2. A firm begins at time t = 0 with a capital stock of size Ko. The firm has been carrying out an R&D program to raise its productivity. The firm expects that at some time T >0, the R&D program will be completed, and its fruit harvested. Before the completion of the R&D program, the technology of the firm is represented by the follow- ing production function: Y = AF[K],0 st 0 is a parameter representing the total factor productivity before the R&D program is completed. After the R&D program has been completed, the technology of the firm is represented by the pro- duction function Yt = (A+AA) F[K],t2T, where AA > 0 is the rise in productivity, and K; is the capi- tal stock at time t, t 2 T. The problem faced by the firm is to find an investment program (It)tzo to maximize the fhe present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: = + v[Ko, 0] = max(!mo fert(AF[K:] le={ x) dt+spett(A+AA) F[K]-1-2x)dt subject to = It, Ko is given. dk dt Here r is the interest rate. Note that in the problem just stated the capital stock cannot be adjusted instantaneously without incurring prohibitive adjustment costs. More precisely, if I, is the amount of capital invested (or dis-invested), then the total cost of investment is given by le+ **, where xis 1 2K, a positive constant. Explain how the investment problem of the firm can be solved. In answering this question, it is not necessary to provide a complete solution to the problem. 2. A firm begins at time t = 0 with a capital stock of size Ko. The firm has been carrying out an R&D program to raise its productivity. The firm expects that at some time T >0, the R&D program will be completed, and its fruit harvested. Before the completion of the R&D program, the technology of the firm is represented by the follow- ing production function: Y = AF[K],0 st 0 is a parameter representing the total factor productivity before the R&D program is completed. After the R&D program has been completed, the technology of the firm is represented by the pro- duction function Yt = (A+AA) F[K],t2T, where AA > 0 is the rise in productivity, and K; is the capi- tal stock at time t, t 2 T. The problem faced by the firm is to find an investment program (It)tzo to maximize the fhe present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: = + v[Ko, 0] = max(!mo fert(AF[K:] le={ x) dt+spett(A+AA) F[K]-1-2x)dt subject to = It, Ko is given. dk dt Here r is the interest rate. Note that in the problem just stated the capital stock cannot be adjusted instantaneously without incurring prohibitive adjustment costs. More precisely, if I, is the amount of capital invested (or dis-invested), then the total cost of investment is given by le+ **, where xis 1 2K, a positive constant. Explain how the investment problem of the firm can be solved. In answering this question, it is not necessary to provide a complete solution to the