Steady State In A Markov Process

It is well known that a Markov process whose transition matrix is regular approaches a steady-state distribution, or equilibrium distribution. To find these steady-state probabilities requires the solution of a system of linear homogenous equations. However, the matrix of this system is singular and thus the system has infinitely many solutions. This obstacle is overcome by replacing one of the equations of the linear homogenous system by the linear non-homogeneous equation that simply expresses the requirement that the steady-state probabilities sum to one. But which equation of the original system should be chosen to be the one replaced. This brief article demonstrates that any of the equations of the original linear system can be selected as the one to be replaced; no matter which one is selected for replacement; the revised linear system will have the same unique solution

The Economics Of The Duration Of The Baseball World Series

This note examines some statistical features of the major league baseball World Series. We show that, based upon actual historical data, we cannot reject the hypothesis that the two World Series teams are evenly matched. Yet, we can also calculate the relative strengths of the teams that would best match the actual outcomes, and we find that those relative strengths are not equal. Including the home field advantage in the calculations indicates that the differential in relative strength between the competing teams can be explained by this advantage. We present the relative team strengths that would maximize the probability of four, five, six and seven game series. We find that a six or seven game series is most likely when the two teams are evenly matched, a four game series is most likely when the probability of the stronger team winning is one, while the probability of a five game series is maximized if one team has a relative strength of 0 .789. We also show that, on average, the expected number of World Series games will be between 4 and 5.81, depending upon the relative strengths of the teams and the home field advantage. Contracts that do not consider the likelihood of less than seven game Series will create windfall gains to MLB and marginal economic losses to broadcasters

Determining Optimal Corporate Capital Structure

This paper considers the mathematical relationship between two variables: independent variable is corporate debt as a percentage of corporate assets while the dependent variable is the present value of the tax savings on the interest paid on the corporate debt. We examine this relationship for any fixed number of future states under the Cox-Rubinstein model. The functional relationship is a saw-tooth function with a discrete set of discontinuities. By examining the behavior of this function we find that there is for each number of states always a unique debt to asset percentage between 0 and 100% for which the present value of the tax savings is a maximum

Investment In An Unstable Tax Environment

While most of the capital budgeting situations are typically micro level problems, the introduction of this dual impact of the corporate tax rate on the project acceptance criterion provides an insight into potential tax regime decisions on long term investments in a given tax jurisdiction.  If we understand this dual behavior well enough, it might be possible for a tax regime to manipulate its corporate tax rate without necessarily jeopardizing acceptability status of capital projects to providers of capital. The present paper is an attempt to model this dual impact of the corporate tax rate on the NPV of projects within the tax regime, and study the implications of the results for policy makers and for corporations facing such policy makers

Life, time, and the organism:Temporal registers in the construction of life forms

In this paper, we articulate how time and temporalities are involved in the making of living things. For these purposes, we draw on an instructive episode concerning Norfolk Horn sheep. We attend to historical debates over the nature of the breed, whether it is extinct or not, and whether presently living exemplars are faithful copies of those that came before. We argue that there are features to these debates that are important to understanding contemporary configurations of life, time and the organism, especially as these are articulated within the field of synthetic biology. In particular, we highlight how organisms are configured within different material and semiotic assemblages that are always structured temporally. While we identify three distinct structures, namely the historical, phyletic and molecular registers, we do not regard the list as exhaustive. We also highlight how these structures are related to the care and value invested in the organisms at issue. Finally, because we are interested ultimately in ways of producing time, our subject matter requires us to think about historiographical practice reflexively. This draws us into dialogue with other scholars interested in time, not just historians, but also philosophers and sociologists, and into conversations with them about time as always multiple and never an inert background

The ‘heritagisation’ of the British seaside resort: The rise of the ‘old penny’ arcade.

Amusement arcades have long been a key component of the British seaside resort. For almost a century, they enjoyed popularity and success and became established as a quintessential feature of the British seaside holiday. However, the advent of home-based video games along with recent gambling legislation has led to a decline of the seaside amusement arcade sector. Arcades gained a reputation as unsavoury places and their appearance and fortunes often mirrored those of the resorts in which they were located. However, over the past decade, a new variant of the seaside amusement arcade has appeared, featuring mechanical machines working on pre-decimal currency. Such ‘old penny arcades’ frequently describe themselves as museums or heritage centres and they offer an experience based on a nostalgic affection for the ‘traditional’ seaside holiday. They have appeared in the context of an increasing interest in the heritage of the British seaside resort and constitute one element of the ‘heritagisation’ of such resorts. This paper argues that such arcades can be important elements of strategies to reposition and rebrand resorts for the heritage tourism market

Linear Algebra with Linear Differential Equations

x, 305 tr. ; 23 cm