Maximal Rules Research Articles

The Theory of the Revenue Maximizing Firm

An endogenous growth model of the revenue maximizing firm is here presented. It is demonstrated that, in a static analysis, a revenue maximizing firm in equilibrium equates the average product of labor to the wage rate. In a dynamic analysis, the maximization rule becomes the balance between the rate of marginal substitution - between labor and capital - and the ratio of the wage rate over the discount rate. When the firm satisfies this rule, it grows endogenously at the rate of return on capital. The firm may also have multiple stationary equilibria, which are very similar to the static equilibrium.

Learning maximal structure fuzzy rules with exceptions

This paper proposes a method to solve the conflicts that arise in the framework of fuzzy model identification with maximal rules (Fuzzy Sets and Systems 101 (1999) 331) where rules are selected as general as possible. This resolution is expressed by including exceptions in the rules, that way achieving a higher model interpretability with respect to other techniques and a more accurate model. Besides, several methods are presented to improve the interpretability, based on compacting the rules and exceptions of the model. Furthermore, in order to reduce the number of conflicts that arise from the maximal rules, a heuristic strategy is proposed to generate those maximal rules. Finally, the method is applied to an example and the results are compared with other identification methods.

Organizational Forms and Investment Decisions

This paper analyzes investment rules for various organizational forms that are distinguished by the characteristics of their residual claims. Different restrictions on residual claims lead to different decision rules. The analysis indicates that the investment decisions of open corporations, financial mutuals and nonprofits can be modeled by the value maximization rule. However, the decisions of proprietorships, partnerships, and closed corporations cannot in general be modeled by the market value rule.

Receptive Field Formation in Natural Scene Environments. Comparison of Single-Cell Learning Rules.

We study several statistically and biologically motivated learning rules using the same visual environment: one made up of natural scenes and the same single-cell neuronal architecture. This allows us to concentrate on the feature extraction and neuronal coding properties of these rules. Included in these rules are kurtosis and skewness maximization, the quadratic form of the Bienenstock-Cooper-Munro (BCM) learning rule, and single-cell independent component analysis. Using a structure removal method, we demonstrate that receptive fields developed using these rules depend on a small portion of the distribution. We find that the quadratic form of the BCM rule behaves in a manner similar to a kurtosis maximization rule when the distribution contains kurtotic directions, although the BCM modification equations are computationally simpler.

Prices and Protocols in Public Health Care

This article addresses the problem of how to determine the optimal allocation of public expenditure in the health sector. The first part poses the question: How should the set of services provided in the public health care system and the fees charged for them is chosen to maximize the health status of the population with a fixed budget? First, the findings show that policy reform should take into account the response of the private sector. Substituting for a reasonably well functioning private sector is not as valuable as providing services the private sector cannot. Second, the assumptions needed to justify the cost effectiveness of medical interventions as a criterion for setting priorities are so restrictive as to make this method usable in few, if any, circumstances. Third, prices for any one service should be set to balance the conflicting goals of encouraging its use and of conserving the budget for more effective services. The second part broadens the objective of policy to cover the standard welfare economics concerns of utility and market failure, the latter being extensive in the health sector. It reexamines welfare maximization rules to show that only the market failure components of shadow prices are needed to calculate the welfare gains from public investments.

The Pricing of Customer Access in Telecommunications

Is the loop, which provides customers with access to the switched network, a service in its own an right, or is it purely an input into the production of the final service, which is usage of the switched network? Agreeing with Kahn and Taylor that the question of whether the loop is an economic good is irrelevant to the pricing issue, this paper goes on to claim that pricing at marginal cost is not an appropriate welfare maximization rule due to network externalities that make the private benefit of access less than the social benefit. Socially efficient pricing is likely to involve pricing below the marginal cost of access to some consumers and above the marginal cost of access to others. One implication is that a contribution to the local loop from Interexchange Carriers (IXCs) or IXC customers may be optimal. Copyright 1996 by Oxford University Press.

Orderly marketing for oranges: Public interest versus private interest

The consequences of three rules arguably consistent with the orderly marketing objective of Federal marketing orders for managing weekly product flows of navel oranges are empirically examined. Regardless of whether the rules are executed in an environment of certainty or uncertainty, growers always gain from revenue maximization, handlers are unaffected, buyers always gain from constant prices, and net social welfare is always slightly larger for constant prices. Buyers never gain from stable product flows. Growers gain from using a more information-intensive decision making policy under uncertainty only when following the revenue maximization rule. Buyers, by contrast, always gain from the more information-intensive decision-making policy under uncertainty, regardless of the rule.

The generalization probability of a perceptron using the Delta -rule

Compares the generalization probability of a perceptron using the Delta -rule with other learning algorithms. The numerical results indicate that the Delta -rule gives results which are superior to Hebb's rule, and comparable with the maximal stability perceptron rule (minover), both for randomly generated linear separable example sets and for optimal queries.

Unsolvable problems for SLDNF resolution

Shepherdson showed that there are maximal safe computation rules R m for SLDNF resolution, such that if a query succeeds under any safe rule it succeeds under R m , and if it fails under any safe rule it fails under R m . Later he showed that such maximal rules also get all possible answers, i.e., if a query succeeds with answer θ under any safe rule, then it succeeds with answer equivalent to θ under R m . The question was raised there, whether there were always recursive maximal rules. We answer this negatively. We also show the unsolvability of the problems of deciding whether a query leads to a dead end, whether the Clark completion comp( P) of a program P is consistent, and whether a query which is known to be a logical consequence of the program succeeds in PROLOG.

Conflict of Interest, Bond Rating and the Value Maximization Rule

A number of authors have noted that when a firm issues risky debt in the absence of binding state-contingent contracts, the maximize-present-value rule becomes ambiguous. This paper shows that incomplete (asymmetric) information can explain why the firm will make value-maximizing decisions when there is a conflict of interest between shareholders and bondholders. The reputation effect of D. M. Kreps and R. Wilson (1982) and its implications for the pricing of securities is at the heart of this explanation. Copyright 1987 by The Review of Economic Studies Limited.

Decision-Directed Diversity Combiners--Principles and Simulation Results

Diversity combining methods for medium- and high-capacity digital microwave radio links employing QAM signaling are studied theoretically and by computer simulations. The selective fading diversity channels are represented by a two-path model with complex envelopes. Emphasis is put to find simple receiver structures where combining is controlled by detected symbols to minimize a given error criterion. Two criteria are discussed-minimum mean-square error (MMSE) and minimum projection (MP). The latter criterion is believed to be new and its behavior is analyzed in two extreme cases. It turns out that the MP combiners obey the maximal ratio rule in the absence of dispersion and the minimum distortion rule in the absence of noise. This versatility is achieved with minor circuit complexity. The results have been verified by computer simulations for a 4 PSK 70 Mbit/s system. The resulting diversity signatures are very narrow on the frequency axis, indicating good performance. Moreover, the MP combining tolerates extremely well nonminimum phase fading in one diversity branch, situations where most cophasing schemes have difficulties.

Organizational forms and investment decisions

This paper analyzes investment rules for various organizational forms that are distinguished by the characteristics of their residual claims. Different restrictions on residual claims lead to different decision rules. The analysis indicates that the investment decisions of open corporations, financial mutuals and non-profits can be modeled by the value maximization rule. However, the decisions of proprietorships, partnerships, and closed corporations cannot in general be modeled by the market value rule.

Systems simulation comparing different decision rules

Applying the expected utility maximization rule often requires that we quantify probabilities and utilities, an undertaking which can be very complicated, time-consuming, and costly for many decision makers. For consequences of moderate to low utility—where not much is at stake–it's often much more sensible to use a heuristic decision rule This paper considers fourteen different decision rules (eight of them drawn from the election literature) using a simulation. Generally the ranking, approval, weighted ranking, and weighted approval decision rules seem to work well relative to the expected utility rule. In some cases, the rule which ignores all events but the most probable is the best These decision rules were frequently able to get 90% of the utility which would have been acquired using the expected utility rule. Thus, clearly–depending upon the expense of using the expected utility rule versus a simpler heuristic—it may, in fact, be rational for a decision maker to use a heuristic decision rule. This paper provides tables describing how our fourteen decision rules performed under various conditions.

The Expectation-Threshold model of reproductive decision making

It is proposed that as expectations about parenting become increasingly high, couples have an increasing tendency to decide to have a(or another) child. Similarly, as parenting expectations become increasingly low, couples have an increasing tendency to decide on sterilization. Couples without extremely high or low expectations continue to use contraceptives. Expectations are defined as Subjective Expected Utilities (SEUs) for having or not having a child. Preliminary results support the model and suggest that the threshold for making these decisions is not at neutral, but is conservative so that couples must have fairly high or low expectations before making such binding decisions are parenting or sterilization. The fact that data reveal that this exists supports the Expectancy-Threshold model, but it also requires a change in SEU Theory's maximization rule for some kinds of decisions.

Economic incentives in health manpower policy.

Policymakers have evidenced continued concern with the issue of maldistribution of physicians among specialties and locations. Many of the recent policy proposals in this area have involved increasing the financial rewards to primary care specialization and to location of practice in underserved areas. This article examines the evidence on current economic incentives to specialize and to locate, including income and the hours of work needed to produce income. Findings suggest that current distributions of physicians among locations and specialties are more consistent with a decision to minimize hours worked, rather than an income maximization rule. Policy implications are discussed with respect to potentially perverse results which may occur if consideration is not given to this aspect of career decisions.

Disaggregated Probabilistic Accounting Information: The Effect of Sequential Events on Expected Value Maximization Decisions

In a previous study reported in this Journal, Ronen [1971] investigated user reaction to disaggregated probabilistic information given about sequential events. The purpose of his study was to determine the effect of providing probabilistic information on sequential events on decision makers' use of expected value maximization rules. In a two-act decision where each act had two events occurring in sequence, Ronen found that when the joint probabilities of success of the two acts were equal (i.e., overall expected values of the alternatives were equal), subjects preferred the act where the probability of success associated with the first event (initial probability) was higher. (This choice will hereafter be termed the sequence effect.) Subjects in his study received both aggregated and disaggregated probabilistic information analogous to that shown in table 1. Subjects preferred Act 1 in this example since p(E,12A1) > p(E12A,2). Ronen also made a limited investigation of two-act decisions where the joint probabilities were unequal. Subjects showed a preference for the act with the higher initial probability but the lower overall expected value. This preference was found when the difference between the expected values of the two acts was less than a specific level.

Maximin Paths of Heterogeneous Capital Accumulation and the Instability of Paradoxical Steady States

If there exist heterogeneous capital goods, a steady state may be in the sense that increasing the rate of interest above the Golden Rule level may lead to an increase in consumption or utility, rather than to the decrease which always occurs in one-sector models. It is shown that, in many cases, a path of capital accumulation which maximizes the minimum consumption or utility level is unlikely to converge to a paradoxical steady state of this kind. IN A ONE-SECTOR SOLOW-SWAN MODEL with homogeneous capital, a fall in the steady state interest rate always is associated with a rise in the steady state value of per capita utility, provided we are considering interest rates above the Golden Rule value. One aspect of the Cambridge controversy in capital theory concerns the fact that such steady state behavior does not always prevail in models with heterogeneous capital: lower interest rates can be associated with steady state equilibria having lower per capita utility. Might such steady states be unstable in some sense so that they would almost never be observed in an economy following some dynamic maximizing rules? Solow conjectured such a relationship, but until recently the question has been ignored.2 Burmeister and Long [5] have studied this question when the dynamic maximization rule is

WEALTH, WELFARE, AND THE PRICE OF RISK

IN THE THEORY of business finance, the most commonly advocated criterion for corporate investment is that such investment (and its associated financing) should be undertaken if and only if it serves to increase the price of the firm's common shares. This rule is often justified on the basis that an increase in the price of shares results in increased stockholder wealth which in turn results in increased stockholder welfare. In this paper, conditions are discussed under which maximum wealth does not correspond to maximum welfare. As one might suspect, these conditions involve situations in which capital investment on the part of the individual firm influences not only the wealth of its stockholders but also the prices and/or characteristics of existing assets available to stockholders in the market. In these situations changes in nominal stockholder wealth due to corporate investment may not correspond in direction to the concomitant changes in the size of stockholders' real opportunity sets. The discussion of conditions under which changes in wealth do not measure changes in welfare naturally leads to consideration of (a) conditions under which the price maximization rule is equivalent to maximization of stockholder welfare, and (b) alternative investment criteria which avoid the problems associated with price maximization. With respect to the optimality of the price maximization rule it is argued that rather stringent conditions on capital market structure are required. This is particularly true of, though not limited to, the case of uncertainty. As for alternative investment criteria, a simple and operational welfare maximizing rule is given of which price maximization is a special case under appropriate conditions. The welfare rule, however, applies to all capital market structures. The motivation for this paper stems largely from the recent development of detailed mathematical valuation models. These models provide, in effect, a formula relating changes in the equilibrium price of a firm's shares to the variables which specify the nature and scale of new investment and its associated financing. This, in turn, offers the opportunity for a rather literal and exact application of the price maximization rule in that mathematical conditions can be derived for maximization of the pricing formula with respect to the investment and financing variables. The capital asset pricing model of Sharpe [14], Lintner [7, 8], and Mossin [13], for example, has been used in this manner by several authors, including Lintner [8] and Mossin [12]. In this paper it is argued that, because of the potential divergence of wealth