Consider the problem of a value maximizing firm whose profit function at time t is given by II(K) =eK! where e is the natural exponent, A denotes fixed the productivity level, K, denotes capital and is a parameter representing the elasticity of output with respect to capital. Assume that there is no depreciation of capital, so the law of motion of capital is given as K+1 = K+I where I, is investments in capital at time t. The price of a unit of capital good is p and investment is subject to a smooth convex installation cost given by C(I. K) = R where is a constant denoting the adjustment cost parameter. Time is discrete and runs to infinity, t = 0, 1... oo. Firm manager discounts future values with the factor 3. Based on the above information, answer the following two questions: 1.1 Write down the Bellman equation and derive the optimal investment decision condition. Define marginal Q and provide an economic interpretation. How is average Q related to marginal Q for this firm? [20%] 1.2 Solve the Bellman equation using dynamic programming. You can calibrate model param- eters as follows 8 = 0.95, 0 = 0.7, y = 0.2 and p = 1.2. Discretize capital grid with 301 uniformly spaced points in the interval [30,80]. Constant Productivity Level is = 1.5. Plot value function and investment policy functions. Interpret these graphs. Explain how optimal investment responds to changes in the adjustment cost parameter. changes in how the firm manager values time. Answer in not more than 500 words. [40%]