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Models for dynamic macroeconomics phần 5

Đầu tư tôi chi phí Vn G (I) = Vn I + 1 I 2. 2 Công ty này tối đa hóa giá trị hiện tại chiết khấu theo tỷ lệ r = 0,25 lưu chuyển tiền tệ của nó. (a) (b) (c) các điều kiện đầu tiên thứ tự của các vấn đề tối ưu hóa năng động, và mô tả giải pháp đồ họa giả sử rằng Vn = 1 (không đổi). | INVESTMENT 99 The usual accumutation constraint has 8 0.25 so K I 0.25K. Investing I costs PkG I Pk l 212 . The firm maximizes the present discounted value at rate r 0.25 of its cashflows. a Write the first-order conditions of the dynamic optimization problem and characterize the solution graphically supposing that Pk 1 constant . b Starting from the steady state of the Pk 1 case show the effects of a 50 subsidy of investment so that Pk is halved . c Discuss the dynamics of optimal investment if at time t 0 when Pk is halved it is also announced that at some future time T 0 the interest rate will be tripled so thatr t 0.75 for t T. Exercise 18 The revenue flow of a firm is given by R K N 2K1 2N1 2 where N is a freely adjustable factor paid a wage w t at time t K is accumulated according to K I 8K and an investment flow I costs G I I 112 . Note that Pk 1 hence q X. a Write the first-order conditions for maximization of present discounted at rate r value of cash flows over an infinite planning horizon. b Taking r and 8 to be constant write an expression for X 0 in terms of w t the function describing the time path of wages. c Evaluate that expression in the case where w t w is constant and characterize the solution graphically. d How could the problem be modified so that investment is a function of the average value of capital that is of Tobin s average q FURTHER READING Nickell 1978 offers an early very clear treatment of many issues dealt with in this chapter. Section 2.5 follows Hayashi 1982 . For a detailed and clear treatment of saddlepath dynamics generated by anticipated and non-anticipated parameter changes see Abel 1982 . The effects of uncertainty on optimal investment flows under convex adjustment costs sketched in Section 2.4 were originally studied by Hartman 1972 . A more detailed treatment of optimal inaction in a certainty setting maybe found in Bertola 1992 . 100 INVESTMENT Dixit 1993 offers a very clear treatment of optimization problems under .