The economics of sharecropping are a classic problem in analytics, going back to John Stuart Mill and the classical economists. Take a look at what modern

The economics of sharecropping are a classic problem in analytics, going back to John Stuart Mill and the classical economists.  Take a look at what modern microeconomists have figured out.


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I understood that this claim was made only in comparison to the previous example of a fixed amount paid up front, with all the profits of the yield beyond that amount going to the tenant. In just those two scenarios, the tenant would be more likely to work harder for the contract with the fixed amount (as the greater the yield, the smaller the percentage of cost attributed to the fixed amount and the greater the ultimate profit the tenant achieved). This would be a significant incentive for the tenant to work harder with the fixed cost (or conversely to work less hard with the split 50-50 of the yield).

You are right to say than in any situation, isolated, that a 50% tax alone may not be sufficient to decrease the incentive to work (it must be compared to an alternative).

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Perhaps it is better to consider a sliding scale. On the left end of the continuum a farmer keeps everything he sows and on the right he must give up all that he produces. Economists would say that as we move from left to right the incentives of the farmer to work the land decrease. As the farmer gets to keep less and less of his product, the opportunity cost of continuing to work the land increases. In the extreme case the farmer is expending all of his labor and getting none of the product. It would clearly benefit him to leave such an arrangement and find a more equitable employment setup. The example can be extended: suppose that for every busshel of wheat the farmer sowed, his employer would throw in an extra busshel free of charge. In this case we would expect the farmer to work even harder than in the case where he kept a "mere" 100% of his product, for in this case the opportunity cost to leisure time -- that is, to not working -- has increased. These economic models are general and simplified and assume "ceteris paribus" -- that all else is equal. It is very true that the exact effects of a tax on output will vary greatly among individuals depending on a great many factors: culture, temperament, family concerns, past experience, the current state of their financial situation, and so on. But individual behavior at this level is too difficult to model, and so economists would simply say that "on the margin" the tax will decrease incentives for labor output. This model, while simple, is extraordinarily powerful, can lead to a great many insights about the world around us, and has been proven empirically true through countless trials in our everyday lives.

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In fact, there's a good chance they might work more because of a tax, especially if they live at an at or below subsistence level where saving is not a big proportion of income allocation.

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Saying there is a good chance that people work more with higher taxation would have to assume that there is a flat tax rate and no alternative to working. It has not been proven that taxation decreases or increases productivity because there is no scenario in the real world where worker A is taxed at a low rate and worker B is taxed at a high rate for doing the same work with the same base earnings and same requirements to maintain an acceptable standard of living. It is a false argument to say that it has not been proven therefore it is likely not true.
In the real world there are many incentives not to work, or not to work to your full potential. When you do not earn much you can get benefits that go a long way to make up for the lost income. Low wage earners can get as little as a 0% tax rate on income, tax credits that give a tax return without any taxes paid, government payments in the form of food stamps or cash payments, free or extremely reduced cost healthcare, etc.
In every other aspect of the economy we see that as there is an incentive to do something, people do it more, and as there is a disincentive to do something, people do it less. Our government is currently structured to give people incentives not to work, or at least not to work to their full potential, while offering disincentives to increasing your earning potential. Your theory is that the more that we offer disincentives in the form of higher taxes the harder people will work to make up for that lost money. You ignore the alternatives of working less, making up for lost earnings with more free time, less stress, and less frustration, or just making do with what they have.
Diminishing returns dictates that at a certain point working harder and harder will earn you a smaller and smaller amount to a point where it is not worth it anymore. High taxation and incentives for not working just ensure that that you reach the point where it is no longer worth it at an earlier point.

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