On the One-shot Two-person Zero-sum Game in Football from a Penalty Kicker's Perspective

A penalty kicker's problem in football has been modelled. The study took into consideration different directions in which the ball can be struck and goalkeepers' success at defending shots. The strategic form of the game that can be used to predict how the kicker should optimally randomise his strategies has been modelled as a non-linear game-theoretic problem from a professional kicker's viewpoint. The equilibrium of the game (i.e., the pair of mutually optimal mixed strategies) was obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method was adopted to solve this problem. The optimal solution to the game indicates that the kicker never chooses to kick the ball off target, to the goalpost or to the crossbar, but rather chooses to kick the ball in the opposite direction to the one where the goalkeeper is most likely to successfully defend from past history. (original abstract

Impact of Plant Utilization on Irreversible Investment Under Uncertainty with Application to Refinery Investment

Why are some regions preferred when investors consider irreversible investment? This study offers an explanation to this question and suggests improvements that will assist disadvantaged regions improve on their bid for funds. The paper considers irreversible investment under uncertainty when installed capacity utilization is incorporated. We develop a normative model for irreversible investment problem under uncertainty using real options approach. Capacity utilization was not a major consideration by previous authors who assumed that installed capacity would be fully utilized. Variations in capacity utilization may be attributed to disruption in input supply or infrastructural bottlenecks that limit firms to get their products to customers. This study modifies the geometric Brownian motion for the value of a project to account for capacity utilization in the derivation of irreversible investment decision rule. The proposed model provides a theoretical explanation of how utilization affects irreversible investment decisions. Data on petroleum refinery margins is used to illustrate application of the proposed model to refinery investment. The study reveals that capacity utilization has an inverse effect on the investment trigger, and so, links irreversible investment decisions to plant utilization. We recommend optimal utilization of installed plant capacity for regions seeking funds for irreversible investment

Determination of the Optimal Exchange Rate Via Control of the Domestic Interest Rate in Nigeria

An economic scenario has been considered where the government seeks to achieve a favourable balance-of-payments over a fixed planning horizon through exchange rate policy and control of the domestic interest rate. The dynamics of such an economy was considered in terms of a bounded optimal control problem where the exchange rate is the state variable and the domestic interest rate is the control variable. The idea of balance-of-payments was used as a theoretical underpinning to specify the objective function. By assuming that, changes in exchange rates were induced by two effects: the impact of the domestic interest rate on the exchange rate and the exchange rate system adopted by the government. Instances for both fixed and flexible optimal exchange rate regimes have been determined. The use of the approach has been illustrated employing data obtained from the Central Bank of Nigeria (CBN) statistical bulletin. (original abstract

On graduation of enrolment size in a multi-echelon educational system

This paper focuses on an educational system wherein demotion and double promotion are not allowed. The total enrolment in such a system is modelled as a linear model within the context of factor analysis. The goal is to represent the total enrolment in terms of latent factors which generate the flows in the system. The notion of matrix spectrum and spectral radius are used to benchmark the specific variances and to approximate the factor loading vector, respectively. Two main theorems are propounded alongside with their proofs. A numerical illustration is given

Integral equation of the Volterra type: an application to a firm-sponsored off-the-job training

W artykule poszukuje  sie funkcji produkcji pojedynczego produktu w przedsiebiorstwie finansującym szkolenia ze środków uzyskanych ze sprzedazy tego produktu.  Funkcja produkcji ma zalozona forme  równania całkowego Volterry a kryterium optymalizacji jest krótkoterminowa  maksymalizacja zysku, w którym praca jest jedynym czynnikiem produkcji.  W badaniu wykorzystano funkcję Cobba-Douglasa z ustalona iloscia kapitału. Wyniki wskazują, że otrzymana funkcja produkcji firmy jest funkcją analityczną, a wymagana część zysku potrzebna do sfinansowania szkolenia leży w przedziale z określoną górną granicą.This paper is concerned with deriving, using the Volterra integral equation, a production function for a single product firm financing off-the-job training from its revenue from output. The short-run scenario where labour is the only variable factor of production is studied within the ambit of the law of diminishing returns and the condition for profit-maximization. The study utilizes the Cobb-Douglas production function wherein capital is fixed as a theoretical underpinning. The results indicate that the production function of the firm is a transcendental function and that the proportion of output required to finance the training lies within an interval with a definite upper bound

On graduation of enrolment size in a multi-echelon educational system

This paper focuses on an educational system wherein demotion and double promotion are not allowed. The total enrolment in such a system is modelled as a linear model within the context of factor analysis. The goal is to represent the total enrolment in terms of latent factors which generate the flows in the system. The notion of matrix spectrum and spectral radius are used to benchmark the specific variances and to approximate the factor loading vector, respectively. Two main theorems are propounded alongside with their proofs. A numerical illustration is given

A control rule for planning promotion in a Nigerian university setting

This paper examines the attainability problem in a graded manpower system, where the objective is to maximise the total throughput. The problem is modelled as a linear programming problem (LPP) and the evolution of structures in the system is described using the Markov chain model. The decision variables are the promotion rates. Results from the LPP provide a guide to the administrative authority of the system on how promotion and retrenchment should be implemented. The utility of the model is demonstrated using a university setting in Nigeria

A Theoretical Framework for Determining the Appropriate Level of Subsidy in Economy

A framework has been developed for determining the subsidy that, in the long run, serves to equalize the per capita income shares across income classes. The framework characterizes the income dynamics by the Markov process and uses the principle of maximum entropy for selecting among alternative subsidy schemes. The study provides a means to forecast the per capita income shares at any instant of time and serves as an objective tool to decide on the appropriate level of subsidy. (original abstract

Inspecting debt servicing mechanism in Nigeria using ARMAX model of the Koyck-kind

The burden of external debt affects the wellbeing of an economy (or a country) by making the economy vulnerable to external shocks and crowding out investment. When dealing with debt management in indebted poor countries like Nigeria, the rational approach is to allocate a portion of export earnings for debt service payments. Along this line, there is a need to identify the link between debt servicing and export earnings. Hence, the current and long-run effects of export earnings on debt service payments are modelled as a single-input-single-output discrete-time dynamical system within the framework of the Autoregressive moving average explanatory input model of the Koyck kind (KARMAX). The KARMAX model is identified for Nigeria using data from the World Bank database from 1970 to 2018 based on the maximum likelihood (ML) method, and the obtained results are compared to the prediction error and the instrumental variable methods. From a theoretical perspective, the KARMAX specification identified by the ML method is more ideal and inspiring. By doing so, this article contributes to the literature on the econometrics of public debt management

A panacea to the asymptotic effect of examination malpractice in a malpractice-stamp-out scenario

This study provides a solution to a recent result by Ekhosuehi and Osagiede [1] on the asymptotic effect of examination malpractice. We prove that in a dense population of candidates seeking admission in an environment saddled with examination malpractice, educational institutions can maintain the enrolment structure at a certain level n * if a specific quota is fixed by the Ministry of Education or its regulating agency for new entrants into the system.Keywords: absorbing Markov chain; examination malpractice; multi-echelon educational system; terminal enrolment structureJournal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 193 – 19