Static Decisions May Be Optimal in a Life Cycle Setting

In a multicommodity life cycle setting with uncertainty and time additive expected utility, this note finds necessary and sufficient conditions on preferences for all but one optimal decision each period to be independent of the future and of uncertainty.Multivariate life cycle, Euler equations.

Anomalous Gluon Self-Interactions and ttˉt \bar{t} Production

Strong-interaction physics that lies beyond the standard model may conveniently be described by an effective Lagrangian. The only genuinely gluonic CP-conserving term at dimension six is the three-gluon-field-strength operator $G^3$. This operator, which alters the 3-gluon and 4-gluon vertices form their standard model forms, turns out to be difficult to detect in final states containing light jets. Its effects on top quark pair production hold the greatest promise of visibility.Comment: Latex file using [aps,aipbook,floats,epsf]{revtex}. 12 pages, 4 Postscript figures. Full PS copy at http://smyrd.bu.edu/htfigs/htfigs.html Talk presented by EHS at the International Symposium on Vector Boson Self-Interactions, UCLA, Feb. 1-3, 199

Correcting Market Failure Due to Interdependent Preferences: When Is Piecemeal Policy Possible?

Generally, implementation of Pigovian taxes to correct for market failure requires an enormous set of information. For each commodity-person combination a different tax is required to correct the resulting market inefficiency. In this paper, we analyse interdependent preferences and inefficiency of the market solution with the aim of finding conditions justifying simple rules for such taxes. We examine the utility possibility curve and Scitovsky community indifference curve, allowing for general utility interdependence and agent heterogeneity. In particular we show the equivalence of taxes derived from the Marshallian and compensated demand approaches. We move on to analyse the welfare cost of consumption externalities and show that it decomposes into part due to individuals choosing suboptimal quantities and part due to individuals using valuations that are not socially optimal. We show what forms of externality can justify simple policy corrections. In particular, we analyse the conditions which are required for the market failure to be corrected by: 1) specific indirect ad valorem taxes on commodities, 2) the same proportional tax rate on every commodity, 3) a proportional income tax rate on each individual. The conditions are related to the restrictions necessary to have H synthetic consumers without externalities who replicate behaviour of individuals with externalities. An example with two individuals and three goods concludes the paper.Consumption externalities; Piecemeal policy

General solution of an exact correlation function factorization in conformal field theory

We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling operators at the two-dimensional percolation point and in a few other cases. The correlation functions are evaluated in the upper half-plane (or any conformally equivalent region) with operators at two arbitrary points on the real axis, and a third arbitrary point on either the real axis or in the interior. This type of result is of interest because it is both exact and universal, relates higher-order correlation functions to lower-order ones, and has a simple interpretation in terms of cluster or loop probabilities in several statistical models. This motivated us to use the techniques of conformal field theory to determine the general conditions for its validity. Here, we discover a correlation function which factorizes in this way for any central charge c, generalizing previous results. In particular, the factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the Q-state Potts models; it also applies to either the dense or dilute phases of the O(n) loop models. Further, only one other non-trivial set of highest-weight operators (in an irreducible Verma module) factorizes in this way. In this case the operators have negative dimension (for c < 1) and do not seem to have a physical realization.Comment: 7 pages, 1 figure, v2 minor revision

Can Liars Ever Prosper.

The paper compares the optimal financial contracts of a firm which has private information over its expost revenues when the finance can be provided by either a single or two groups of investors. When they are the only investors we use a financial contract with non-contractible monitoring, in which the probabilities of cheating by the entrepreneur/firm and monitoring by investors are mutual best responses. The contract is written by the entrepreneur knowing that this equilibrium will subsequently occur. With a second group of investors who have no monitoring rights, we analyse a truth telling contract and a misrepresentation contract in which cheating and monitoring probabilities are chosen in a similar way to those of the single investor contract. The non monitoring investors learn the results of any monitoring for free. Our main results are that: the two investor group truth-telling contract achieves the second best despite the lack of commitment; this contract is only feasible under limited liability of investors if low state revenues are high enough. When low state revenues are too low for this then the two investor misrepresentation contract is optimal. This contract has a negative correlation between repayments to the two investor groups: the contract uses the non-monitoring group to smooth out the repayments of the entrepreneur optimally. This reduces his incentive to make false reports and mitigates the investor's incentive to monitor. A second result is that the two investor scenario is Pareto superior to the single investor model. We show that with unlimited liability on investor groups, the two investor misrepresentation contract is as good as the second best. Generally in this misrepresentation contract investors may have to make repayments to the firm rather than receive them. A further result is that the three party contract is always renegotiation-proof, as well as collusion-proof so long as the low state revenues are below the expected repayments of the monitor. Last we show that under limited liability the share of finance provided by the two is strictly positive and uniquely determined.financial contracts; multiple investors; no commitment.

Efficient Allocations, Equilibria and Stability in Scarf's Economy

Scarf's economy has been a vehicle in understanding stability properties in exchange economies. The full set of market equilibria and Pareto optimal allocations for this economy has not been analysed. This paper aims to do that. Firstly, we examine the Pareto optima and we find three different classes. Only Class I exhausts the aggregate endowments of all the goods. Class II and III involve throwing away partially or totally one good in order to achieve Pareto efficiency. Secondly, we explore the price and endowment distribution combinations which sustain the different Pareto Optima as market equilibria. A Pareto optimum which involves throwing away the whole endowment of one of the goods is globally stable.Exchange economy, Complements, Stability

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

In this paper, we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple-input multiple-output (MIMO) $d\times d$ antenna amplify-and-forward (AF) relay networks. In particular, we model these networks as random dynamical systems (RDS) and calculate their $d$ Lyapunov exponents. Our analysis can be applied to systems with any per-hop channel fading distribution, although in this contribution we focus on Rayleigh fading. Our main results are twofold: 1) the total transmit power at the $n$th node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the $i$th eigenchannel at the $n$th node will follow a deterministic trajectory through the network governed by the network's $i$th Lyapunov exponent. Before concluding, we concentrate on some applications of our results. In particular, we show how the Lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other, and how this relates to the amplification strategy and number of antennas at each relay. We also use them to determine the extra cost in power associated with each extra multiplexed data stream.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Transactions on Information Theor