Problems Set Related to the Solow Growth Model

Question 1 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, and output 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 (that is, total output, not output per worker).

Question 2 Suppose that the production function is Cobb-Douglas. Find expressions for k*, and y* as functions of the parameters of the model, s, n, 8, g, and a.

Question 3 Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time jump in the number of workers.

(a) At the time of the jump, 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 appear, 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?