Consider the following model on investment without adjustment costs. Current investment and the capital stock are related according to: I, =K,-(1-5)K,, where 8 = 0 is the rate of depreciation. Assume that the production function takes the form Y = BK/2, where B is productivity parameter. Assume the interest rater. is constant over the planning horizon; the firm sells its output in a perfectly competitive market, and that the capital market if efficient. Let the unit price of output be P and the unit price of capital goods be denoted by P- What role does depreciation rate and interest rate play in investment decisions? Explain. Assume that a representative firm buys a unit of capital at time t=0 and expect to use it forever, taking into consideration the cost of purchasing the capital good. What is the present value of a stream of profit from using the capital good. Setup the firm's maximization problem and derive the first-order condition. Explain the implications of the first order condition derived. Derive the investment function from the above maximization problem. What factors influence investors behaviour? Carefully explain each.