Econ 441 Alan Deardorff Problem Set 1 International Equilibrium Page 1 of 1 Problem Set 1 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. 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? 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. d. Differentiate the definition of “Homogeneous of Degree k “ with respect to λ, and evaluate the result at λ=1. Then use this result to show that, if factors of production are paid the value of their marginal products as assumed under perfect competition, then factor payments will exactly equal the value of output
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