Consider the production function Y=K N . Assume thatN is constant and equal to 1. Note that if z = x^a, then g_z ag_x,where g_z and g_x are the growth rates of z and x.

a. Given the growth approximation here, derive the relation between the growth rate of output and the growth rate of capital.

b. Suppose we want to achieve output growth equal to 2% peryear. What is the required rate of growth of capital?

c. In (b), what happens to the ratio of capital to output overtime?

d. Is it possible to sustain output growth of 2% forever in thiseconomy? Why or why not?