وجود و یکتایی تعادل در اقتصادهای پویا تحریف با سرمایه و نیروی کار

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exists and is unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a lattice based approach to the problem. The class of economies for which we are able to obtain our existence and uniqueness result is considerably larger than those considered in previous work. We conclude by applying the new results to some important examples of monetary economies often used in applied work. Journal of Economic Literature Classification Numbers: C62, D51, D90, E10.

We thank John Coleman, Michael Jerison, Stefan Krasa, Olivier Morand, Manuel Santos and Charles Van Marrewijk, as well as the seminar participants at the University of Florida, Florida State University, the 1999 Summer Meetings of the Econometric Society, Fourth Conference of the Society for the Advancement of Economic Theory, the MidWest Economic Theory (October 1999), Southern California Theory meetings (March 2000), MidWest Macroeconomics meetings (April 2000), Theory and Methods in Macroeconomics (May 2000), and the annual meetings of the Society of Economic Dynamics (June 2000), as well as the faculty workshop at Arizona State for helpful discussions. In addition, Kevin Reffett thanks the Tinbergen Institute at the Erasmus University for their gracious support during his visit (Fall 1998) and the Dean's Award for Excellence at College of Business at Arizona State for summer funding of this research. The authors are responsible for any errors and omissions that remain in the paper.This paper studied the existence of competitive equilibrium in a large class of dynamic recursive economies with capital accumulation and elastic labor supply. The type of equilibrium distortions considered encompasses a broad class of non-optimal environments including distortionary taxation policies, situations where firms face equilibrium production externalities, and various monetary economies where there exists a functional equiv- alence between monetary and real economies. This class of infinite horizon dynamic equilibrium models continues to be the standard setting used to model many issues in applied macroeconomics.2 Relative to the existing literature concerning the existence of equilibrium for these models, we are able to make progress in a number of important directions. First, we are able to provide conditions under which there exists a competitive equi- librium for situations where both the equilibrium distortions and the period preferences are allowed to be quite general. To accomplish this, we develop a class of concave, monotone operator methods for these economies with elastic labor supply. In particular in our setting, period preferences and equilibrium distortions are allowed to take a more general form than in previous work.

In this paper we have presented a set of sufficient conditions for the existence of equilibrium in representative agent distorted dynamic economies with capital and elastic labor supply. What is important here is that we require none of the homogeneity assumptions for equilibrium dis- tortions and preferences that have been required in the previous literature. In many applications, these assumptions prove problematic. In addition, we are able to characterize sets of sufficient conditions under which the equilibrium policies vary in a monotone manner with respect to theparameters of policy and technology. We feel that given the importance of applied work in general equilibrium of distorted stochastic growth models with both capital and elastic labor supply (many with production exter- nalities), the added level of generality is important. There are many additional interesting questions to ask in future research. One issue concerns the existence and characterization of equilibrium in representative agent models with multisector production and meaningful fluctuations in relative prices within each period. Such economies (with many goods and many sectors) offer a wide range of questions concerning the robustness of our results. In addition, similar questions can be asked in multiagent settings. Work by Kehoe, Romer, and Woodford [30] provides some initial results on this problem, but their methods do not exploit either the recursive nature of these economies or the monotonicity of operators which can be used to pose the existence of equilibrium problem. In this work (as in the work of Santos and Vigo-Aguiar [38]), the differentiability of optimal plans are both potentially very important for the existence and characterization of equilibrium. Applications of (and generalizations of) the implicit function theorem to non-smooth environments appear to be criti- cal if progress is going to be made along these lines (see Shannon [39] for a discussion of regular, nonsmooth methods for solving systems of equa- tions). More important, since order is what is critical when conducting comparative analytic statements, a purely latticed based approach based upon the concerns of supermodularity and lattice programming such as in the work of Topkis [40, 41] along with the use of a more general ordered based fixed point theory adapted for correspondences found in Zhou [42] might provide a very powerful alternative to the topological approaches often take to such problems. Such an approach would allow for concerns of monotonicity to stand paramount, as opposed to assumptions concern- ing the strong concavity of the primitive economic data such as found in Coleman [9]. The results in Mirman, Morand, and Reffett [35] show that such an order-based alternative is available for the class of models con- sidered in Coleman [9]. In future work, we plan to pursue these issues in multiagent settings and dynamic games more generally.