Consider the following production functions for output and new knowledge. Y = K (A(1 sR)L) 1 (1) A = L AA , < 1 (2)

a) On the balanced growth path A dot/A = g A , where g A is balanced growth-path value for gA. Use this fact and equation

(2) to derive an expression for A on the balanced growth path in terms of , sR, , n, , and L.

b) Assume there is no capital (K = 0). Use your answer in part (a) and production function of output to obtain an expression for Y on the balanced growth path. Find the value of sR that maximized output on the balanced growth path.