1.7. Factor payments in the Solow model. Assume that both labor and capital are paid their marginal products. Let w denote aF (K, AL)/L and r denote OF (K, AL)/OK.

(a) Show that the marginal product of labor, w, is Alf(k) - kf'(k)].

(b) Show that if both capital and labor are paid their marginal products, con- stant returns to scale implies that the total amount paid to the factors of production equals total output. That is, show that under constant returns, WL+ rK = F(K, AL).

(c) Two additional stylized facts about growth listed by Kaldor (1961) are that the return to capital (r) is approximately constant and that the shares of output going to capital and labor are each roughly constant. 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?