Single-period Models Research Articles

The Asset Pricing Effects of Fixed Holding Costs: An Upper Bound

The Capital Asset Pricing Model predicts that investors will hold diversified portfolios, but many households actually hold very few assets. The paper examines the asset pricing implications of one possible explanation for this phenomenon, fixed costs of holding assets. While earlier authors found the exact asset pricing effects of such costs in single-period models under restrictive assumptions, I derive a general upper bound on these effects that is also valid in continuous time. Illustrative calculations reveal that large holding costs must be postulated to generate significant asset pricing effects.

Adverse Selection, Commitment, and Renegotiation: Extension to and Evidence from Insurance Markets

Under conditions of asymmetric information, to long term contracts may permit markets to approach first best allocations. However, is fragile and may be undermined by opportunistic behaviour, notabley renegotiation. This paper examines the role of in insurance markets. It shows that fully separating strategies, when renegotiation proofed, offers the same ex ante welfare as a replication of single period equilibria. The authors present an alternative model (which extends Laffont and Tirole's 1990 model of procurement to address uncertainty and competition), which involves partial pooling in the first period followed by separation. This, and competing models (e.g. models, single period models and no commitment models) have different testable predictions concerning the temporal patterns of insurer profitability. While fairly broad tests using U.S. property liability insurers favor the no commitment model, more focussed tests on California data suggest that some automobile insurers do use to attract selective portfolios comprising disproportionate numbers of low risks. (A)

Pressure control for leakage minimization in water supply networks Part 1: Single period models

The issue of minimizing leakage in water supply networks by appropriate control of the settings of pressure-reducing valves is addressed. The problem is first formulated as a non-linear, non-convex optimization problem. The limitations of iterative linearization are then discussed. Alternative linearized models based on separable programming are presented. Results of case studies to assess the efficacy and computational efficiency of the proposed models are presented and discussed.

Models of Marital Status and Childbearing

The authors review the microeconomic models of marital status and childbearing that have implictions for female labor supply. The geographic focus is on developed countries primarily the United States. 2 contains a review for the United States of trends in those demographic variables which are strongly associated with female labor supply: age at first marriage marital dissolution age at first birth the number of children born over the life cycle and the age pattern of fertility. Section 3 is concerned with demographic models and the empirical regularities in demographic behavior. The microeconomic models that attempt to explain the facts described in Sections 2 and 3 are then considered. 4 explores models of marital status and in Section 5 the single-period models of lifetime fertility decisions are reviewed. Section 6 is concerned with the efforts of Wolpin (1984) Newman (1985) and Hotz and Miller (1985) to extend the single-period fertility models to dynamic settings with uncertainty. (EXCERPT)

Endogenous Investment, Current Account and the Rybczynski Theorem

The purpose of this paper is to construct a simple intertemporal model of investment and international trade. The bulk of trade theory explores the behavior of an economy in a single period framework, and the traditional trade models assume that the agents in the economy save and invest nothing. The bulk of trade theory is also unable to analyze problems concerning the current account imbalance of an economy, since the traditional models assume that the economies never experience an imbalance in their current accounts. We remedy these shortcomings. We extend the standard, single-period two sector model of production to a two-period setting, while explicitly introducing endogenous saving, endogenous investment and international debt. In addition, we focus on some trade theorems traditionally derived from single period models. Bruno [1], Marion [4], and Marion and Svensson [5] have indeed employed two period models to study the effects of oil price changes on the current account of an open economy. The emphasis of their work, however, is quite different, and their models are not readily comparable with the standard two-sector general equilibrium model, largely because they assume perfect international mobility of capital. Dornbusch [2] and Svensson and Razin [7] have also utilized intertemporal models to examine the effects of terms of trade changes on the current accunt. Their emphasis also is quite different from that of the present paper. Further, Dornbusch, and Svensson and Razin focus more on the intertemporal consumption smoothing, and utilize a relatively simplified production structure of the economy. We simplify the consumption side of the economy by introducing proportional consumption (and hence, saving) functions, and develop a more elaborate intertemporal production structure.

The Replication of Multi-year Solutions Using Single Period Models of Electric Utility Capacity Expansion Planning

Abstract When fuel prices are projected to change over the planning horizon, a standard approach is to formulate a multiperiod capacity expansion model for a utility. However, multiperiod models are considerably larger and more cumbersome than a single period model. An alternative strategy is to develop a single period model whose optimal solution replicates the first period part of the multiperiod optimal solution. This allows the model builder to trade-off a more aggregate multiperiod model for a more detailed single period, rolling horizon model without increasing computational complexity. When and how this can be accomplished in a model of electric utilities is the subject of this paper.

Disequilibrium cutting rules

This paper derives cost–benefit rules to be used when examining whether unemployment and other market imbalances provide justification for national forest managers to depart from the classical Faustmann rotation rule. It turns out that a high level of unemployment in a particular year is not normally a sufficient condition to justify increased cutting in that year (even if full employment is expected to prevail in the future). Moreover, it may very well be socially unprofitable to increase cutting when there is excess demand for timber. These results are in stark contrast with those found in textbooks on applied welfare economics, saying that unemployment and (or) excess demand for goods always justify a higher level of production than the profit maximizing one. This is so because the latter rules are derived for ordinary produced goods in single-period models, while forest management must be considered in an explicit intertemporal framework.

The Determination of Fair Profits for the Property-Liability Insurance Firm

Single period and dynamic valuation models in continuous time, under certainty and uncertainty, are developed for a property-liability insurance contract to determine the “fair” (competitive) premium and underwriting profit. The intertemporal stochastic model assumes that the claim frequency and the price index of claim settlements are functions of a set of underlying state variables which follow a multivariate Wiener process. The competitive premium is shown to be proportional to the claim frequency and the price index for claim settlements at the time the policy is issued. The factor of proportionality varies directly with the claim settlement rate and the length of coverage, and inversely with the risk-adjusted real interest rate on the dollar-valued claim rate.

EVIDENCE ON THE EXISTENCE OF COMMON STOCK INFLATION HEDGES

Previous researchers have been unable to identify (on an ex ante basis) inflation hedge portfolios consisting of common stocks. This study demonstrates a procedure for forming common stock portfolios that offer returns that vary positively with unexpected inflation. The strategy could have been used to hedge against purchasing power risk during the 1974-1979 period. In addition to its practical value, the research has important implications for capital asset pricing theory since the existence of hedge portfolios is a necessary condition for the superiority of the multi-period CAPM over the single-period models.

An expository critique of the Takayama—Judge models of interregional and intertemporal market equilibrium

In this paper an attempt is made to expound the spatial-temporal multi-product allocation and price equilibrium models originally proposed by Takayama and Judge (1971). Certain restrictive features of these models are highlighted and an alternative specification which overcomes these restrictions and replaces both the single and multiple storage period models of Takayama and Judge is outlined. The enhanced realism of this new model and its relatively simple structure should commend it to regional economists concerned with policy questions involving the production and distribution of a wide range of commodities.

Decomposition of a Multi-Period Media Scheduling Model in Terms of Single Period Equivalents

This paper develops a method for choosing advertising media plans for the next T-periods in order to maximize net discounted profits. Using the discrete maximum principle of Optimal Control Theory, it is shown that under certain conditions a T-period media model can be decomposed into a sequence of T one-period models together with the determination of the corresponding carry-over effects using an iterative procedure. The single period models with their objective functions modified to include the carry-over effects can be solved by conventional methods. Although the conditions for decomposition are not always satisfied, the heuristic solution procedure defined by the decomposition approach has been found to give close to optimal solutions in randomly generated test problems. The solutions obtained in these tests are usually better than the corresponding solutions obtained by the Little and Lodish type of heuristic applied to the present model. Finally, the T-period model is specialized to derive a steady-state formulation of an infinite horizon media planning problem.

Reaction Functions as Nash Equilibria

A for the ith firm, xit = i(xt.1), is a decision rule which selects a price for the firm in period t as a function of the observed price vector of period t -1. A Nash [11] non-cooperative equilibrium for this model, in which the equilibrium strategies were reaction functions, would be characterized by n reaction functions (xt), ..., +P*(xt), one for each firm, which have the following property: For the ith firm, no sequence of prices, xit, xi,t+ , ... will yield a higher value for equation (1) than will Xi?= t4(x1) (' = t, t+ 1, ...), given that all other firms will choose their prices by Xjt = ql*(x,_1) in all periods. This condition holds.for i = 1, ..., n.1 The purpose of this paper is to establish conditions under which the equilibrium outlined above approximately exists. Thus this paper is in the reaction function tradition of oligopoly which has its earliest roots in Cournot [2] and its main early development at the hands of Bowley [1], Stackelberg [12] and Fellner [5].2 These writers worked with single period models of the firm, while discussing how the firms ought to behave given that they are really concerned with profits over a long time horizon. Taking explicit account that the firm's objective is to maximize a discounted stream of profits (as in equation (1) above) is first done, so far as I am aware, in my article on duopoly [6]. The present paper continues the research begun there and carried on in [7], [9]. While each of these papers makes steps in the direction of Nash type reaction function equilibria, existence was not proved in them for' any class of models, nor was any satisfactory equilibrium found to exist; therefore, the present paper is an advance in this line of research. Section 1 gives the basic assumptions and pertinent results from earlier work, and Section 2 defines and shows existence of the approximate equilibrium for a large class of models.

A BAYESIAN MODEL FOR PORTFOLIO SELECTION AND REVISION

IN PORTFOLIO ANALYSIS, the basic setting is that of an individual or a group of individuals making inferences and decisions in the face of uncertainty about future security prices and related variables. Formal models for decision making under uncertainty require inputs such as probability distributions to reflect a decision maker's uncertainty about future events and utility functions to reflect a decision maker's preferences among possible consequences [30]. Moreover, when a series of interrelated decisions is to be made over time, the decision maker should (1) revise his probability distributions as new information is obtained and (2) take into account the effect of the current decision on future decisions. In terms of formal models of the decision-making process, probability revision can be accomplished by using Bayes' theorem and the interrelationships among the decisions can be taken into consideration by using dynamic programming to determine optimal decisions. Since portfolio selection and revision involves a series of interrelated decisions made over time, formal portfolio models should, insofar as possible, incorporate these features. A search of the extensive literature concerning portfolio models indicates, however, that such models have ignored one or both of these features. Since Markowitz [18] developed his original model of portfolio selection, a considerable amount of work has been conducted in the area of mathematical portfolio analysis, and much of this work is summarized by Sharpe [31] and Smith [33]. Although the emphasis in portfolio analysis has been primarily on single-period models and portfolio selection, multiperiod models and portfolio revision are investigated by Tobin [35], Smith [32], Mossin [21], Pogue [22], Chen, Jen, and Zionts [3], and Hakansson [13, 14]. In addition, general multiperiod models of consumption-investment decisions are developed by Hakansson [10, 11, 12], Merton [19], Samuelson [29], Fama [6], and Meyer [20]. However, it is generally assumed that the probability distributions of interest are completely specified and that they are unaffected by new information, implying that the portfolio revision models do not involve probability revision over time. Bayesian models have received virtually no attention in the portfolio literature. Mao and Siirndal [17] present a simple, discrete, single-period Bayesian model in which the returns from securities are related to the level of general business activity and information is obtained concerning business conditions. Kalymon [16] develops a model

THE MULTI-PERIOD CONSUMPTION INVESTMENT PROBLEM AND SINGLE PERIOD ANALYSIS

IN recent years multi-period consumption investment models have received increasing attention in the economic literature. This represents a departure from economists' early preoccupation with single-period models. Given the vast number of normative and descriptive models which have been derived based on the assumption that single-period decisions were appropriate, it would be fortuitous if the multi-period formulation of the problem led to results which were consistent with those produced by single-period models. The purpose of this paper is to synthesize the work that has been done on the multi-period consumption-investment decision in order to examine the implications for the validity of single-period models in the multi-period setting. Throughout this paper we will assume that the investor's objective is maximization of multi-period consumption. This objective function is sufficiently general to encompass all multi-period objective functions.'

Portfolio Models with Stochastic Cash Demands

The problem of unifying portfolio planning and transaction demands for cash in a single model is considered. We distinguish between portfolio selection and portfolio revision problems. Each problem is formulated as a single-period model allowing exogenous stochastic cash demands and: (1) deterministic returns on the earning assets, (2) stochastic returns on the earning assets. Thus, four single-period models are presented. An analytic solution for one of the models is derived, and numerical examples given. The other models are nonlinear programming problems, two of which are computationally tractable. Implication's of the models are discussed.

Mathematical models for regional planning

This paper provides a discussion of the mathematical methods used in regional economic planning models. Particular attention is given to the relationships between (1) the economic assumptions embodied in the models, (2) the computational methods used to solve the models, and (3) the degree of disaggregation achievable with reasonable computational expense. The paper begins with a discussion of the particular characteristics of regional models which distinguish them from economy wide planning models and then includes sections on single period and multi-period models. Both simulation and optimizing models are discussed.

INTEREST RATES ON MORTGAGES AND DIVIDEND RATES ON SAVINGS AND LOAN SHARES: COMMENT

The Journal of FinanceVolume 22, Issue 3 p. 467-470 Comment INTEREST RATES ON MORTGAGES AND DIVIDEND RATES ON SAVINGS AND LOAN SHARES: COMMENT Paul A. Meyer, Paul A. Meyer Assistant Professor of EconomicsAssistant Professor of Economics, University of Maryland.Search for more papers by this author Paul A. Meyer, Paul A. Meyer Assistant Professor of EconomicsAssistant Professor of Economics, University of Maryland.Search for more papers by this author First published: September 1967 https://doi.org/10.1111/j.1540-6261.1967.tb02981.xCitations: 4 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume22, Issue3September 1967Pages 467-470 RelatedInformation