Read e-book online Advanced Macroeconomics Solutions PDF

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If f o ( z pdJ

Hence, from (57), nh-1 C 58 p=o A,+, 2 i = O , 1 , 2 , 3 ,.... 26 > 0, = rnax(l1 h 11% I h E S } exists and for all j such that z, E B(z*, 6,). Let s(p) be as defined in assumption (iv) (see (44)), with p as in (54), and let 59 r]i = m w , Y S(P)}, f o r i = 0 , 1 , 2 ,.... Then, making use of (44) and (48), 60 c(zi+,) - c(zJ < c(zi + r],h,) - c(zi) < -r],p/2 for all ziE B(z*, 26,). 26 1 PRELIMINARY RESULTS Hence, for all zj E B(z*, 8J, Making use of (58) and (59), we now obtain, 62 We now conclude from (61) and (62) that 63 c(zj+,(j)) 1%.

Step 2. Compute Vfo(z,). Step 3. If Vfo(z,) = 0, stop; else, compute H(z,) and go to step 4. Step 4. Set h(z,) = -H(zZ)-' Vfo(zz). Step 5. Set p = 1 in (33) and use this subprocedure to compute A,. Step 6. Set z,+~= z, A,h(z,), set i = i 1 , and go to step 2. We shall discuss modifications of the Newton-Raphson method which apply to nonconvex functions and which also enlarge the region of convergence of the method (39) in the next section. In the meantime, the reader should attempt the following exercises: + + 43 Exercise.

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