t buy too much tractors in relation to land.
Even if labor wasn't held constant the diminishing returns from capital would apply. Having to pay another person to run the tractor diminshes the gains from having another tractor.
Well, but you may another tractor as backup or to decrease the amount of time you spend on harvesting.
You may use the tractor for these purposes, but going from 0 tractors to 1 tractor will increase your production by a larger amount than going from 1 tractor to 2 tractors.
I finally found a comprehensive example for "Diminishing Marginal Productivity" and "Diminishing Returns.” :
http://spiritofjefferson.com/blog/2013/02/hiring-heed-three-guys-and-a-p...
This may be where my antiquated math experience catches up with me. At approximately 2 minutes, you begin your evaluation of the equation by first holding all components other than K constant. Fine. But, at that point, you begin making assumptions (as near as I can tell,) about the relationship of K to Y. The first is the assumption there is a diminishing rate of return associated with increases in K. I'm willing to accept the assumption, but... what's the premise? Why is that relationship a logical assumption? Aren't the permutations of the assumptions about that relationship somewhat unlimited? Could the assumption be just as easily that it is a doubling of returns? The mathematical assumptions being made seem to compound from this point forward in this segment.
I think he's making these assumptions based on the generally understood relationship between physical capital and production. Without math, economists have believed for centuries that having more physical capital increases production with diminishing returns.
Assuming you have someone to drive the tractor. But in the example you *just* have more 'K'apital. Labor is held constant.