Financial Control of a Competitive Economy without Randomness

The monetary and fiscal control of a simple economy without outside randomness is studied here from the micro-economic basis of a strategic market game. The government's bureaucracy is treated as a public good that provides services at a cost. A conventional public good is also considered.Dynamic programming, Public goods, Bureaucracy, Taxation

A Strategic Market Game with Secured Lending

We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money market, and a continuum of agents. These use fiat money in order to offset random fluctuations in their endowments of the commodity, are not allowed to borrow more than they can pay back (secured lending), and maximize expected discounted utility from consumption of the commodity. Their aggregate optimal actions determine dynamically prices and/or interest rates for borrowing and lending, in each period of play. In equilibrium, random fluctuations in endowment- and wealth-levels offset each other, and prices and interest rates remain constant. As in our related recent work, KSS (1994), we study in detail the individual agents' dynamic optimization problems, and the invariance measures for the associated, optimally controlled Markov chains. By appropriate aggregation, these individual problems lead to the construction of stationary Markov competitive equilibrium for the economy as a whole. Several examples are studied in detail, fairly general existence theorems are established, and open questions are indicated for further research.

Information and the Existence of Stationary Markovian Equilibrium

We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial conditions: (i) low information -- agents are ignorant of both total endowment and their own endowments when they make decisions in a given period, and (ii) proportional endowments -- the endowment of each agent is in proportion, possibly a random proportion, to the total endowment. When these conditions hold, there is a stationary equilibrium. When they do not hold, such equilibrium need not exist.Information, stochastic process, money, and disequilibrium

A Stochastic Overlapping Generations Economy with Inheritance

An overlapping generations model of an exchange economy is considered, with individuals having a finite expected life-span. Conditions concerning birth, death, inheritance and bequests are fully specified. Under such conditions, the existence of stationary Markov equilibrium is established in some generality, and several explicitly solvable examples are treated in detail.Overlapping generations, inheritance, stochastic process, life span

Optimal primitive sets with restricted primes

A set of natural numbers is primitive if no element of the set divides another. Erd\H{o}s conjectured that if S is any primitive set, then \sum_{n\in S} 1/(n log n) \le \sum_{n\in \P} 1/(p log p), where \P denotes the set of primes. In this paper, we make progress towards this conjecture by restricting the setting to smaller sets of primes. Let P denote any subset of \P, and let N(P) denote the set of natural numbers all of whose prime factors are in P. We say that P is Erd\H{o}s-best among primitive subsets of N(P) if the inequality \sum_{n\in S} 1/(n log n) \le \sum_{n\in P} 1/(p log p) holds for every primitive set S contained in N(P). We show that if the sum of the reciprocals of the elements of P is small enough, then P is Erd\H{o}s-best among primitive subsets of N(P). As an application, we prove that the set of twin primes exceeding 3 is Erd\H{o}s-best among the corresponding primitive sets. This problem turns out to be related to a similar problem involving multiplicative weights. For any real number t>1, we say that P is t-best among primitive subsets of N(P) if the inequality \sum_{n\in S} n^{-t} \le \sum_{n\in P} p^{-t} holds for every primitive set S contained in N(P). We show that if the sum on the right-hand side of this inequality is small enough, then P is t-best among primitive subsets of N(P).Comment: 10 page

Long Duration Exposure Facility (LDEF) space environments overview

The Long Duration Exposure Facility (LDEF) was retrieved from Earth orbit in January 1990 after spending almost six years in space. It had flown in a near-circular orbit with an inclination of 28.5 degrees. Initially, the orbit altitude was approximately 257 nautical miles; however, when the LDEF was retrieved the orbit altitude had decayed to approximately 179 nautical miles. The LDEF was passively stabilized about three axes while in free flight, making it an ideal platform for exposing experiments which were measuring the environments of near-Earth space and investigating the long-term effects of these environments on spacecraft. A brief overview of the encountered environments that were of most interest to the LDEF investigators is presented

A method to study complex systems of mesons in Lattice QCD

Finite density systems can be explored with Lattice QCD through the calculation of multi-hadron correlation functions. Recently, systems with up to 12 $\pi^+$'s or $K^+$'s have been studied to determine the 3-$\pi^+$ and 3-$K^+$ interactions, and the corresponding chemical potentials have been determined as a function of density. We derive recursion relations between correlation functions that allow this work to be extended to systems of arbitrary numbers of mesons and to systems containing many different types of mesons, such as $\pi^+$'s, $K^+$'s, $\bar{D}^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and for the study of high-density systems.Comment: JLAB-THY-10-1121, NT@UW-10-01, journal versio

A Strategic Market Game with Active Bankruptcy

We construct stationary Markov equilibria for an economy with fiat money, one non-durable commodity, countably-many time periods, and a continuum of agents. The total production of commodity remains constant, but individual agents' endowments fluctuate in a random fashion, from period to period. In order to hedge against these random fluctuations, agents find it useful to hold fiat money which they can borrow or deposit at appropriate rates of interest; such activity may take place either at a central bank (which fixes interest rates judiciously) or through a money-market (in which interest rates are determined endogenously). We carry out an equilibrium analysis, based on a careful study of Dynamic Programming equations and on properties of the Invariant Measures for associated optimally-controlled Markov chains. This analysis yields the stationary distribution of wealth across agents, as well as the stationary price (for the commodity) and interest rates (for the borrowing and lending of fiat money). A distinctive feature of our analysis is the incorporation of bankruptcy, both as a real possibility in an individual agent's optimization problem, as well as a determinant of interest rates through appropriate balance equations. These allow a central bank (respectively, a money-market) to announce (respectively, to determine endogenously) interest rates in a way that conserves the total money-supply and controls inflation. General results are provided for the existence of such stationary equilibria, and several explicitly solvable examples are treated in detail.