Question

1.8 Suppose that investment as a fraction of output in the United States rises permanently from 0.15 to 0.18. Assume that capital’s share is 13

(a) By about how much does output eventually rise relative to what it would have been without the rise in investment?

(b) By about how much does consumption rise relative to what it would have been without the rise in investment?

(c) What is the immediate effect of the rise in investment on consumption? About how long does it take for consumption to return to what it would have been without the rise in investment?

1.9. Factor payments in the Solow model. Assume that both labor and capital are paid their marginal products. Let ω denote ∂F(K, AL)/∂L and r denote [∂F (K, AL)/∂K] − δ.

(a) Show that the marginal product of labor, w, is A [ f(k) − kf′(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, ωL + rK = F(K, AL) − δK.

(c) The return to capital (r) 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 ω growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?

Answer 1

as per the HomeworkLib rules answering the first question