Monotone Methods for Distorted Economies

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The Effects Of Reinforcement Inclusions On Wear Tolerance, Playing Quality And Physical Properties In A Silt Loam And Sand Rootzone Matrix

Reinforcement inclusions have been advocated to alleviate wear, compaction, and unstable surfaces in sports fields, but little research on the effects of these materials has been conducted in the USA. Experiments were established on a native silt loam and a sand rootzone matrix, seeded with a Kentucky bluegrass (Poa pratensis L.) blend, at the Joseph Troll Turf Research Center, University of Massachusetts, Amherst, USA to determine the effects of reinforcement inclusions on wear, surface hardness, traction, ball roll, ball bounce resilience, water infiltration rate, soil bulk density, air porosity, total porosity, and root weights. Three types of reinforcement inclusions (Sportgrass, Netlon, Turfgrids) were tested along with a non-reinforced control in a three year study. The treatments were set out in a randomized complete block design with four replications in both soils. No inclusion provided less wear or greater infiltration or air-filled porosity relative to the control. Reinforcement inclusions showed significant differences, however, in surface hardness, traction, and ball roll relative to the control, although this varied with the time of year. Infiltration rates, airfilled porosity, total pore space, bulk density, hardness, traction, ball roll, and ball rebound were greater on the sand rootzone than on the silt loam. Significant correlations were present between soil bulk density, surface hardness, traction, and ball roll. Based on our study, the use of reinforcement inclusions to provide better wear tolerance for sand or native soil athletic fields is not warranted. Certain playing surface characteristics, however, may be slightly improved with the use of reinforcement inclusions. The use of sands for sports surfaces is justified based upon the improvement in playing quality characteristics and soil physical properties important to a good playing surface.

Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production

This paper provides new sufficient conditions for the existence, computation via successive approximations, and stability of Markovian equilibrium decision processes for a large class of OLG models with stochastic nonclassical production. Our notion of stability is existence of stationary Markovian equilibrium. With a nonclassical production, our economies encompass a large class of OLG models with public policy, valued fiat money, production externalities, and Markov shocks to production. Our approach combines aspects of both topological and order theoretic fixed point theory, and provides the basis of globally stable numerical iteration procedures for computing extremal Markovian equilibrium objects. In addition to new theoretical results on existence and computation, we provide some monotone comparative statics results on the space of economies.