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Question: 1 the production function consider a cobbdouglas production function with...

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1 The Production Function Consider a Cobb-Douglas production function with two inputs, capital (K) and labor (L. The production function is where A denotes total factor productivity 1. Derive an expression for the marginal product of labor. How does an increase in the quantity of capital affect the marginal product of labor? 2. Does the above production function exhibit constant returns to scale with respect to the number of workers L and the quantity of capital K? Why or why not? Give a brief interpretation Now suppose that labor L does not only depend on bodies but also on the workers level of education. In particular, the production function is now Y = AK (AD1-0, where h denotes the number of years of schooling per worker. 3. Derive an expression for the marginal product of labor. How does an increase in the years of schooling affect the marginal product of labor? Does an increasein education increase or decrease the demand for labor? 4. Let the total supply of workers and capital be L and K respectively. Calculate the equilibrium wage w and the equilibrium return to capitalR. How does w depend on h, L and K? How does R depend on h, L and K? 5. Use the two production functions i (1) and (2) to argue why total factor productivity A and the level of education h are mathematically very similar.
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