08 Jun Question University of Toronto Mississauga Department of Economics
Question
University of Toronto Mississauga Department of Economics
ECO 325H: Advanced Economic Theory−Macro
Prof. Kambourov
Problem Set 2
Tuesday, September 29, 2015
1. Romer, Chapter 1, Problem 1.5.Suppose that the production function is Cobb-Douglas.
(a) Find expressions for k∗, y∗, and c∗as functions of the parameters of the model, s, n, δ, g, and α.
(b) What is the golden-rule value of k?
(c) What saving rate is needed to yield the golden-rule capital stock?
2. Romer, Chapter 1, Problem 1.6.Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls.
(a) What happens to the balanced-growth-path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these variables as the economy moves to its new balanced growth path.
(b) Describe the effect of the fall in population growth on the path of output (thatis, total output, not output per worker).
3. Romer, Chapter 1, Problem 1.9.Assume that both labor and capital are paid their marginal product. Let wdenoteand rdenote .
(a) Show that the marginal product of labor, w, is A[f(k) −kf0(k)].
(b) Show that if both capital and labor are paid their marginal products, constantreturns 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) −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 wand ron a balanced growth path?
(d) Suppose the economy begins with a level of kless than k∗. As kmoves toward k∗, is wgrowing 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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