All answers should be handwritten.

5 Solow model (30 points) Take the Solow model, but assume that the production function is given by: a-1 e 5 Vi [f_-t- (A K= + (1 a) (AL) = |7 where A, is capital-specific productivity and Ay, is labor specific productivity. Ay, grows at constant rate g4, and Ay, grows at constant rate g, . As in the Solow model from the slides, K, = sY, 0 K,. Population L, grows at constant rate n. 1. Show that under perfect competition, we would have that Y, = R, K, + WL, where R, is the rental rate of capital and W} is the wage. 2. Show that there is no balanced growth path with g4, > 0. For the remainder of the question, assume that A, = 1. 3. Assume there is a balanced growth path. Solve for the growth rate of total output and income per capita on the BGP. Does n have a growth effect on either? 4. Show that on the BGP, sY; = (g4, + n+0) K. 5. Show that to maximize consumption on the BGP, we need r = g, where g is the growth rate of total output. What does this imply about the importance of the Cobb-Douglas production function assumption for the golden rule result? 6. Prove that there is a BGP. Does have a level effect