Models for dynamic macroeconomics phần 10

Với các yếu tố bên ngoài phức tạp giữa các hành động của các doanh nghiệp và người lao động, tính chất của chức năng phù hợp và xác định cơ chế tiền lương là rất quan trọng để xác định xem tỷ lệ thất nghiệp sẽ được ở trên hoặc dưới mức hiệu quả xã hội. | ANSWERS TO EXERCISES 239 b If the price of capital is halved the q 0 schedule rotates clockwise around its intersection with the horizontal axis and q jumps onto the new saddlepath c From T onwards the q 0 locus returns to its original position. The combination of the subsidy and higher interest rate is exactly offset in the user cost of capital and the marginal revenue product of capital is unaffected throughout. Investment is initially lower than in the previous case q jumps but does not reach the saddlepath its trajectory reaches and crosses the k 0 locus and would diverge if parameters did not change again at T. At time T the original saddlepath is met and the trajectory converges back to its starting point. The farther in the future is T the longer-lasting is the investment increase in the limit as T goes to infinity the initial portion of the trajectory tends to coincide with the saddlepath 1 K 240 ANSWERS TO EXERCISES Solution to exercise 18 a The conditions requested are K1 2 N-1 2 w 1 I A - K-ỉ 2 N1 2 SA -r A A. b From K1 2N-1 2 w we have N K w2 hence F t 2K1 2 N1 2 - G I - w N - K - G I - K ww A 0 r e- r S td dt r e- r S t- -dt. 0 d K t 0 w t c A 1 r S w is constant with respect to K. The form of adjustment costs and of the accumulation constraint imply that I A - 1 and that K 0 if I SK that is if A 1 SK as shown in the figure. d One would need to ensure that G is linearly homogeneous in I and K. For example one could assume that G I K I 12. 2K Solution to exercise 19 Denote gross employment variations in period t by ÃNt positive values of ÃNt represent hiring at the beginning of period t while negative values of ÃNt represent firings at the end of period t - 1. Noting that effective employment at date t is given by Nt Nt-1 à Nt - SNt-1 we have à Nt ANt SNt-1 for each t. ANSWERS TO EXERCISES 241 If turnover costs depend on hiring and layoffs but not on voluntary quits we can rewrite the firm s objective function as Vt Et R Zt i Nt i w Nt i - G ANt i sNt .