Problem 2: Solow Model (10 points) Consider a Solow model in discrete time with A(t) = L(t) = 1 and the following production function 0 if KE (0, K) F(K) = VK -K if K E [ K, too)' Other parts of the model including the capital depreciation rate o and saving rate s are still constant parameters. (a) Prove that for V(6, s) E (0, 1)2, there exists K > 0 s.t. the model has two steady-state equilibria. (2 points) (b) When there are two steady-state equilibria, find the range of K(0) s.t. K(t) converges monotonically to at least one of the steady-states. (4 points) (c) Given parameters {6, K}, find the range of parameter s, s.t. the economy always fails to grow. (4 points)