Before the completion of the R & D program, the technology of the firm is represented...

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Before the completion of the R & D program, the technology of the firm is represented by the follow- ing production function: Y₁ = AF[K], 0 st<T, where Y, is output, and K, is the capital stock - both at time t, 0 st<T. Also, A>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], tz T, where AA> 0 is the rise in productivity, and K, is the capi- tal stock at time t, tz T. The problem faced by the firm is to find an investment program (l)o to maximize the fhe present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: viko. 0] = max(AF[K₁] -4 -x)dt + ((A+AA) F[KJ-I-x)dt subject to = I, Ko is given. Herer 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 + 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 problem. Before the completion of the R & D program, the technology of the firm is represented by the follow- ing production function: Y₁ = AF[K], 0 st<T, where Y, is output, and K, is the capital stock - both at time t, 0 st<T. Also, A>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], tz T, where AA> 0 is the rise in productivity, and K, is the capi- tal stock at time t, tz T. The problem faced by the firm is to find an investment program (l)o to maximize the fhe present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: viko. 0] = max(AF[K₁] -4 -x)dt + ((A+AA) F[KJ-I-x)dt subject to = I, Ko is given. Herer 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 + 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 problem.

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The firm is trying to solve an investment problem in order to maximize the present value of profits Heres a summarization of the problem and a general ... View the full answer