Exercise 3 At least since Maithus. some have argued that the fact that some factors of production {notably land and natural resources} are available in nite supply must eventually bring growth to a halt. This problem asks you to address this idea in the context of the Solow model. Let the production function be Y = K"{AL]3R1'\""'3. where R is the amount of land. Assume nr 2: . ,6 ::> [i and r1 + )3 w: L The factors of production evolve according to K25Y5K, 51:54, t=nL and ft=a {a} [3 pts] Does this economy have a unique balanced growth path? That is, does the economy converge to a situation in which each of Y, K, L, A and R are growing at constant [not necessarily equal} rates? If so, what are those growth rates? If not, why not? [b] [2 pts} In light of your answer to {a}. does the fact that the stock of land is constant imply that permanent growth is not possible? Explain intuitiyely