3. Assume that both labor and capital are paid their marginal products. Let w denote F...

 

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3. Assume that both labor and capital are paid their marginal products. Let w denote F (K, AL)/L and r denote [OF (K, AL)/K] 8 where F exhibits constant returns to scale in capital and labor. a) Show that the marginal product of labor, w, is A[f(k) k'(k)]. b) Show that if both capital and labor are paid their marginal products, constant returns to scale imply that the total amount paid to the factors of production equals total net output. That is, show that under constant returns, wL+rK = F(K, AL)-8K. c) The return to capital e is roughly constant over time, as are the shares of output going to capital and to labor. Does a Solow economy on a balanced growth path exhibit these properties? What are the growth rates of w and r on a balanced growth path? d) Suppose the economy begins with a level of k less than k*. As k moves toward k*, is w growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r? 3. Assume that both labor and capital are paid their marginal products. Let w denote F (K, AL)/L and r denote [OF (K, AL)/K] 8 where F exhibits constant returns to scale in capital and labor. a) Show that the marginal product of labor, w, is A[f(k) k'(k)]. b) Show that if both capital and labor are paid their marginal products, constant returns to scale imply that the total amount paid to the factors of production equals total net output. That is, show that under constant returns, wL+rK = F(K, AL)-8K. c) The return to capital e is roughly constant over time, as are the shares of output going to capital and to labor. Does a Solow economy on a balanced growth path exhibit these properties? What are the growth rates of w and r on a balanced growth path? d) Suppose the economy begins with a level of k less than k*. As k moves toward k*, is w growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?

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a To show that the marginal product of labor w is Afk kfk we start with the definition of the marginal product of labor w partial FKALpartial L Using ... View the full answer