5. To solve the general Solow model analytically one can apply a trick as in Exercise 3 of Chapter 3. Define z "' k1 - a . Show that z is the capital- output ratio, k/y. Then show that:

z = (1 -a)s-)z, {50)

where A."' {1 - a)(n + g + o). Note that {50) is linear. Show that the steady state value of z is z* = {1 - a)s/J = sf (n + g + r5). Solve (50) by finding the characteristic roots, etc., and show that {given an initial capital-output ratio z0) the solution is: