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The Cobb Douglas Production Function is widely used in economic models. It takes the following form: | The Cobb Douglas Production Function is widely used in economic models. It takes the following form: | ||
- | Q(L,K) = A Lβ Kα | + | Q(L,K) = A L<sup>β</sup> K<sup>α</sup> |
L:labor \\ | L:labor \\ | ||
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{{:en:linear-production-function-example.png?nolink|}} | {{:en:linear-production-function-example.png?nolink|}} | ||
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+ | ===== Example 3: One Input Production Function with Diminishing Returns ===== | ||
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+ | In this example we will see the case of a production function that has only one factor of production: robots: But if we keep adding robots, the output of each robot will decrease. Maybe because the robots start to chat with each other and it's productivity decreases :-) | ||
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+ | In this example, the production function is: | ||
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+ | Q = 100 * K <sup>0.9</sup> | ||
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+ | If there is only one robot, the output will be the same as in the linear example: 100. But if we add a second robot, the output will be lower: | ||
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+ | 100*2<sup>0.9</sup>= 186 | ||
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+ | Where in the linear example, two robots would have produced 200 T-Shirts | ||
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+ | The charts of both examples is: | ||
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+ | {{ :en:diminishing-returns-production-function-example.svg |}} | ||
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+ | We can see that as we keep adding robots, the difference in the quantity produced between the diminishing returns example and the linear example keeps growing. |