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?