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 s t 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 Y, = (A+ AA) F[K.], t > T, 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 (/Jao to maximize the the present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: v[Ko. 0] = max(4) [er (AFIK]-1 - ; x )at + for(A+ DA)FIK]-1,- ]x *)dt subject to = I Ko is given. 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 /, is the amount of capital invested (or dis-invested), then the total cost of investment is given by / + : 2, where x is 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