Models for dynamic macroeconomics phần 2 pot

... e „ 2 Ë 2 Û 2 ε 2 = „Ë 2 Û 2 ε 2 . (1.57) The dynamics of consumption over time and its level in each period are then given by c t+1 = c t + „Ë 2 Û 2 ε 2 + Ëε t+1 , c t = r(A t + H t ) − 1 r „Ë 2 Û 2 ε 2 . The ... as in (1 .27 ) to allow for non-stationarity, and imposing Ï = 0 for simplicity—and saving: y t = a 11 y t−1 + a 12 s t−1 + u 1t , (1.31) s t = a...

Ngày tải lên: 09/08/2014, 19:21

... − 1 2 Û 2  2 +2 2 r  > 0, ‚ 2 = 1 Û 2  −  Ë − 1 2 Û 2  −   Ë − 1 2 Û 2  2 +2 2 r  < 0. Thus, there exist two groups of solutions in the form (2. 52) , q 1 (K , Z)= A 1 Z ‚ 1 and q 2 (K , Z)=A 2 Z ‚ 2 . ... 2. 12. Installed capital and optimal irreversible investment 88 INVESTMENT The quadratic equation has two distinct roots if Û 2 > 0: ‚ 1 =...

Ngày tải lên: 09/08/2014, 19:21

... V 12 > 0, we can COORDINATION AND EXTERNALITIES 21 5 the first equation by V 1 11 and the second by V 2 22 ,wehave: de ∗ 1 +  V 1 12 V 1 11  de ∗ 2 +  V 1 13 V 1 11  dÎ 1 =0,  V 2 21 V 2 22  de ∗ 1 + ... y P t and  ˜ y P t ,is var(y P t )=¯ 2  Û 2 1 +  1 1+r  2 Û 2 x  , var( ˜ y P t )=¯ 2 (Û 2 1 + Û 2 x ), where ¯ ≡ r/(1 + r −Î), Û 2 1 ≡ var(ε 1...

Ngày tải lên: 09/08/2014, 19:21

... 45 2 Dynamic Models of Investment 48 2. 1 Convex Adjustment Costs 49 2. 2 Continuous-Time Optimization 52 2 .2. 1 Characterizing optimal investment 55 2. 3 Steady-State and Adjustment Paths 60 2. 4 ... efficiency 20 6 Appendix A5: Strategic Interactions and Multipliers 21 1 Review Exercises 21 6 Further Reading 21 7 References 21 9 ANSWERS TO EXERCISES 22 1 INDEX 27 4 DETAILE...

Ngày tải lên: 09/08/2014, 19:21

... periods only, with consumption c 1 and c 2 and incomes y 1 and y 2 . Suppose that the utility function in each per iod is u(c)=  ac − (b /2) c 2 for c < a/b; (a 2 /2b) for c ≥ a/b. (Even though the above ... Cochrane (1999) “By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,” Journal of Political Economy, 2, 20 5 25 1. INVESTMENT 57 Figure...

Ngày tải lên: 09/08/2014, 19:21

... Z) − wN ∗ + 1 2 ∂ 2 [(N, Z) − wN] ∂ N 2     N ∗ (N − N ∗ ) 2 , we can conclude that the choice of employment level N = N ∗ implies a loss of surplus equal to 1 2 ‚(N − N ∗ ) 2 . As a result ... p) 2 ;the second one, in which we observe two consecutive variations of opposite sign, has p 2 . Hence, P 1,3 =(1− p 2 )+p 2 =1−2p(1 − p)ifx 1 = x g . Similar reasoning implie...

Ngày tải lên: 09/08/2014, 19:21

... consumption/capital ratio is therefore constant over time under our assumptions. Imposing ˙ k k = ˙ c c in (4.19) and in (4 .21 ), we get c(t)= (Û − 1)b + Ò Û k(t). (4 .22 ) Equation (4 .22 ) implies that the initial ... − Ò). (4.17) Since the law of motion for capital is given by ˙ k = f (k) − c, (4.18) we can therefore study the dynamics of the system in c, k-space. 4 .2. 2. STEADY STATE...

Ngày tải lên: 09/08/2014, 19:21

... EXERCISES Exercise 42 Consider the production function Y = F (K )=  ·K − 1 2 K 2 if K < ·, 1 2 · 2 otherwise. 1 82 COORDINATION AND EXTERNALITIES The artificial economy here described highlights ... Economy, Cambridge, Mass.: MIT Press. Heijdra, B. J., and F. van der Ploeg (20 02) Foundations of Modern Macroeconomics, Oxford: Oxford University Press. Jones, L. E., and R. Manuell...

Ngày tải lên: 09/08/2014, 19:21

... M ∗ : ∂W P ∂ M = ‚ U r x[(1 − 2x) − 2M ∗ (1 − x)]=0 ⇒ 1 − 2x =2M ∗ (1 − x) ⇒ M ∗ = 1 − 2x 2 − 2x . (5 .22 ) Since 0 ≤ M ∗ ≤ 1, for x ≥ 1 2 we get M ∗ = 0. When each agent is willing to consume at ... qualitatively realistic enough to offer practical implications for the dynamics of labor market flows, for the steady state of the economy, and for the dynamic adjustment process towa...

Ngày tải lên: 09/08/2014, 19:21

... two first-order conditions, which yields V 1 11 de ∗ 1 + V 1 12 de ∗ 2 + V 1 13 dÎ =0, V 2 21 de ∗ 1 + V 2 22 de ∗ 2 + V 2 23 dÎ =0. 26 2 ANSWERS TO EXERCISES Solution to exercise 45 (a) Calculating ... + 1 dt  ∂v(·) ∂Á E (dÁ)+ ∂ 2 v(·) ∂Á 2 (dÁ) 2  = Á + ∂v(·) ∂Á Á(Ë + ‚‰)+ ∂ 2 v(·) ∂Á 2 Á 2 Û 2 , with solutions in the form v(Á)= Á r − Ë − ‰‚ + K 1 Á · 1 + K 2...

Ngày tải lên: 09/08/2014, 19:21