(b) It can be a closed economy (or a large open economy), but then the as-sumption that R=1/βhas to be changed. E,{n,T=,[l +(I -z)r,]}-’ BTzO. Solutions Problem Set 3 Macro II (14.452) Francisco A. Gallego 04/27/2005 1 Qtheory of investment in continuous time and no uncertainty Consider the inﬁnite horizon model of a ﬁrm facing adjustment costs to invest- ... (you have to use the transversality condition to rule out transversality condition lim,, 3. condition holds, the left-hand side of the ∂C Euler equation is constant, so λ is constant, and both Euler equations hold. Because of the in nite dimension of the opti-mization problem, we also have to consider the transversality condition. • Macro theories can broadly be classiﬁed as follows: (1) Models with aggregate shocks (e.g. In addition, there is the transversality condition: lim t!1 tB t+1u 0(C t) = 0 (7) 2.1.2 The Firm Problem There is a representative rm. The relevant terminal condition for the in–nite-horizon case, just as in the –nite-horizon case, can be derived, however, from eq. cash ows). Characterization of Equilibrium Household Maximization Household Maximization II Passing to the limit, the latter condition becomes the transversality condition, lim T!1 T(1+n)Tu0(c T)k T+1 = 0: (7) More detailed discussion of the necessity of this condition can be found else- (e) Determine a set of (W−1,C−1) pairs for which a constant-growth path is feasible and satisﬁes the transversality condition. It is useful to transform the model above into a … But if under some incompletely specified conditions the central planner burns part of the crops or something, in order to guarantee that everything is consumed in the last period, then that may be a significant difference. (3). The transversality condition says that the present discounted value of the capital stock at the \end of time" is zero: lim t!1 E 0 t tk t+1 = 0 (9) An alternative way to nd the rst order conditions is by setting the problem up as a dynamic programming problem. The transversality condition is a necessary condition for the vanishing of the first variation of a functional. The arbitrary constants on which the solution of the Euler equation depends are determined by means of the tranversality condition. Let’s adopt the Option (a) ﬁrst, and later address Option (b). For the problem in 1.4 the transversality condition is given by lim T!1 T 1 @u(c T) @c T k T+1 = 0: (1.6) To understand the form and the reason for the transversality condition, consider The state variable here is k t(A tis also a state, but I’m going to ignore it for 6 in (3) is the rate of depreciation of physical capital. The transversality condition, with constant C growth, is βt times a constant times Cˆ Transversality condition. It discounts future cash ows by the stochastic discount factor. Omer¨ Ozak (SMU)¨ Economic Growth Macroeconomics II 22/101. The rm wants to maximize the present discounted value of (real) net revenues (i.e. Now, the transversality condition implies that there is a limit to what a person can consume in one period. A necessary condition for optimality in variational problems with variable end-points. the corresponding transversality conditions, which imply the natural borrowing constraints. In solving this problem he takes z, the stochastic sequences {G,), {T,), {r,} and the initial level of capital and government debt as given. Notice transversality condition is written in terms of the current-value costate variable. The first variation of a functional consume in one period the left-hand side of the in nite of... 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