Pro Rata Research Articles

Estimation of the Quantity of a Drug in a Consignment from Measurements on a Sample

A consignment of individual packages is thought to contain illegal material, such as drugs, in some or all of the packages. A sample from the consignment is inspected and the quantity of drugs in each package of the sample is measured. It is desired to estimate the total quantity of drugs in the consignment. Sampling variation is present in the original measurements and it is not sufficient just to adjust the sample mean pro rata. An analysis is described which takes account of the uncertainty concerning the proportion of the packages that contain drugs and provides a probabilistic summary of the quantity of drugs in the consignment. In particular, a probabilistic lower bound for the quantity of drugs in the consignment is given, which is dependent on the required standard of proof. This is in contrast to the approach based on confidence intervals which assumes that in the long run, the interval will contain the correct quantity the appropriate proportion of the time, but gives no measure of uncertainty associated with the particular consignment under consideration.

Transmission loss allocation: a comparison of different practical algorithms

A pool-operated electricity market based on hourly auctions usually neglects network constraints and network losses while applying its market-clearing mechanism. This mechanism determines the accepted and nonaccepted energy bids as well as the hourly market-clearing prices. As a result, ex post procedures are needed to resolve network congestions and to allocate transmission losses to generators and demands. This paper focuses on transmission loss allocation procedures and provides a detailed comparison of four alternative algorithms: (1) pro rata (PR); (2) marginal allocation; (3) unsubsidized marginal allocation; and (4) proportional sharing. A case study based on the IEEE RTS is provided. Different load scenarios covering a whole year are analyzed. Finally, conclusions and recommendations are stated.

Don’t get mad, get even

HOW IS this for a new contract? You are going to receive a 20 per cent pay increase, a limit on the number of hours you have to work, extra cash for ‘emergency’ work and freedom to practise pnvately in your free time This is the bare ones of the agreement the government has struck with consultants. The devil is not in the details in this case - consultants have negotiated to have their cake and eat it too. For example, a new consultant will now have to undertake two four-hour sessions for the NHS before being allowed to practise privately This will be paid pro rata by the way, lifting the basic salary from ￡63,000 to ￡75,600. If a new consultant goes ahead with private work anyway, refusing the enticements of extra NHS work, he or she will lose entitlements to salary increments. But if the consultant does no private work and instead takes the time for leisure, he or she will not lose the increments. In short, if a consultant wants more time to sail around the Greek islands on a yacht, the government has said ‘OK’.

Job Sharing in Australia: Possibilities, Problems and Strategies

AbstractThis paper defines job sharing and explores its potential benefits. An overview of its origins and growth in Australia and overseas is followed by discussion of management issues. Organisational issues concern aspects of planning, implementation and operation. Issues for job sharers include finding an appropriate job share partner, maintenance of the job sharing relationship, protection of voluntary participation and preservation of pro rata benefits and other working conditions. A process for facilitating effective liaison between management, job sharers and trade unions is proposed. Job sharing is uncommon in Australia but may assist workers to balance work and family responsibilities or pursue interests outside work while avoiding many disadvantages of precarious work. For employers, it may facilitate retention of valued staff, reduce turnover, enhance recruiting or reduce staff costs. These propositions have not been rigorously tested, however, and avenues for future research are therefore explored.

Transmission Loss Allocation: A Comparison of Different Practical Algorithms

A pool-operated electricity market based on hourly auctions usually neglects network constraints and network losses while applying its market-clearing mechanism. This mechanism determines the accepted and nonaccepted energy bids as well as the hourly market-clearing prices. As a result, ex post procedures are needed to resolve network congestions and to allocate transmission losses to generators and demands. This paper focuses on transmission loss allocation procedures and provides a detailed comparison of four alternative algorithms: (1) pro rata (PR); (2) marginal allocation; (3) unsubsidized marginal allocation; and (4) proportional sharing. A case study based on the IEEE RTS is provided. Different load scenarios covering a whole year are analyzed. Finally, conclusions and recommendations are stated.

Reviewing Allocation Law in The Wake of Con Edison

INTRODUCTION Generally, there are two approaches to allocating long-term toxic tort claims like asbestos or environmental contamination. One is the “prorata” allocation method, whereby each party, including policyholders in certain circumstances, is held responsible only for its “fair share” of the liability. Courts who adopt this position rely on the policy language that states that the insurer will only cover bodily injury or property damage taking place during the policy period. The difficulty lies in determining how to calculate the “fair share.” Courts have approached the calculation issue in different ways, such as straight time on the risk, time on the risk in relation to limits, or horizontal exhaustion before any excess carrier pays. However, pro rata allocation is not favorable to policyholders because it usually places responsibility on them for periods of insurance gaps, whether by reason of missing policies, insolvencies, self-insured retentions/deductibles, or periods of no insurance. The second method is known as “joint and several liability” or “pick and choose”. This method is more favorable to policyholders because it places the burden of allocating “fair share” responsibility for the claim on the insurers. Specifically, pick and choose allows the policyholder to select the policy (and sometimes policies) that will respond to a tendered claim. Notwithstanding that the loss takes place over a long period of time, under a pick and choose method of allocation, the insurer issuing the selected policy becomes responsible to pay for the policyholder’s entire liability up to its policy limit. Thereafter, that insurer is entitled to seek contribution from any other insurer that may have responsibility for the loss, but not from the insured.

Share Price Changes and the Arrival of Limited Liability in California

What effect does limited liability have on share values? This question is difficult to answer because active stock markets did not develop until the rise of corporate limited liability in the nineteenth century. Previous research has shown that one company with pro rata limited liability, American Express, was actively traded until the 1960s. However, no one has examined the price effect of a change from unlimited to limited liability. The history of corporate law in California provides a natural experiment that can be used to examine the effect of limited liability. Until 1929, all California corporations had pro rata unlimited liability. By a process that lasted until 1931, California adopted limited liability for corporations. In the paper I provide the first empirical examination of the effect that this move had on share prices. I find no evidence of share price changes associated with the change in the liability regime.

Minority Discounts and Control Premiums in Appraisal Proceedings

In a merger, a stockholder often has a statutory right of dissent and appraisal under which the stockholder may demand to be paid fair value exclusive of any gain or loss that may arise from the merger itself. Most courts and commentators agree that a dissenting stockholder should ordinarily receive a pro rata share of the fair value of the corporation without any discount simply because minority shares lack control. In several recent cases, the courts have indicated that a minority stockholder is thus entitled to a share of the control value of the corporation even though the merger does not constitute a sale of control (as in a going private transaction) and even though control of the subject corporation is not contestable (as where a single stockholder owns a outright majority of shares). In a similar vein, several courts have ruled that reliance on market prices for purposes of appraisal results in an inherent minority discount, thus requiring that a premium for control be added. In short, the emerging rule appears to be that fair value is the price at which a controlling stockholder could sell control, because failure to do so amounts to imposition of a minority discount. It is the thesis here that the routine addition of a control premium - even though the transaction does not involve a cognizable transfer of control - is inconsistent with settled corporation law and good policy. First, it is based at least in part on the unwarranted assumption that the source of a control premium must be a minority discount. Second, it is inconsistent with the well settled rule that the circumstances of a transaction should be considered. Third, it is inconsistent with the idea that a controlling stockholder may sell control at a premium as long as the sale of control is not to the detriment of the minority. Fourth, it is contrary to public policy in that it encourages dissent by holding out the prospect of a control premium even in cases in which a majority of the minority has approved the deal. Fifth, and perhaps most important, the addition of a control premium (whether routine or not) may amount to double-counting. The Capital Asset Pricing Model (CAPM), which is the generally preferred method of valuation, implicitly adjusts for any minority discount by measuring the value of the subject company (based on its riskiness) relative to the market as a whole. Indeed, CAPM may actually add on an implicit premium in that it values a stock as if it is part of a well diversified portfolio, ignoring firm specific risk. Even if fair value is determined by reference to the prices of comparable companies, the routine addition of a premium presumes that market prices are inherently discounted. And if fair value is based on premiums in comparable transactions, the premium may arise from the fact that other target companies were trading at a discount prior to the comparable transaction. To be sure, the courts should adjust for a minority discount if one is found. But the routine addition of a control premium as part of fair value creates a windfall for dissenting stockholders and infringes the legitimate rights of majority stockholders.

The effects of ownership concentration on investment and performance in privatized firms in Russia

AbstractThis paper provides new survey evidence on effects of concentrated ownership on restructuring and performance in privatized firms in Russia. The major findings are that large‐block shareholding is negatively associated with the firm's investment and performance, and this relationship does not depend on the identity of controlling shareholders. These results are consistent with the assumption that when minority shareholders' rights are not adequately protected, the entrenched controlling shareholders may be engaged in extracting ‘control premium’ before pro rata distribution of dividends. The issues raised have relevance to other transitional economies where the privatization process has been followed by an increase in ownership concentration. Copyright © 2001 John Wiley & Sons, Ltd.

Paying for Minimum Interest Rate Guarantees: Who Should Compensate Who?

Defined contribution pension schemes often have a mandatory minimum interest rate guarantee as an integrated part of the contract. The guarantee is an embedded put option issued by the institution to the individual who is forced to invest in the option. As argued in this paper, the individual may in this way face a constraint on the feasible set of portfolio choices. We quantify the effect of the minimum interest rate guarantee constraint and demonstrate that guarantees may induce a significant utility loss. We also consider the effects of the interest rate guarantee in the case of heterogenous investors sharing a common portfolio on a pro rata basis.

Islands of Conscious Power: Law, Norms, and the Self-Governing Corporation

This article provides a theory of the relation between legal and non legally enforceable rules and in the corporation, and then uses that theory to analyze a variety of prominent features of corporate law. In the first part, we draw on recent developments in the theory of the firm to identify key problems facing participants in the firm. In developing this approach, we combine the property strand in the theory of the firm with the transaction cost approach. From this perspective, the main issue is solving the related problems of coordinating activities, choosing the firm's assets, and developing appropriate incentives for specific investments. In part II, we argue that the firm so understood will largely be governed through norms, by which we mean non-legally enforceable rules and standards (NLERS). Indeed, the raison d'etre of firms is to replace legal/contractual governance of relations with NLERS. Using this framework, in part III, we analyze the duty of loyalty. In part IV, we analyze the duty of care and the business judgement rule, and a variety of other puzzling features of corporate law. From our perspective, corporate law can be understood as a remarkably sophisticated mechanism for facilitating governance by NLERS. Centralized management is used to determine the assets over which the corporation must have residual rights of control and to develop a governance structure for protecting the match-investments of insiders in these assets. Legal rules provide the default settings through which centralized management operate and prohibit non pro rata distributions (a combination of ex ante rules and the ex post duty of loyalty), which pushes controlling shareholders to maximize the value of the firm. Having established an incentive compatible legal form that facilitates NLERS governance, the law must be careful not to undermine that governance by midstream interference. Here, the duty of care and the business judgment rule are critical. The business judgement rule acts as a jurisdictional rule that facilitates a self governing NLERS relationship by preventing parties from turning to third party adjudicators. As such, it plays a role very similar to the role of the employment at will doctrine in employment law and for the same reasons. This analysis provides an explanation for why the duty of care, despite its appearance, does not function as a negligence rule, and why liability for directorial malpractice is so much less common than liability for other forms of professional malpractice, such as, legal or medical. The principal contexts in which the BJR does not apply are situations in which NLERS governance breaks down, generally because of last period temptations to defect. The difference in the ability of NLERS to govern midstream and end games provides the key to understanding a variety of corporate law puzzles. These puzzles include: the asymmetry between the legal governing purchases and sales of assets; the asymmetry between judicial review over decisions to resist all bids for control (just say no) versus the review of sales of control; and the demand requirement in derivative litigation.

Control of Orobanche aegyptiaca and O. ramosa in potato

Potato ( Solanum tuberosum) is a susceptible host of the root holoparasites Orobanche aegyptiaca and Orobanche ramosa in the Mediterranean region, and suffers severe yield losses due to high levels of field infestations. Sulfonylurea and imidazolinone herbicides are selective acetolactate synthase-inhibiting herbicides that have been found effective for Orobanche control. In greenhouse and field experiments, O. aegyptiaca and O. ramosa were controlled in potato-infested soils by split foliar applications of low rates of the herbicides imazapic and rimsulfuron. Three doses of imazapic at 4.5 g/ha each, sprayed 2 weeks after crop emergence and re-applied at 2-week intervals, prevented Orobanche infestation. Although imazapic treatments increased crop vigor and potato yield, potato tuber quality was severely damaged in light sandy loam fields, where tubers were deformed pro rata to imazapic applied doses. A single application of 7.5 g/ha triasulfuron sprayed on potato foliage, severely damaged the crop. Three repeated applications of rimsulfuron at 12.5 or 25.0 g/ha at identical timing to imazapic, selectively controlled Orobanche and were found safe for potatoes as well as tuber quality. Rimsulfuron has approval for use on commercial crops of potato.

Islands of Conscious Power: Law, Norms and the Self Governing Corporation

This article provides a theory of the relation between legal and non legally enforceable rules and in the corporation, and then uses that theory to analyze a variety of prominent features of corporate law. In the first part, we draw on recent developments in the theory of the firm to identify key problems facing participants in the firm. In developing this approach, we combine the property strand in the theory of the firm with the transaction cost approach. From this perspective, the main issue is solving the related problems of coordinating activities, choosing the firm's assets, and developing appropriate incentives for specific investments. In part II, we argue that the firm so understood will largely be governed through norms, by which we mean non-legally enforceable rules and standards (NLERS). Indeed, the raison d'etre of firms is to replace legal/contractual governance of relations with NLERS. Using this framework, in part III, we analyze the duty of loyalty. In part IV, we analyze the duty of care and the business judgement rule, and a variety of other puzzling features of corporate law. From our perspective, corporate law can be understood as a remarkably sophisticated mechanism for facilitating governance by NLERS. Centralized management is used to determine the assets over which the corporation must have residual rights of control and to develop a governance structure for protecting the match-investments of insiders in these assets. Legal rules provide the default settings through which centralized management operate and prohibit non pro rata distributions (a combination of ex ante rules and the ex post duty of loyalty), which pushes controlling shareholders to maximize the value of the firm. Having established an incentive compatible legal form that facilitates NLERS governance, the law must be careful not to undermine that governance by midstream interference. Here, the duty of care and the business judgment rule are critical. The business judgement rule acts as a jurisdictional rule that facilitates a self governing NLERS relationship by preventing parties from turning to third party adjudicators. As such, it plays a role very similar to the role of the employment at will doctrine in employment law and for the same reasons. This analysis provides an explanation for why the duty of care, despite its appearance, does not function as a negligence rule, and why liability for directorial malpractice is so much less common than liability for other forms of professional malpractice, such as, legal or medical. The principal contexts in which the BJR does not apply are situations in which NLERS governance breaks down, generally because of last period temptations to defect. The difference in the ability of NLERS to govern midstream and end games provides the key to understanding a variety of corporate law puzzles. These puzzles include: the asymmetry between the legal governing purchases and sales of assets; the asymmetry between judicial review over decisions to resist all bids for control (just say no) versus the review of sales of control; and the demand requirement in derivative litigation.

Private Information and Spin‐off Performance

Following pro rata spin-offs, shareholders, including insiders, trade their stock holdings in public subsidiaries independently of trades in parent firms. This article examines the predictive ability of informed trading with respect to post-spin-off stock performance and corporate control transactions. I find that subsequent to spin-offs, insiders are substantial purchasers of stock in public subsidiaries and sellers in parent firms. The trades of insiders are significantly related to post-spin-off stock returns, takeovers, and delistings of spun-off firms. The results are highly significant for senior managers of public subsidiaries, but they do not generally hold for outside directors or large blockholders. Copyright 2001 by University of Chicago Press.

Navigating Failure: Bankruptcy and Commercial Society in Antebellum America

Navigating Failure: Bankruptcy and Commercial Society in Antebellum America. By Edward J. Balleisen. (Chapel Hill: The University of North Carolina Press, 2001. Pp. xv, 322. Illustrations, maps. Cloth, $55.00; paper, $19.95.) In Navigating Failure, Edward J. Balleisen seeks to show how bankruptcy both sprang from and helped shape commerce during the antebellum period. He clearly describes the wide range of difficulties facing commercially inclined (3) during the era and gives a sympathetic view of the real lives of people who bought into the idea of capitalism, but who could not quite make the dream work for them. Navigating Failure is worth reading if only for its fascinating description of business life in America from 1820 to 1860. A host of pitfalls awaited merchants in the complicated web of antebellum credit: international economic cycles, bad debt, fraud, fire, and cut-throat competition. To make matters worse, in these far-flung networks, a single person's failure to cover his obligations could bring down businessmen he had never met. This is not to say that the structure of the antebellum economy was solely to blame for bankruptcy-quite the contrary. Balleisen argues that most bankrupts played a role in their own demise. Inexperience in the ways of business was a typical source of trouble, but greed also played a role when merchants overextended themselves or consumed more luxuries than they could afford. When failure did come, it could be a catastrophic experience. Moralists urged debtors to face problems manfully (77), rather than scramble to hold off creditors until the last possible moment, but accepting failure was almost unthinkable in the American commercial culture of the time. Creditors also ignored the moralists and their pleas for reason and forbearance. The fact was, those who pushed hardest earliest were most likely to see their debts paid. Compromise between debtors and creditors was possible, however, because both parties were enmeshed in the same network of professional connections from which neither could afford to alienate themselves. At the center of Balleisen's book, both literally and figuratively, is the United States Bankruptcy Act of 1841. The act largely favored debtors, allowing them to declare bankruptcy and seek shelter from creditors. It allowed debtors to keep $300 in personal property and excused them from any debt remaining after court-appointed agents sold off their goods and distributed the proceeds on a pro rata basis. The act also helped create a cottage industry revolving around failure. Creditors might not have seen much money from a bankruptcy judgment, but the officials who handled the claims could do very well indeed. Judges offered clerk positions as political plums, and at least some officials used inside information to speculate on assets sold at bankruptcy auctions. These vulture capitalists (18), as Balleisen calls them, initially were scorned as immoral, but began to achieve respectability by the 1850s as Americans began to accept the fluctuations and risks of the capitalist economy. Declaring bankruptcy held out the prospect of a clean slate, but it was not the only strategy that could allow the debtor to start anew. …

Social Security Transition in Italy: Costs, Distortions and (Some) Possible Corrections

This paper focuses on alternative money's worth measures of the Italian (public) pension system for representative cohorts, considering both the present transition and the future steady state envisaged by recent reforms. Micro-based calculations of the aggregate budget effects induced by further possible policy changes are also presented. The main results of the simulation exercise are: i) young and future generations face a steady and strong reduction of their social security's worth mainly due to the 1992 and 1995 reforms and accentuated by the discontinuities characterizing the reforms; ii) throughout most of the transition period, the increase in benefits for an additional year of work, after reaching seniority pension requirement, does not offset the financial costs generated by additional contributions and shorter expected retirement. The implied loss still represents a strong incentive to early retirement; iii) the extension, from the year 2000, of the pro rata mechanism to all new pensioners would generate a non-negligible smoothing effect on microeconomic distortions, but a comparatively small reduction in pension expenditure; iv) a much larger reduction can be obtained if seniority pensions are determined according to actuarial fairness: i.e., by taking into account life expectancy at retirement; v) considering the introduction of an opting out clause, all generations hit by recent reforms have an incentive to quit; the younger the cohort, the stronger the incentive. The paper finally highlights aspects of the social security problem which deserve to be addressed in a more complete analysis, such as risk adjustments, welfare implications and general equilibrium feedback effects. Even without these extensions, we think our conclusions are quite robust, and may help policy discussion.

An Empirical Analysis of Price and Time Priority and Pro Rata Trade Execution Algorithms in Screen-Traded Markets

One of the biggest issues in futures markets today is the introduction and proliferation of all-electronic exchanges and the procedures they will adopt for trading. This article looks at the impact of a 1998 change in trading procedures for Eurodollar futures on the Globex2 system used for after-hours trading by the Chicago Mercantile Exchange. The original system, which maintained price and time priority for limit orders on the book, was replaced by one with pro rata allocation for all orders at the same price, regardless of time arrival. The existence of the regular hours open outcry system operating without change during the same time period provides a control sample against which the behavior of Globex2 prices in the two different regimes can be compared. The results suggests that the change in the trading algorithm had no significant effect on the bid-ask spread or on the volatility in this market.

Warranty cost analysis for second-hand products

For second-hand products sold with warranty, the expected warranty cost for an item to the manufacturer, depends on 1. (i) the age and/or usage as well as the maintenance history for the item 2. (ii) the terms of the warranty policy. The paper develops probabilistic models to compute the expected warranty cost to the manufacturer when the items are sold with free replacement or pro rata warranties.

A finite difference type algorithm with pro rata resource allocation

We describe an algorithm that uses pro rata allocation between inter-pool flows to meet conservation of mass/energy constraints and avoid execution order dependence. More commonly used clipping methods do not satisfy these constraints when multiple flows from small pools exceed the total size of the pool. Overrun, which occurs when a pool is increased or decreased beyond its capacity, typically a decrease below zero, leads to failure to conserve mass. Clipping avoids overrun by restricting the size of pools, usually by setting negative values to zero, which can in turn lead to unacceptable error levels in the simulation's output, particularly in terms of sensitivity to execution order. In addition to the normal ‘current’ and ‘next’ copies of the system's state variables, this algorithm requires an ‘output’ copy, which sums outputs from each pool. Individual flows from a pool are divided by the output sum to determine the proportion of the pool each flow receives. Additionally, the approach allows tracking of individual mass flows, which are sometimes more interesting than their net effect on the pools on which they operate. Implementation details and a comparison with a clipping type algorithm are given in terms of a GIS based meadow ecosystem hydrology submodel. In a simple test case, also presented, the pro rata algorithm more consistently tracks the target solution (given by an extremely small time step).

Lessons from Fiascos in Russian Corporate Governance

Bad corporate governance is often invoked to explain poor enterprise performance, but the catch phrase is never precisely defined. Neither its consequences for the real economy, nor its causes in particular countries has been adequately explained. This paper uses Russian enterprise examples to address these open questions in corporate governance theory. We define corporate governance by looking to the economic functions of the firm rather than to any particular set of national corporate laws. Firms exhibit good corporate governance when their managers maximize residuals and, in the case of investor-owned firms, make pro rata distributions to shareholders. Using this definition, we develop a typology that shows the channels through which bad corporate governance can inflict damage on the real economy. The typology helps identify vulnerabilities to corporate governance problems that may appear in any country and it suggests a new way to tailor policy responses. Second, we explain the causes of poor corporate performance in Russia by looking to the particular conditions prevailing at privatization - the untenable initial firm boundaries and the initial allocation of shares primarily to insiders -- and the bargaining dynamics that followed. The focus on initial conditions helps expand a comparative corporate governance literature built on United States, Western European, and Japanese models. Lessons from Russian fiascos counsel caution as to stakeholder proposals including labor or local communities in formal corporate governance and generate testable hypotheses regarding potential losses from the multiple large block share ownerships typical of many U.S. firms, especially close corporations.