1. Consider a Cobb-Douglas production function that features capital-augmenting technology: Y(t) = [A(t) K(t)]aL(t)¹-a. Assume thattechnology A(t) grows at rate u: A(t) = μA(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y andK on the balanced growth path.2. Let the production function be Y(t) = J(t)aL(t)1-a, where J(t) is the effective capital stock. The dynamics of J(t) are given byj (t) = sA(t)Y (t) — 8(t). The presence of the A(t) term in this expression means that the productivity of investment at t depends on thetechnology at t. Show that the economy converges to a balanced growth path. What are the growth rates of Y and J on the balanced growth path?dy* Sas y*3. Find the elasticity of output on the balanced growth path with respect to s: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 ofpopulation growth falls.1. What happens to the balanced growth path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of thesevariables as the economy moves to its new balanced growth path.2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).250227POLA2250150

*Hi there , as multiple questions are posted we are solving the complete question with 2 sub parts .…

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. 1. 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. 2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).

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. 1. 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. 2. Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter16: Economic Growth

Section: Chapter Questions

Problem 13E

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