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Consider the version of the Solow model with a general production function that exhibits constant-returns to...

Consider the version of the Solow model with a general production function that exhibits constant-returns to - scale in capital and effective labor. Suppose that the growth rate of the labor force increases permanently from n0 to nN .

(a) Draw the actual investment curve and the break-even investment line

with the original and the new n. How does k∗ change between the initial BGP and the new one?

(b) Suppose that the economy is at its original BGP where the growth rate of the labor force is n0. Let t0 denote the period when n increases permanently to level nN and tN denote the period in which the economy converges to the new BGP. Plot the following figures one below the other in sequence:

(i) First, plot the growth rate of the labor force n against time denoted by t.

(ii) Next, plot the rate of change of capital in units of effect labor k dot against time.

(iii) Finally, plot capital in units of effective labor k against time.

(c) Plot the growth rate of output per worker against time and then ln (Y / L) against time. What can you conclude about the level and growth effects on Y / L caused by the increase in n?

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