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2. Assume that both capital and labor are paid their marginal products. Let w denote OF(K, AL)/OL and r denote OF(K, AL)/ƏK – 8. (a) Show that the marginal product of labor, w, is A[ƒ(k) — kf¹(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 (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 w growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?

2. Assume that both capital and labor are paid their marginal products. Let w denote OF(K, AL)/OL and r denote OF(K, AL)/ƏK – 8. (a) Show that the marginal product of labor, w, is A[ƒ(k) — kf¹(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 (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 w growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2. Assume that both capital and labor are paid their marginal products. Let w denote F(K, AL)/ƏL and r denote ƏF(K, AL)/ƏK – 8. (a) Show that the marginal product of labor, w, is A[ƒ(k) — kf¹(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) – SK. (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 w growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? What about r?
Transcribed Image Text:2. Assume that both capital and labor are paid their marginal products. Let w denote F(K, AL)/ƏL and r denote ƏF(K, AL)/ƏK – 8. (a) Show that the marginal product of labor, w, is A[ƒ(k) — kf¹(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) – SK. (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 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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