Economics Summer 4.2 Suppose that a firm's only factor of production is its capital stock, K, and that its production function is given by the relation Q = K - ak2 Where Q is output of the firm and a > 0. Assume that capital depreciates at the rate 6 > 0, then the change in the capital stock is equal to the firm's investment (I) less depreciation and the initial level of capital is Ko. Assume also that the price of the firm's output is a constant, p, and the cost of investment is b/ where b is a positive constant. The firm wants to maximize profit over time. a) Define the dynamic optimization problem for the firm, by clearly enumeratiog the objective function and all constraints [2 marks] b) Derive the necessary and sufficient conditions for the optimal solution [1.5 marks] c) Succinctly state (or describe) the steps involved in finding the optimal solution [1.5 marks] a. Bonus question d) Find the optimal solution. [3 marks]