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Factors Affecting Labour and Leisure Time Decision: Evidence from Small and Medium Enterprises in Masvingo Urban

The paper establishes the factors considered when making labour-leisure time decisions among employees in the Small and Medium Enterprises. A qualitative study was conducted using two different interview guides, one for shop floor employees and the other one for managers who acted as key informants. Twenty two employees were interviewed and four key informants also took part in the study. Participants were selected using purposive sampling. Data were analysed using thematic analysis. It has emerged from the study that employees in SMES sector know the factors that affect labour-leisure time decisions but they do not affect their work and non-work activities decisions. Some participants also highlighted that wage rate; culture, substitution and income effect affect labour-leisure time decisions but in reality they do not consider these factors due to unemployment and low wage rate in the industry which forced them to attach more value on work than leisure. Participants also revealed that due to low wage rate they prefer to work during weekends and holidays because are guaranteed of an extra income than going for leisure. As recommendations, it is argued that employees value leisure time as it reduces work related stress and death from exhaustion and companies must intervene in some of these extreme cases whereby employees go for years without taking leave days by forcing them to utilize their leave days (forced leave). Journal of Business & Financial Affairs J o u r n a l o f B usi ness & Finncial Af f a i r s

Introduction
The roles of work and leisure may be assessed from a number of different perspectives, and the analyses of the various dimensions may not lead to congruent results. According to neoclassical theory, individuals maximize utility subject to a budget constraint, and can freely choose their preferred working hours. Under perfectly competitive markets with rationale agents and full information, actual and preferred hours worked should be the same. However, it is, in any case, a fact that the leisure time available is not purely a matter of preference. Theory and empirical evidence show, however, that individuals are not free to choose their working hours, resulting in a divergence between actual and preferred hours worked. Relevant literature offers some explanations for this misalignment; notably, long-term contracts, fixed wages [1], job insecurity, poor matching [2], government regulations and taxes [3] and asymmetric information regarding the productivity of employees Sousa-Poza and Ziegler, Landers, Rebitzer and Taylor [4,5] are some of the rigidities in real life situations. Most importantly, attitudes towards the importance of work call for similarly complex interpretations. In some countries, the importance of work stems from its unavailability. That is, a shortage of jobs and a low employment rate increase the value of work. For example, unemployment in Zimbabwe coerces people to attach more value to work and attach little value to leisure. Fuess indicates that labor market conditions should affect peoples' free time. A higher unemployment rate among a group of persons could mean more idleness, and thus, more time for leisure. It is against this background that a research be conducted to analyze factors affecting labour-leisure time decisions.

Background of the study
Over time, the researcher has observed that most small and medium enterprises usually employ one or two employees who work long unsocial hours including weekends and public holidays. Labourleisure time decisions provides employees the chance to balance organizational work and family responsibilities so as to satisfy the competing claims of work and home by meeting their own needs as at home (17 h per week), while women were employed for 26 h and worked at home for 31 h. The study concluded that, the differences in hours worked is as a result of the choices made by every single workingage person regarding work hours, home duties and leisure.
Zimbabwe is not spared from labour-leisure time conflicts among its workforce and as such the Labour Act (Chapter 28:01) give provisions which aims at balancing leisure and labour time. Section 14A of the Labour Act in Zimbabwe provides for vacation leave to employee who has completed first year of employment with an employer. Paid vacations leave accrue to an employee at a rate of 1/12 per year to a maximum of 90 days. Regardless of these provisions, workers in Masvingo still come to work on weekends, holidays and even when they are on leave and this give rise to symptoms of labourleisure time conflicts ranging from worker exhaustion, work related stress and work related accidents. It is against this background that a research be conducted to assess factors that affect labour-leisure time decisions among Small and Medium Enterprises in Masvingo.

Literature Review
This research is guided by the Neo-classical theory of labor supply commonly known as backward bending curve. The theory posits that each individual disposes of a limited amount of time and chooses to allocate between paid work and leisure. Each individual selects the combination of hours of work and leisure that maximizes his or her utility (level of satisfaction). The opportunity costs for individuals who are working an additional hour are the wage rate. Individuals choose not to work if the value of leisure time exceeds the market wage. This can be illustrated using the backward bending labour supply curve.

Backward bending labour supply curve
The backward bending labour supply curve shows that if real wages were to increase from W1 to W2, the substitution effect for an individual worker outweighs the income effect therefore, the worker would be willing to increase hours worked for pay from L1 to L2. However, if the real wage increased from W2 to W3, the number of hours offered to work for pay would fall from L2 to L3 since the strength of the income effect now exceeds that of the substitution effect, the utility to be gained from an extra hour of unpaid time is now greater than the utility to be gained from extra income that could be earned by working the extra hour ( Figure 1).
Maryke argues that the backward-bending labour supply curve shows that as wage increase beyond a certain level, people tend to substitute leisure for paid work time and so higher wages lead to an increase in the labour supply up to some point. He further posits that labour-leisure tradeoff is the tradeoff faced by wage-earning human beings between the amounts of time spent engaged in wagepaying work and satisfaction-generating unpaid time, which allows participation in leisure activities. The key to the tradeoff is a comparison between the wage received from each hour of working and the amount of satisfaction generated by the use of unpaid time. Such a comparison generally means that a higher wage entices people to spend more time working for pay. However, the backward-bending labour supply curve occurs when an even higher wage actually entices people to work less and consume more leisure or unpaid time.

Factors that determines labour and leisure choices
The choice between work and leisure can be affected by a number of factors, including: The substitution effect and income effect: It is worthwhile to note that when wage rate falls, two effects will result. Maryke propounds that, as wages increase, so does the opportunity cost of leisure. He further states that, as leisure becomes more costly, workers tend to substitute more work hours for fewer leisure hours in order to consume the relatively cheaper consumption goods, which is the substitution effect of a higher wage. However, an income effect is also associated with a higher wage. A higher wage leads to higher real incomes, provided that prices of consumption goods remain constant [6]. As real incomes rise, individuals will demand more leisure, which is considered a normal good. In other words, the higher an individual's income, the easier it is for that individual to take more time off from work and still maintain a high standard of living in terms of consumption goods. Fuess states that the substitution effect of higher wages tends to dominate the income effect at low wage levels, while the income effect of higher wages tends to dominate the substitution effect at high wage levels. The dominance of the income effect over the substitution effect at high wage levels is what accounts for the backward-bending shape of the individual's labor supply curve. Therefore, with the substitution effect, leisure is less expensive and the, so consume more leisure and work less. The opposite is true for income effect.

Changes in preferences:
A change in attitudes toward work and leisure can shift the supply curve for labour. If people value leisure more highly, they work fewer hours at each wage, and the supply curve for labor will shift to the left. If they decide they want more goods and services, the supply curve is likely to shift to the right. Davis and Henrekson suggest that different workers will typically view this tradeoff differently. In other words, some persons may like to devote a great deal of time and effort to their jobs, whereas other persons would prefer to devote most of their time to leisure. Garcio-Perez posits that the tradeoff between consumption and leisure is shown with the help of a utility function proper to each individual. These interpersonal differences in preferences imply that the indifference curves may look quite different for different workers. Interpersonal differences in the tastes for work are obviously important determinants of differences in labor supply in the population. Workers who like leisure a lot will tend to work few hours. And workers who do not attach a high value to their leisure time will tend to be workaholics. Similarly, Fuess states that, an increase in the net advantages of work will shift the supply curve to the right. leisure. Akerlof and Kranton [7] envisage corporate culture as the division of the workers into different groups as prescribed by their behavior and respective goals. Thus culture and lifestyles would determine the tradeoffs of leisure and labor time. Fuess supports that if people have started to live a more leisure-oriented lifestyle, we should observe more time spent in leisure activities for the latter observations. If a more leisure-oriented lifestyle has developed, other things equal, then more leisure time and less labor time. For example, Japanese employees work long hours. In spite of the Labour Law, it is not unusual for employees to work 60 h a week. This has led to a phenomenon called karo-shi (death from overwork), where corporate employees have been known to spontaneously drop dead of exhaustion. He further state that, the major reason for the extraordinary number of hours that Japanese work is a promotion culture that is still rooted in a seniority system.

Health status and age:
Numerous studies have shown a direct correlation between working hours and health. A recent paper based on data from the Whitehall II study finds that 3-4 h of overtime work per day is associated with 1.60-fold increased risk of heart disease compared to employees with no overtime work. Older workers often gain more utility from leisure. Societies with a higher proportion of older people tend to have comparatively long leisure hours, since only a fraction of older cohorts are employed. Munostori et al. [8] put across the view that as we move from younger to older age groups, people's preference for work over leisure tends to increase, although it cannot be established whether this is the result of the different experiences and value systems of the earlier generations in the sample.

Direct taxes:
Higher income tax rates may increase the utility of leisure and reduce the labour supply. Prescott [9] argues that the entire difference between the United States and Europe is due to taxes. Davis and Henrekson posit that high taxation increased working hours and reduce leisure time.
Wage rate: The wage rate can be the major determinant of laborleisure decisions. On one hand, perhaps the well paid choose to work more because each additional hour worked is highly lucrative, thus earning more simply because they work more [10]. On the other hand, they may not work as much because they can earn enough to fulfill their needs in a shorter amount of time. Perhaps those earning low salaries must work more because that is the only way to earn an adequate income. It is also possible that those earning less work less because they do not see it as worthwhile to spend additional time working for low wages. An income rise increases leisure, reduces paid work, and leaves home production unchanged. Empirical work by Bloch and Gronau using United States and Israeli data suggests that leisure amongst couples is positively related to the husband's wage income, negatively related to the wife's wage income, and positively related to non-wage income.

Research methodology
The research adopted a case study research design in which qualitative technique was used. The case study was chosen because the researchers had insufficient funds to carry a census of all SMES in Masvingo. Results of the findings will be used to infer to the population of all SMES in Zimbabwe.

Data collection instruments and sampling method
Two interview guides were administered on the sampled elements using purposive sampling technique. Twenty six interviews were conducted. Key informant interviews were also used to obtain in-depth data from the selected few.

Data entry
Table below depicts the responses on the factors affecting labourleisure decisions. Data interpretations were based on the results that emerged from the analysis ( Table 1).

Findings and Discussion
Factor 1 which focused on substitution and income effect showed an affirmative response rate of 73%. The same sentiments were echoed by Fuess who state that, the substitution effect of higher wages tends to dominate the income effect at low wage levels, while the income effect of higher wages tends to dominate the substitution effect at high wage levels. The dominance of the income effect over the substitution effect at high wage levels is what accounts for the backward-bending shape of the individual's labor supply curve. Therefore, with the substitution effect, leisure is less expensive, so workers will consume more leisure and work less (income effect). In relation to this theme, participant 10 had this to say; Unemployment and low wage rate forced me to attach more value on work and attach little value on leisure. I am even better off at work during weekends and holidays because I am guaranteed of an extra income than going for leisure. This trend is in line with Constant and Otterbach's sentiments that as real incomes rise, individuals will demand more leisure, which is considered a normal good. In other words, the higher an individual's income, the easier it is for that individual to take more time off from work and still maintain a high standard of living in terms of consumption goods.
23% of the respondents revealed that wage rate affect labour-leisure decisions. Sharing the same views is Blanchard [10] who posits that well paid choose to work more because each additional hour worked is highly lucrative, thus earning more simply because they work more. He further states that those earning low salaries must work more because that is the only way to earn an adequate income. In contrast Kahn and Lang postulate that higher wage rate induce workers to work less because they can earn enough to fulfill their needs in a shorter amount of time [1]. Participant 1and 19 have this to say respectively: I earn peanuts and i must work more because that is the only way to earn an adequate income. I earn less and I must work less because it is not wise to spend additional time working for low wages.  wage on leisure and market work is indeterminate. He further posits that, an income rise increases leisure, reduces paid work, and leaves home production unchanged [11].
Factor 3 showed 65% of the participants are of the view that culture affects labour-leisure choices. Similarly, Akerlof and Kranton propound that culture and lifestyles determine the tradeoffs of leisure and labor time [7]. Sharing the same thinking is Fuess who argues that if people have started to live a more leisure-oriented lifestyle, they spent more time in leisure activities. If a more leisure-oriented lifestyle has developed, other things equal, then more leisure time and less labor time [12]. Participant 14 has this to say: It's our culture as prescribed by the Holy bible that a man shall work for the family and only rest on the Sabbath day.
The above statement was also said by Fuess who states that long hour working culture determines whether to forego labor time and enjoy leisure or the other way round [13,14]. He further postulates that in spite of the Labour Law, it is not unusual for Japanese employees to work 60 h a week. This has led to a phenomenon called karo-shi (death from overwork), where corporate employees have been known to spontaneously drop dead of exhaustion.
50% of the participants state that health and age affect their leisurelabour choice. In support, a study by Virtanen et al. revealed that there is a direct correlation between the number of working hours and health. Sharing the same view is a paper based on data from the Whitehall II which showed that 3-4 h of overtime work per day is associated with 1.60-fold increased risk of heart disease (mainly risk of heart attack and angina pectoris also known as chest tightness) compared to employees with no overtime work. Older workers often gain more utility from leisure. They further argue that, societies with a higher proportion of older people tend to have comparatively long leisure hours, since only a fraction of older cohorts are employed. Participant 26 has this to say: I am growing older and as such I want more time with my grandchildren rather than being at work.
The above argument cements Munostori's view that as we move from younger to older age groups, people's preference for work over leisure tends to increase. The preference for work over leisure naturally comes with older age. It was suggested that health status and age convince the labor force to choose leisure and forego work or the other way round.
Factor 5 showed a 31% of respondents accepted that taxes affect their labour-leisure choices. Sharing the same view is Davis who states that higher income tax rates may increase the utility of leisure and reduce the labour supply. In addition, Prescott [9] argues that the differences between the United States and Europe can be explained by the tax rate if we assume a log-log utility function on consumption and leisure. Obviously, leisure is used here in the broad sense of the term, that is, any nonmarket (and not taxed) activity such as home production, work in the black economy, or indeed having fun. Seconding is Davis and Henrekson, they state that high taxation increased working hours and reduce leisure time [11].

Conclusion
The study sought to unravel the factors that affect labour-leisure choices of SMES employees. The study was informed by the Neoclassical theory of labour supply commonly known as backward bending supply of labour curve. It has emerged from the findings that employees are driven by a number of factors to choose between leisure and labour time. Participants highlighted that their choice of labourleisure time is determined by substitution and income effect, wage rate, culture, health and age and taxes. The study has also revealed that some employees forgo their leisure because of harsh economic conditions and lower wage rate. Some participants highlighted that they come to work even on weekends and holidays because they want to earn an extra income to supplement their peanuts earnings. In general, the majority of employees substitute their leisure for labour time due to lower wage rate, high taxes and harsh economic conditions.

Recommendations
Management of SMES must review their human resource policies if they wish to take full advantage of their personnel. Leisure time is important since it allows employees to refresh their minds and this goes a long way in reducing work related stress. Management of SMES must also adjust their pay rates or use performance based pay so that employees will save for leisure. Refreshed employees are more committed and productive than stressed workers. Employees must also be made to realize that leisure time is important as it reduces work related stress, overwork death and exhaustion.


MODELLING OF INVESTMENT PROCESSES IN THE SPHERE OF SOCIAL HOUSE BUILDING

The problem of not enough public housing for low-income citizens is very urgent in the entire world. This article is dedicated to the topical question; how do we select optimal investment projects and implement successful investment programs to fund public housing projects better. We have formulated basic principles for the formation of an optimal portfolio to use as a standard for investment programs for public housing construction projects. As selection criteria, instead of profitability and risk offered in classical portfolio theory to which private investors are paying attention, we propose the use of social satisfaction survey results and amount of available funding to determine the effectiveness of the programs. We have developed several mathematical models that help aid in the selection of investment projects based on these new requirements. The application of these models in the selected projects selection within the framework of investment programs of public housing construction will allow the most effective use of funds directed to the development of the public housing. JEL Classification Numbers: R39; DOI: http://dx.doi.org/10.12955/cbup.v5.904 UDC Classification: 332.05

Introduction
Regardless of the form of government, comfortable housing is always high on the hierarchy of human needs (Heijden, Haffner, & Hoekstra, 2006). Originally, the role of the social housing sector was to provide universal access to adequate housing (Zhuk, 2012). Today, a majority of the population buy and rent housing based on a market that is a product of the state's interaction with vulnerable citizens. Improving the interaction between all participants of public housing investment has occurred since the beginning of XVII century. This sphere differs in complexity and versatility. Therefore, it requires a scientific approach to its investigation (Selyutina & Bulgakova, 2014). Without competent control of investments, it is impossible to implement the programs of modern housing, form a favorable investment climate in the region, and carry out structural reforms and responsible housing policy (Berens & Havranek, 2007). The principle of competent control also works in the opposite direction to increase of people's quality of life, which is impossible without economic growth. Therefore, during the development of the programs for social housing one should not forget about economic efficiency. Theoretical Frameworks Financial theory became a science in the early to mid-20th century when the Fisher income discounting technique (2003) was used for the first time. In this economist's opinion, to correctly assess future income in the present, one needs to relate the cost of services with capital cost. An evaluation of the main (capital) assets was central in the works of Williams (1995), a recognized investor in the United States of America. Economists have offered several approaches to evaluate assets to allow controlling investment portfolios. However, all pre-war works were created with a hypothesis about the definiteness of conditions of financial solutions. Therefore, in financial analysis, elementary financial mathematics was used. The work of Knight (1921) in 'Risk, Uncertainty and Profit' contains the first quality analysis of the probability-theoretic mathematical methods of risk events influence. In addition, the recommended set of projects was called investment programs. Some scientists reason that these two concepts are equal. Some economists complete the concept of the investment program, opening it as an element of the investment strategy of the state. For example, Tyrtyshov (2004) emphasizes that the program is a commitment that can create and mobilize resources for its implementation.
Possibly, the term 'investment program' has a wider meaning than the notion of 'investment portfolio' used more so today, but these terms frequently coincide in practice. Therefore, within the framework of this current research, the two terms are considered identical. Modern investment theory is closely connected with Markowitz (1959;1987). His models allowed investment projects that were selected because of risk and profitability to be translated into mathematical language. The main results of scientists-economists, acknowledged in the 20th century, are focused on the works of Markowitz, the essence of which being that a project's portfolio is created using the relation of risk-profitability or certain combinations of risk and profitability (Markowitz, 1959;1987). To maximize profit and minimize risks, investors deal not only with one asset but allocate capital to different projects. A combination of projects creates new investment qualities and perspectives. Evaluation of separate assets and their portfolios. Modern investment theory considers two characteristics: risk and profitability, which are assessed quantitatively to allow the investor to form an optimal investment portfolio. The theory of 'Efficient set of portfolios' remains a summit of classic economic theory (Merton, 1969). As stated by Investopedia (2017), "Portfolio variance is calculated by multiplying the squared weight of each security by its corresponding variance and adding two times the weighted average weight multiplied by the covariance of all individual security pairs."

Data and Methodology
Main Argument Based on the assumption that, for the solution of the portfolio formation, the method and order of steps can be determined explicitly, a model is formed under a determined set of characteristics in various investment projects (Pr), where: Pr = Pr 1 , Pr 2 , Pr 3 … Pr n (1) Where the program of social house building (SPr) is derived from the suggested investment-building projects, the program was described as a subset of investment projects from the set, as follows: SPr ⊂ Pr (2) In the investment program, the characteristic vector, X (Х1, Х2,..., Хn) was used to define the structure of the program. In this case, Xi was '1' when the i-th project (Pri) was included in the program and '0' when not. For selecting optimal projects within the framework of socially-affordable housing, the new representation was social satisfaction (SSi) by the i-th investment project (Pr). This representation can be interpreted as direct, for example, by the number of citizens having improved housing conditions, as well as indirect, for example, the decrease of tension in society and the formation of new working places. Social satisfaction was evaluated subjectively by each expert based on hypotheses and formulations of this study. All social investment programs balance the contradictive conditions of limited financing and social effect requirements. The coefficient of social satisfaction, SS, was determined by experts by estimating the following local social satisfaction factors: ▪ The number of families who improved their living conditions; ▪ The features of social adaptation of citizens; ▪ The load on the existing infrastructure in the area; and ▪ Possibilities for further construction. Representations of a social effect and, consequently, social satisfaction were subjective, and every expert calculated these independently. Representations of social satisfaction were considered deterministic variables or random variables defined on the following probability space: where S = sample space of all possible outcomes; B = Borel algebra of events on the sample space S, collection of all events we consider; and P = probability measure defined for every event A∈ B; P(S) = 1. A is the coefficient of investor's risk sensitivity. The random variable, SSi, of social satisfaction from every investment project available for evaluation was based on: r i = (r i1 , r i2 , … r ik ) (4) where k = sample size of expert values, and rik = value ≥ 2 derived by experts from the set of projects, characterized by a distribution function, Fi(t). The study considered Fi0 as a class of all possible distribution functions, Fi(t), from which a random sample, ri (return of i-th asset), could be drawn. Another criterion in selecting an investment project was the amount of financing for an investment program (V). Based on the above-mentioned criteria, a mathematical model of the investment project was built for the program of social housing. The characteristics and conditions of investment projects were defined, a task rarely performed in practice. Hence, every investment project was characterized by the following descriptions: ▪ SS, a coefficient of social satisfaction of the project; and ▪ V, the required amount of financial means calculated for the project. The resulting models allowed one to determine optimal social projects with maximal social effect under a budget constraint. Where V suggested financing of the program during a certain period, it was assumed that the total demand for financing should not exceed the possible financing during that fixed period. As a result, the social satisfaction of components of the program, consisting of various investment projects, were determined as: = ∑ =1 (5) An investment program of social housing can be constructed using different approaches depending on the choice of criteria and constraints. Based on two key factors, two main models for forming a social housing program were proposed. Model 1 This model was based on maximizing social significance under limited financing needs. From the set of investment projects, a subset of projects was chosen to form programs that satisfy the constraint of limited financing. Then, among those programs, the program with the maximal social significance was chosen. It was necessary to use a set of vectors X = (X1, X2, …, Xn), where each Xi had a value of '0' or '1' and Model 2 This model was based on minimizing finances based on the required level of social satisfaction. In this case, from the full set, the only investment projects selected to form the programs were those that satisfied constraints, in particular, those with the level of satisfaction at least or lower than SS0. Then, among those programs one with the minimally expected financing was identified. It involved a set of vectors X = (X1, X2, …, Xn), where each Xi had a value of '0' or '1' and The value for SS0 represented the required level of social satisfaction of project components. The solution of the program formation resulted with the help of the typical optimization programs.
A mathematical expectation of return in classic theory of investment was an expected return and the variance of return represented the expected risks of investors or risks in general. In the suggested models, the mathematical expectation of significance for projects and programs defined the expected social satisfaction and the variance of significance the risk of investment program or risk in general (Modigliani, 1949). In practice, investment projects were usually characterized not only by the determined demand in financing but by the random subjective value of social satisfaction, since it depended to a large extent on the experts' opinion.
The value representing the sample of expert values was k ≥ 2, and some general population were characterized by the distribution function Fi(t). In this, F0i is a class of possible distribution functions Fi(t), from which sampling ri can be derived as: r i = (r i1 , r i2 , … r ik ) (8) The evaluation of the mathematical expectation and dispersion of characteristics was applied to social satisfaction as follows: where mi = a mathematical expectation of social satisfaction of i-th investment project; Di = variance of social satisfaction of members of i-th investment project; i = standard deviation of social satisfaction of the members of the i-th investment project. The mathematical expectation of social satisfaction of investment program was determined by the formula: (12) For the case of dependent results of satisfaction regarding investment projects, the variance of socially oriented investment program was determined as: where D = the covariance between returns of two investment projects in the case of i = j being a variance. It was assumed that V0 was the potential amount for financing the socially oriented program during a certain period. Consequently, the total demand for financing of the socially oriented investment program could not exceed this potential amount. Socially oriented investment programs can be formed and implemented within a day or in a few periods, depending on the established criteria. From this study, under random characteristics of social satisfaction, the following models of formation of optimal socially oriented projects were developed. The first model of program formation is based on the maximization of expected social satisfaction of investment program under acceptable risk and financing limitations. Then, the economic and mathematical model will be formulated in the following way: it is necessary to choose from the given set of projects such a subset that form programs which satisfy the constraints of limited financing and limited risks. From those programs from the 'feasible region' chose the one with the maximal expected social satisfaction. In other words, it is necessary to find such a set of vectors X= (X1, X2, …, Xn), where every Xi takes two possible values (0 and 1) to meet the following constraints and among them chose the one which satisfies the maximization criterion: where D0 = upper bound of the investor's risks; V0 = upper bound of possible financing of the program; Vi = financing of the i-Pr. The model describes the optimization problem of finding the program, which gives maximal social satisfaction under the terms of limited risks, and limited financing. Its solution can be calculated with the help of typical optimization program. The second model of program formation is based on the minimization of financing of the program under acceptable risk limitation and achievement of required level of social significance. Such conditions can be described by the following economic and mathematical model. From the given set of investment projects, it is necessary to choose such a subset of projects that form programs which fulfill the constraints. It means that the chosen programs do not need to exceed the maximally acceptable risk D0 and in the same time their expected social satisfaction should be at least as high as minimally acceptable level SS0. Those programs form a feasible set of the programs. Moreover, our task is to choose the one program from the feasible set with the minimal financing demands. That is, the task is to find such a set of vectors X= (X1, X2, …, Xn)to achieve for which constraints of achievement at least minimal expected significance of the program SS0 and not to exceed maximal acceptable risk D0 are mutually fulfilled. From the set of received programs choose the one with the minimal financing requirements. In mathematical language, this task can be described in the following way: where SS0 = minimal social significance, lower bound of the social significance to be reached; D0 = upper bound of the investor's risks, this level of risks cannot be exceeded.

Results and Discussion
Thus, for selecting social housing investment projects, one can apply the following principles: ▪ Social significance. To form project portfolio, the authors suggest using new representations of social significance that are of importance of the project for society. ▪ a posteriori return. Evaluation of investment projects of social housing is secondary and can be carried out a posteriori. ▪ Collective decision. Decisions on investment to any project should be made together with experts and investor, using subjective judgments about their advisability. Experts' opinions and evaluations are considered as random values of some allocation. ▪ Adaptability. All chosen investment projects should react operatively to changes of external environment, and mainly to continue developing and realization in dynamically changing conditions of the external environment. ▪ Complexity. Investment program should be, first of all, oriented to complex socially-economic development of the region. Therefore, experts' decision on projects should be systemic and consistent. ▪ Consistency (balance of interests). All members of the expert group should serve to the achievement of common goals, and personal goals of each member should not cause contradictions between the links. ▪ Transparency. The procedure of projects selection, formation, realization, and evaluation of program should be maximally transparent and available to ensure awareness of all desiring investors about the possibility of participation in the program, changes in projects, their possible social significance, return and risks. ▪ Rationality. Investment budget should be rationally allocated to maximally and minimally effective projects. ▪ Professionalism. Only competent members should be attracted to investment projects, e.g., government employees, investors, facility managers, appraisers, and other interested persons.
▪ Objective evaluation. There is a need for introducing a united system of monitoring and accounting that will help to evaluate social and economic effects of project realization maximally. ▪ Management resonance. The great value is assigned to identify investments and resonance in the system and maximizing economic and social effect.

Conclusion
The models produced in this study will help with forming an optimal portfolio of investment projects in the framework of limited budget and limited acceptable risks with maximization of social satisfaction. Consequently, to form an optimal package of projects with the minimal financing requirements will provide at least the required number of citizens with housing. Projects will form without exceeding acceptable risks. The key task for the realization of the social housing programs is an increase of regional quality of life from achieving the programs. As a result, more citizens will be provided with comfortable housing and thus, relations between society and state will potentially stabilize. With the most 'vulnerable' citizens protected social tension in society should automatically reduce (Selyutina, 2016).


PUBLIC-PRIVATE PARTNERSHIP RISKS AND POSIBILITIES IN CONDITIONS OF THE UP-TO-DATE ECONOMICADVANCEMENT

The article is devoted to the study of the public-private partnershippossibilities to achieve the system of goals as well as risks in the implementation of the public-private partnership because of their classification. Theempowerment effective ways through reducing and preventing risks are proposed herein too.

The public-private partnership has not practically widespreaded yet as well as the theoretical analysis multifaceted in conditions of the up-todate economic progress of Ukraine. Ways and shapes of some economic growth, especially itsmotivated and strategically prospective grounds exist in spite of the fact that there are not any contradictions that such a partnership is new with its many specific features. The current conditions of the world economy development inall its diversity are characterized not only by some commercial interests of the subjects which are at the heart of the economic relations,but also by the social orientation clearly evident herein and the state spirit to ensure the decent life for its citizens and its priming on general civilizational values (Heiets, 2009).
Both the state and the business try to find opportunities to join efforts for the fuller and faster results. The partnership in and of itself acquires such importance. Every subject in each sector is looking for a reliable partner with unidirectional goals and appropriate ways to implement them, and a private business often became such a partner forthese states in practice, and each state, in its turn, became the partner for the social business. The world experience of any partnership between the state and business has taken the form of the publicprivate partnership widely spreaded in many countries with high development. The publicprivate partnership implementation allows to carry out themonitoringfor the process from the state and provides opportunities for any business to get profits from this cooperation as well asto be responsible for final results. Any private financing of the public important tasks assists to reduce the risks both for the public sector and for the private business. Therefore,the analysis of the empowerment and reduction of risks in the public-private partnership for the further economic development havean important theoretical and practical importance.

Remaining Open Issues
The analysis of many theoretical studies and practice of the public-private partnership project implementation confirms the expansion ofthe private enterprises and private companiesreasonably considering the state as a prospective partner. Then, the convincing conclusions about the opportunities that anyprivate business will get and the risks, which it will avoid when participating in the public-private partnership as a partner of the state, should be made. Only after that, ways both to increase opportunities and to reduce risks for the longterm development through the public-private partnership can be offered.

Purpose of the Article
To study the opportunities and risks a rising in the joint activities of the state and business in the public-private partnershipimplementation, as well as ways to increase the opportunities and to reduce the risks both to the partners and to the society resulting in the facilitation of the economic developmentthe purpose of the article.

Key Findings
The analysis of the theoretical background and practice of the public-private partnership in up-to-date economic development conditions of many countries shows that either theoretical understanding of the public-private partnership or the practice of the publicprivate partnership has its own specific nature. So, the partnership is sometimes identified with the private finance initiative as well as it is seen as a way of the economic development of cities, and as one of the effective mechanism to combat the social inequality, and as a factorof the civil society development.
The world practice consideres the "public-private partnership" in three vectorsexplainingit as: -a system of relations between the state and business being used as a tool for the economic and social development or as some cooperation being implemented jointly by the government agencies and the private companies at the sites of the state and municipal property.
-a form of the business project implementation of the government using the resources of the private sector to meet the public needs.
Therefore, the theoretical consideration of the public-private partnership takes into account these three vectors whose features and directions are interpreted through the practice. And the theory reveals the essence of the public-private partnership is much broader than the practice sees it today including the following four aspects: 1) forms of the cooperation between the state and business for the realization of the socially significant projects on mutually beneficial terms; 2) cooperative relationships between the government and business to implement such socially important projects in various areas; 3) social institutionswhereboth the joint activities of the public authorities and the private sector meet the society needs; 4) agreements between the public and the private parties in the production and provision of the infrastructure services and means of the budget financing effectivization.
The legislation of Ukraine involves both the world practice and the theoryof the publicprivate partnership understanding. Any partnership is regarded herein as the cooperation based on the contract between the state and the local authorities on the one hand and the legal entities and natural persons -entrepreneurs (private partners) on the other hand on terms determined by the legislative standards (Varnalii, 2007).
The public-private partnership is the cooperation among Ukraine, the Autonomous Republic of Crimea, local communities represented by the respective state authorities,the local self-government (public partners) and legal entities, except the state and municipal enterprises or individuals -entrepreneurs (private partners) if it is based on the agreement in the manner prescribed by this Law and other legislative acts.
The public-private partnership is understood as official relations or agreements on fixed / endless time between the public and private parties where these two sides interact in the decision-making process and invest some limited resources, such as money, personnel, equipment and information to achieve particular purposes in the specific field of science, technology and innovation (Mazur, 2007).
According to the definition given by the World Bank, the public-private partnership is an agreement concluded between the public and private parties on the production and provision of the infrastructure servicesin order to attract the additional investment and, more importantly, as a means of the budget financing improvement of the effectiveness (Publicprivate partnerships in Europebefore and during the recent financial crisis, 2010).
The European Commission's Green Paperconcerning the public-private partnership defines it as a form of some cooperation between the public authorities and the business community, whose aim is to provide funding, construction, renovation, management and maintenance of the infrastructure or provision of services (Comission of the European Communities).
The International Finance Corporation (IFC) determines the public-private partnership as the relationshipsused by the private sector to provide the public with some infrastructure assets and public infrastructure services traditionallyprovided by the state (Graeme, 2004).
The United Nations Economic Commission in Europe (UNECE) states that the publicprivate partnership is a contractual arrangement between the public and private sectors in the provision of some public services and infrastructure development. They will combine all the best that there is in these sectors: the private sector resources and its qualification potential, as well asthe public sector capacity in the economic regulation and protection of public interests (Institute for Public-Private Partnerships, 2013).
As can be seen from the above, and taking into account all these definitions of the public-private partnership, we can determine its directions and such specific traits as: -the public-private partnership is organized to achieve socially significant goals, and specific objectives of the economic and social development;

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-the outcome of the public-private partnership is the improvement of public services and the effective use ofthe resources of the public and private partners in the current and longrun period.
Given this, we can conclude that the direction of the public-private partnership, its purpose and the results determine the essential characteristics of any public-private partnership. They are: -any social and public control of the government and businessinteraction; -some equality of the partnership, members of the public and private sectors; -the partnership realization through the investment activities; -common efforts and resources of the partners and reduction of their risks; -parties' relationshipsbeing built as the contractual relationship based on the contracts having been defined and fixed before.
Some determined characteristics of the public-private partnership allow us to clarify those forms of the cooperation, which had not been defined as a public-private partnership between the private and public entities without such an orientation and characteristics. This significantly not only extends an understanding of the public-private partnership as a special form of the cooperation between the state and business, but also stresses that any publicprivate partnership is a new practical consolidation of efforts by all entities for the economic development.
Under the Green Book of the European Commission on the public-private partnership, such a partnership is characterized by: -some relatively long duration of the relationship involving the cooperation of the public partner with the private partner in various areas of the planned project.
-project financing which is partly due to the private sector, partly due to the complex arrangements between the various actors but in some caseswith the possible involvement of public funds, including those which are in large amounts.
-service provider which is determined as well as its role at various stages of the project design, financing, implementation and completion which are specified.
-public partner's significance mainly focusing on the definite objectives to be achieved to meet the public interest, quality of services and pricing policy which are determined. The public partner is responsible for the project monitoring and the implementation of the requirements for each partner to achieve these goals.
-riskswhich are identified and allocated between the public and private partners, and the allocation of risk usually taken on the public partner.
One of thepublic-private partnershipparticular feature providing the same partnership, but not a temporary mutual cooperation is the coordination of risk-sharing, where the private partner assumes all the risks, or even most of them (Methods Identifying Types of Risks of the Public-Private Partnership to Assess and Determine the Risk Management Form, n.d). The exact distribution of risk is determined in each case according to the ability of the parties to control and to cope with risks . It promotes the public-private partnership in the European Union and makes actual needsto complete the legal acts of Ukraine to promote the cooperation between the state and business, the improvement of the regulatory activity and the regulation of the public-private partnership, the procedure of its establishment, implementation, and the monitoring which is consolidating the distribution of risks. The legislationof Ukraine defines such peculiarities of the public-private partnership as:

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-the technical and economic performance ratioguarantee, which is rather higher than in the case of such an activity performed by the public partnerwithout the involvement of the private partner; -the relationship length from 5 to 50 years; -the transfer of risks to the private partner in the implementation of the public-private partnership; -the private partner investments in the partnership objects withsources not prohibited by law.
As we can see, such features of the public-private partnership are different from the public-private partnership specific traits defined in European legislation. They primarily involves such differences in: -the vision or duration of the partnership terms of its functioning; -the vision of financing side allowingto involve various forms of the project financing including the public funds and their use; -the definition of the roles of the public-private partnership parties, the identification of the serviceproviderand the public partner; -the vision and approach to the risk allocation, taking into account the ability of the parties to deal with such risks, as well askeeping the proportionality in the distribution of such risks.
So, specific traits of the public-private partnership determined clearly and in detail in the European legislation convince the potential participants in partnership with the state that the cooperation of the state with the private partner provides a number of benefits for each side. Improving legislation as to the detailed opportunities and risk sharing in the publicprivate partnership will promote the development of the public-private partnership in Ukraine.
The public partner of the public-private partnershipgets the opportunities subject to the ways of the economic development and achievements both for the state and for the society. Wedivide them into two groups: opportunities for the state and society development and opportunities for the economic advancement.
The first group of the state capacities for the development of state and society and public-private partnerships include: -Urgent implementation of only socially important projects; -Quality improvement and expansion in number of public goods and services; -Public infrastructure improvement; -Expansion of the control and the overall development strategy influence; -Integration of science, education, manufacturing promotion; -Public and private R&D and design works; -Corporate cocial responsibility. The second group of the state opportunities for the public-private partnership economic development include: -state property effective use; -modernization initiatives in key sectors; -new technologies to attract foreign investments; -more financial and material resources; -budget savings; -management experience expansion; -development of the project financinginnovative forms; -avoidance of risks and threats; and -increase in jobs and employment. However, the private partner in the implementation of the public-private partnership gets opportunities that can be divided into two groups: -opportunities to have the status and play a significant role in the economy; -economic and investment priorities. The first group of opportunities involves the following features: -participation in the economic development of own country and the effective assistance to itssocial development and welfare of citizens; -project status advance because of its importance in the economy and the participation of the public partner in it; -improvement of relations and the regulatory framework through the forward and backward linkages like "society -the state -business"; -creation of the positive business image in the society; The second group of the economic opportunities and investmentsconsists of the: -expansion of own market share; -entrypreviously closed sectors of the economy (infrastructure, utilities, social, etc.).
-availability of loans and concessional loans, including credits against the state guarantees; -involvement of the budget for the project development; -reimbesment of credit guarantees; -security of sales and implementation services; -reduction of the competitive pressure and the need for the constant improvement of competition; -decrease in the investment risks; -avoidance in the number of risks in the long run. Some difficultiesappear together with the public-private partnershipcapacities, whichwe offer consider as tasks to perform. Such tasks ensure the implementation of the: 1) budget planning -the implementation of the individual projects where the source of income is the cost of the budget and there is some need in a detailed budget planning; 2) expansion of the managerial skills and abilities, and continuous qualification improvement of civil servants who control the implementation of the public-private partnership; 3) analysis of potential risks, their assessment and possible consequences. Therefore, we consider the nature and characteristics of risks in the public-private partnership. The term "risk" means such circumstances which, according to the parties, may have an adverse effect on the benefits which the partners plan to get implementing the project.
The risks for each participant in the public-private partnership arise at each stage of a public-private partnership from its planning to the implementation of goods and services. The appetite for risk will be different for each side of the partnership depending on its role in the implementation of the public-private partnership. We define the following four groups of risks. The first group of risks focused on risks of the legislative provision and regulation.The second group of risks consists offinancial, monetary and associated with changes in the exchange rate risks.The third group of risks involvestechnical and technoeconomic risks in the design of the construction and operation.The fourth group of risks deals withmarket risks associated with changes in market prices or demand for manufactured goods and services.
Any risk assessment of each group foresees their detalization in each the public-private partnershipproject and determines the likelihood of their occurrence, possible adverse effects and the size of possible losses. The result of the risk assessment should be the formation of the mechanism of risk sharing based on the following principles of: -proportional distributionsof any risk amongthe public and private partners; -possibilities for each partner to evaluate and control the hazards and their impact on the performance of the contract; -timely implementation of measures to prevent risks or minimize their effects. The risk sharing mechanism and its application in practice requires the risk assessment in each situation with taking into account the resource capacity to the partnership (Klimov, 2012).
The public-private partnership world practice offers to reduce these risks through the government guarantees, insurance coverage or through the guarantees from the international financial institutions or export credit agencies and investment promotion.
As to the assessment and measurement of risks, we propose to divide the risks which can be assessed and the risks that are difficult to be deductible. The risks being difficult to assess and to reduce include risks associated with the the legislative framework imperfection and monetary instability in the current conditions of the economy. This is particularly true when we talk about issues of licenses, permits, taxation and contract enforcement,and risks associated with currency fluctuations, especially the depreciation of the national currency.
Therefore, measures reducing risks may be as follows: -involvement of the public or private partners' additional resources havingbeen defined and agreed by the partners before; -contract review because of the risk including the extension of its actions; -termination of the agreement by one of the partners with a simultaneous settlement of issues dealing with the compensation of the related losses; -insurance against failure or improper performance of the contract because of the risk of the partnership.
Taking into consideration the fact that any funding of the infrastructure projects from the private sources provide an opportunity to reduce the cost of public funds and resources allocated for the development and operation of any infrastructure, then, the state support for these projects must be at the regional level. Such projects must be included into the plans of the regional develoopment by reducing the risks for the participants of the public private partnership.
Thus, proportional and equitable distribution of all the groups of risks among partners is essential for the successful implementation of any public-private partnership. Conversely, the disproportionate allocation of risks, or itsshuffling off the burden on one of the partnerwill slow down the project implementation and reduce its effectiveness, despite the great opportunity for each participant of the public-private partnership and the desire to participate in such a partnership for the development of economy and society.

Conclusions
1.Any public-private partnership is to achieve socially significant goals and to clear objectives of the economic advancement, as well as to improve the efficiency of public services and the effective use of resources.
2. The legislation features of any public-private partnership should be clearly defined and convince the potential participants of the public-private partnership that their mutual beneficial participation in the long term as defined in European legislation where the terms of the partnership functioning is not governed, allowes various forms of the project financing, in particular, the use of public funds. Theparticipants define the public-private partnership significanceas an organization -the service provider and the public partner, the devision of risks with regard to the ability of the parties to deal with such a risk. To follow some proportionality is recommended in the allocation of risk to facilitate the cooperation between the public and private partners and increasing benefits for both parties.
3. Any participation in the public-private partnership projects extends the capabilities of each partner, whichare complementaried and mutually provided.
4.Together with the possibilities of public-private partnership, some difficulties need to be considered as a task to be performed. They ensure the realization of the opportunities like budgeting in case of the individual project implementation where the budget expenditures foreseen andthe expansion of managerial skills and abilities of the public servants controlling the implementation of public-private partnership.
5.Both the analysis and evaluation of all the groups promotethe mechanism of the effective risk management as well as the public-private partnership partners' capability implementation grounding on the following aspects: -proportional distributions of each riskamongthe public and private partners; -possibilitiers for partnersto evaluate and control the hazards and their impact on the contract performance, -measures timely implemented to prevent risks or minimize their effects. 6. The mechanism for the efficient risk sharing and its application in practice requiresthe risk assessmentin each situation and taking into account the resource capacities of all thepartnership participants. 7. Ways expanding opportunities and reducing risks is to improve the legal framework regulating the activities of the partners and their responsibility with taking into account the business proposals and theprevention of the corruption ellements in the contractual relations among the public and private partners.
8.Considering the fact that the infrastructure projects create an opportunity to reduce the cost of public funds and to accelerate the economic advancement and growth, different ways of motivation to develop any public-private partnership should involve the state support for these projects at the regional levels and its inclusion into the plans of the regional development.


Fraction of Negligence Costed The Life: (a Fatal

India is a country having 2nd largest network of railway lines in the world and rail is the most used public transportation system. First rail way in India started in 1853 between Bombay and thane, since then Indian railway has spread its branches in all directions to connect all parts of country. Indian railway passes through cities, towns and villages. Many dwelling/ settlements are located close to the tracks and are usually unmanned without any barricades/ signals. The trains of our country are usually overcrowded with people and hence are prone to meet fatalities. Fatal railway injuries may be sustained while crossing the track, jumping in front of train, lying on tack, fall from moving train, collide of trains or derailing of the train. The grievance of injury will depend on the manner of injury. Accidental deaths are more common and in accidental deaths pedestrian accidents are more common [1]. The injury in pedestrian accidents varies from trivial trauma to amputation/ mutilation of the body. Here we are presenting a fatal case of railway runover of an 18 year old girl while she was trying to cross unmanned level bridge in hurry.

Introduction
India is a country having 2 nd largest network of railway lines in the world and rail is the most used public transportation system. First rail way in India started in 1853 between Bombay and thane, since then Indian railway has spread its branches in all directions to connect all parts of country. Indian railway passes through cities, towns and villages. Many dwelling/ settlements are located close to the tracks and are usually unmanned without any barricades/ signals. The trains of our country are usually overcrowded with people and hence are prone to meet fatalities. Fatal railway injuries may be sustained while crossing the track, jumping in front of train, lying on tack, fall from moving train, collide of trains or derailing of the train. The grievance of injury will depend on the manner of injury. Accidental deaths are more common and in accidental deaths pedestrian accidents are more common [1]. The injury in pedestrian accidents varies from trivial trauma to amputation/ mutilation of the body. Here we are presenting a fatal case of railway run-over of an 18 year old girl while she was trying to cross unmanned level bridge in hurry.

Case Report
An 18 year old female was brought to hospital in 3 parts (SSIMS, Davangere) with alleged history of accidental railway run over, where she died within an hour of arrival and was shifted to mortuary.
Female aged about 18years, Reconstituted body length measuring 80+65cm (145cm), moderately built and nourished. Wheatish in skin complexion. Black scalp hair measuring 35cm. Post-mortem staining was faintly seen at back and was not fixed. Rigor mortis had developed over the head and neck. Blood stains were present over the arms, abdomen & back of the body. Lips, ear lobules and nail beds appeared pale. Oil and grease stains seen over the chest, abdomen and amputated lower limbs. Blood soaked hospital bandage was present over amputated end of the thighs (Figure 1).

External injuries
Crush injury with amputation of both the lower limbs present at the level of upper thirds of both thighs, situated 16cm below the anterior superior iliac spine. The crushed and lacerated muscles, vessels, nerves, adipose tissue and bones are exposed through amputated cut ends and oozing of blood is seen. Both the amputated lower limbs were completely separated from the trunk. Margins of the crush injury showed oil and grease stains. Laceration measuring 2cm x 1cm x bone deep present over the dorsal aspect of left 3 rd toe ( Figure 2). A. Internal Examination Findings: a) All internal organs were intact and pale.

B.
The external injuries mentioned were of ante-mortem and fresh in nature.

Cause of Death
"Death is due to Hemorrhagic Shock consequent upon crush injuries of both the thighs as a result of railway run over."

Discussion
Trains are one of the most important modes of transportation in our country & have become part of the day to day life of the people. Deaths have occurred in association with railways since the inception of the railway industry. A study conducted by Basavaraj et al. [2] depicted that the males are the commonest victims of railway related deaths. Most vulnerable age group is 21-30 years. Railway deaths are caused by a number of reasons such as; A person under the influence of alcohol loose selfcontrol & capacity to judge, Many suffer injuries while boarding in and out of the train, While crossing the level bridges etc. While some are caught accidentally, many of the victims with a strong intent to end their life lye own on the track committing suicide.
A retrospective study conducted by Ramesh et al. [3] depicted that accidental deaths are more common 68.8% and there is male predominance of92.78%. A study conducted by Mohanty et al. [4] on 88 railway related deaths showed that males are more prone for such injuries, accidental deaths are more common (80.7%), with 64.8% of victims been pedestrians. Decapitation or amputation was common in suicidal cases. Decapitation and mutilation of body is most commonly see in suicidal cases [1,5,6]. In present case it was mere negligence on part of deceased and inappropriate safety measures on part of the government / railway department that made this 18 year old girl to lose her life.

Conclusion
There are various cases of railway injuries the pattern of wounds depends on the position of the victim at the time of incident. Mutilations of body, decapitation or amputation are more commonly see in suicidal cases. But in this cases accidental fall on rail track has let to railway run-over and the body of victim was served in pieces. The injuries sustained on railway track are usually most fatal & can occur accidentally due to mere lack of attention, usage of phones, urgency to catch train etc.
These injuries can better be prevented rather than treated.

Prevention
The accidental railway deaths in future can be reduced by a) Implementing safety measures, b) Reducing the public access to railway tracks by strict vigilance, c) Educating the public about dangers of railway trespassing. d) Displaying signal boards, e) Construction of overhead pathways and manned crossing levels.