04 Jun Question Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time decrease in the number of workers. (a) At the time of the fall, does output per unit of effective labor rise, fall, or stay the same? Why? (b) After the initial change (if any) in output per unit of effective labor when the new workers disappear, is there any further change in output per unit of effective labor? If so, does it rise or fall? Why? (c) Once the economy has again reached a balanced growth path, is output per unit of effective labor higher, lower, or the same as it was before the new workers appeared? Why? 2) Suppose that the production function is CobbDouglas. (a) Find expressions for k, y, and c as functions of the parameters of the model, s, n, , g, and . (b) What is the golden-rule value of k? (c) What saving rate is needed to yield the golden-rule capital stock? 3) 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 rises. (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 increase in population growth on the path of output (that is, total output, not output per worker). 4) Draw the Solow-Diagram and the time paths for k(t), y(t), g, and ln(Y(t)/L(t)) for an increase in the growth rate of technological progress
Question
Consider an economy with technological progress but without population growth that is on its balanced
growth path. Now suppose there is a one-time decrease in the number of workers.
(a) At the time of the fall, does output per unit of effective labor rise, fall, or stay the same? Why?
(b) After the initial change (if any) in output per unit of effective labor when the new workers disappear, is
there any further change in output per unit of effective labor? If so, does it rise or fall? Why?
(c) Once the economy has again reached a balanced growth path, is output per unit of effective labor
higher, lower, or the same as it was before the new workers appeared? Why?
2) Suppose that the production function is CobbDouglas.
(a) Find expressions for k, y, and c as functions of the parameters of the
model, s, n, , g, and .
(b) What is the golden-rule value of k?
(c) What saving rate is needed to yield the golden-rule capital stock?
3) 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 rises.
(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 increase in population growth on the path of output (that is, total output, not
output per worker).
4) Draw the Solow-Diagram and the time paths for k(t), y(t), g, and ln(Y(t)/L(t)) for an increase in the
growth rate of technological progress
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