Consider a model that is identical to the Solow model we presented in class, except for a change in the production technology.

Consider a model that is identical to the Solow model we presented in class,

except for a change in the production technology. In particular, denote the depreciation rate

by , the population growth rate by n, the constant saving rate by s, and TFP by A.

The production function f(k) in this model is S-shaped" and not always concave. In partic-

ular, assume that the production function is (i) concave when 0 < k  k1; (ii) convex when

k1 < k  k2; and (iii) concave again when k > k2.

(a) Plot the production function and the saving curve for this model.

(b) Plot the depreciation line for the model.

(c) Show that the level of  and n may change the number of potential steady states for this

model. In particular, show that there exist a case where only one steady state exists (other

than k = 0), and that there is a case with three potential steady states.

(d) Use the case with three steady states and answer the following for each steady state:

(i) Assume that you start with a slightly lower level of k than the steady state level.

Will the economy converge to that steady state?

(ii) Assume that the economy starts with a slightly higher level of k than the steady

state level. Will the economy converge to that steady state?