3. The production function of a representative firm is given by where K, is capital stock at period t, and t = 1,2. Take A > 0 to be a constant technology index. F(K+) = AK+. The cost of investment C(I) is given by the following quadratic cost function C(I)=I+ where It is investment at period t, and t = 1. Let 0 (1+r1). What is present value of the marginal productivity of capital in period 2, i.e. MPK2? And what is the marginal cost of investing in one more unit of capital in period 1 (i.e marginal cost of adding one more unit of K)? (c) Draw the graph of MPK2 against K2 and the graph of MC against K2 on the same diagram [You can start the x-axis (for K) at K since capital level cannot be less than K (no depreciation)]. Identify the point where the two graphs intersect. What is the capital level, K2, at that point? (d) Is it possible that I = 0? When does this happen in real life? (e) Still assuming 8 = 0 and that A> (1+r). Suppose that for every unit of capital that the firm invests in, the government now gives a subsidy such that its cost function now becomes C(I) (1 s) It + 1 where 0