Set01a-Equilibrium

Set01a-Equilibrium - Econ 441 Problem Set 1 - Answers Alan...

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Econ 441 Alan Deardorff Problem Set 1 - Answers International Equilibrium Page 1 of 5 Problem Set 1 - Answers International Equilibrium 1. a. Explain how it is possible for a production function to have the property of constant or increasing returns to scale and still satisfy the Law of Diminishing Returns. Returns to scale refers to what happens to output when all inputs are expanded in the same proportion, while the Law of Diminishing Returns refers to expansion of one input holding another input fixed. Thus, the Law of Diminishing Returns says that expansion of the labor input, say, holding the capital input fixed, causes output to rise by smaller and smaller amounts, so that at least eventually the rise in output is smaller than proportional to the expansion of labor. But if that increase in labor were instead accompanied by an increase in capital also, the latter would increase output by more. This would make it possible for output to rise by an equal or greater proportion than the increase in both inputs, thus displaying constant or increasing returns to scale. b. If a production function has only one input, say labor, and displays constant returns to scale, does it then violate the Law of Diminishing Returns? With constant returns to scale and only labor as an input, output is simply proportional to the amount of the input. It is true, therefore, that the marginal product of labor is then constant and does not diminish as more and more labor is used. Whether that is a violation of the Law of Diminishing Returns, however, is debatable, since we are not fixing the input of any other factor, there not being any other factor available to fix. c. Suppose that a production function has two inputs, K and L , and that, contrary to the Law of Diminishing Returns, an increase in L alone always causes output to rise by the same proportion that L has increased. Show that the production function must therefore display increasing returns to scale. If K and L both rise by some proportion λ, we can break the effect into two
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Set01a-Equilibrium - Econ 441 Problem Set 1 - Answers Alan...

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