9 Optimal growth with linear utility Consider the optimal growth model with a constant relative risk aversion (CRRA) utility function, Cobb-Douglas production function, and 100% depreciation every period. The social planner maximizes: t=0 t t c Subject to the constraints: t t t k = Ak c + 1 ct 0 0 t k 0 k0 > given. a) Prove that there exists a solution to this optimal growth problem. You can by finding any finite number which is bigger than the highest possible utility level. b) Describe as best you can the solution to this planner's problem. You should note that mechanical application of the first-order conditions and the Euler equation is unlikely to find the solution. c) Suppose instead that we have an "AK" model. Identify conditions under which there is a solution to the planner's problem, and describe the solution under these conditions.