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We present a model of the electricity market which has a simple connection to the rest of the economy, due to a quasi-linear utility function.A key stochastic parameter shifts electricity demand between points of time.The correlation between these demand shifts and the variation of supply from variable renewable electricity (VRE) sources is crucial for the equilibrium price of electricity.Based on these equilibria we compute the value factors of VREs, as well as producer and consumer surpluses.An outcome of the model analysis is that value factors of VREs decrease as their penetration gets higher, which is also commonly found empirically, but only up to a point.

This paper explores the interaction between human capital and innovations in the process of economic growth. Using a model of endogenous economic growth, the focus of our analysis is on the incentives to acquire human capital and how they are affected by taxes on human capital and other policy instruments. In contrast to many other growth models we find that the taxation on human capital has a substantial negative effect on the accumulation of it. This in turn lowers the income growth rate. While subsidies to research and to intermediate inputs have positive effects on growth (and must be strictly positive in social optimum), they do not necessarily imply that there will be larger stock of human capital in the economy. If the elasticity of intertemporal substitution in consumption is sufficiently low, these policy instruments stimulate growth by inducing a reallocation of a shrinking stock of human capital in the direction of research.

This paper explores the interaction between human capital and innovation in the process of economic growth. Using a model of endogenous growth, we focus on how taxes and other policy instruments affect the incentives to invest in human capital. In contrast to many other growth models we find that the taxation of human capital has a substantial negative effect on its accumulation. This in turn reduces innovation and, consequently, the income growth rate. More surprisingly, other policies that are intended to stimulate growth may have opposing effects on innovation and the accumulation of human capital. For example, while subsidies to research and to intermediate inputs do have positive effects on innovation and growth, they lead to a lower stock of human capital, in the empirically relevant case when the elasticity of intertemporal substitution in consumption is low.

This paper analyzes a simple microeconomic model of electricity market equilibrium. The parameter that shifts the demand between different points of time appears as an additive term. The equilibrium analysis can then be conveniently focused on the relation between two quantities, namely the electricity supply from intermittent sources and the subsistence level of electricity use. Our model is able to mimic the common empirical finding that a higher penetration of variable renewable electricity leads to a lower value factor for this type of power sources.

Power systems with a large share of inherently intermittent renewable energy sources require new approaches to system operation. Demand response is seen as a potential possibility for contributing to maintaining power balance in a future energy system with large amounts of volatile renewable energy generation (Bartusch et al., 2011; Torriti, Hassan & Leach, 2010). It would be a measure to reduce costs for maintaining the power balance, which is believed to become more expensive if traditional measures is to handle the increasing intermittency (Albadi & El-Saadany, 2008; Kirschen, 2003; Siano, 2014). The study of the flexibility of electricity demand is an essential key to exploring the current and future potential of demand side response for power system services.  

For both solar and wind power, forecasts for several hours ahead may have a lower accuracy. Statistically, the forecasts become better the closer they approach real operation. In practice however, this does not happen in each case. This means that the flexibility need for a certain hour will be different, depending on when the need is identified, i.e. different notice times.

For consumers to be flexible, there are several parameters that impact their ability and willingness to react to incentives with a change of load. Elasticity (self- and cross-elasticity) has been defined in literature to describe consumer flexibility with respect to a change of electricity price and is often referred to when modelling the flexibility of consumers (Albadi & El-Saadany, 2008; Lijesen, 2007). Flexibility with respect to electricity prices or other financial incentives has been widely studied in literature on smart grids and demand response.

Another important parameter for electric demand to be flexible is the notice time, i.e. the time span between informing the consumer about a future need for reorganizing their consumption and providing a change of consumption as a system service. The impact of notice time on the flexibility of electricity consumers has not yet been systematically researched. It is logical that the willingness and ability of certain consumers to provide flexibility decreases as notice time becomes shorter. There are, however, some loads that even may become more flexible, the shorter the notice time, such as e.g. the charging of electric vehicles.  

An essential basis for flexible consumers is the communication infrastructure that is used for sending price signals, bids and further market parameters depending on the demand response program. The type and information content of such communication is enabled through technological devices. These smart devices – which in most cases must exceed the function of only smart metering (Siano, 2014) – can have different properties and requirements that are determined by the demand response program and its respective requirements on data exchange. Therefore, the technological implementation and the impact of the limitations originating from the same are discussed in this study as well.  

For a quantitative analysis of customer flexibility, both price and notice time are imperative parameters. Former has been studied in numerous references (Bartusch et al., 2011; Gyamfi, Krumdieck & Urmee, 2013; Kirschen et al., 2000; Lijesen, 2007) whereas the impact of the latter has not yet been examined in depth. In this paper, a study on consumer flexibility with respect to notice time is presented. It is analyzed how the ability to reschedule electricity demand during a time interval in the future is impacted by terms of notifying and updating flexible consumers. For this, a market and demand response program optimizing social welfare is developed that allows for an analysis of notice time dependent consumers.

This paper evaluates the efficiency of personal cars by using the non-parametric data envelopment analysis (DEA) approach. Analysis and comparison is performed in a normative manner since all the economic and technical parameters used (four and ten respectively) are not explicitly weighted. The data set covers 121 different car models in 1997, as appeared in the German Auto Motor und Sport magazine.

Using a Non-Linear Integer Programming (NLIP) model, I examine if wage differencesbetween Super talents and Normal players improve the performance of four teams whichparticipate in a tournament, such as in the UEFA Champions League (UCL) group matches.With ad-hoc wage differences, the optimal solutions of the model show that higher wageequality seems to improve the performance of all teams, irrespectively if the elasticity ofsubstitution between Super - and Normal- players is high or low. In addition to that, a U-typeperformance exists in two teams with the highest and the second high elasticity ofsubstitution. With team data from the 2011-12 UCL group matches and from the Italian SerieA over 2010-12 seasons, the wage d ispersion has no effect on team performances.

Official match-play statistics from the Champions League tournament between 2001-02 and 2006-07 are used to estimate the impact of various variables on the performance of the teams, measured by goal difference. We find that offensive tactics measured by simple variables, such shots on goals, for both home and away teams, as well as the ranking of the teams, or measured by transformed variables, such as such as shots on goal and corners per ball possession, have a strong positive effect. Variables with negative effects are: the punishment of the teams, measured by own yellow and red cards per fouls committed, or simply the red cards, the shots wide, the corners, the ball possession difference and how smart the defendants are playing, measured by the number of the opposite teams’ offside per own ball possession. In addition, the multinomial logistic regressions show that the differences in some match statistics and the ranking of the teams explain 9 out of 10 home victories and almost 6 out of 10 home defeats. Finally, one of the strongest explanatory variables, the positive difference in shots on goal, compared to equality in shots on goal between teams, leads to a probability of a home team victory by 66%.

Assuming a monopoly with a dynamic cost function, with both economies of scale and learning effects over time and a dynamic linear demand function, this demonstration shows how the optimal decisions change over time and also how the profit surface in three dimensions, as a function of output and time, changes.

The ranking of football players has always engaged media and supporters worldwide. The different views on ranking are due to two reasons. First, leagues are heterogeneous with various qualities. Second, fans often rely on different performance measures and statistics, or just unmeasurable actions. Despite the fact that team and player bias will never disappear, this paper aims to objectively evaluate the efficiency of 42 top scorers who have played in the UEFA Champions League (UCL) over a six years period, (2006/07 - 2011/12), based on official match-play “multi-input and output” statistics, using input- and output oriented DEA models.

When some firms of a cartel cheat and produce more than their allocated quota, cartels fail to maximize their profit or surplus, while consumers benefit. Similar effects appear when more fringe (or noncartel) firms exist in a market, which is called an "imperfect cartel". Consequently, the cartel firms would welcome more fringe firms to join their cartel. On the other hand, when some firms have joined the cartel, other fringe firms would prefer to stay out: they can increase their production because of higher prices due to the cartel. [more] A numerical example (modified [1]), illustrates the effects of both the number of cartel and fringe firms. The market consists of up to 40 identical firms (without entry), with cartel firms and fringe firms, facing a linear demand curve, . The fringe firms are price takers, while the cartel behaves as a monopolist for the residual demand. Both fringe and cartel firms' Marginal Costs are, . The graphic shows two representative firms, the fringe (left graph) and the cartel (right graph). The left graph displays also, the total production, the total cartel production and the total fringe production, as well as the representative fringe's production. The right graph displays the cartel surplus (green) and the Dead Weight Loss (red) from the cartel price. Notice however, that the Residual Demand is discontinuous below €10 and should be identical to the Total Demand, but that part is of no interest.

The size of stable cartels has been investigated by some researchers since early 1980s. Most papers, based on simple cost and demand functions, have proposed various conditions to find the optimal number of k-firms. Other researchers recently have conducted numerical simulations or an analytic approach to determine the size of stable cartels. In this paper I provide numerical solutions as well as dynamic graphs, with more parameters in demand and cost functions, based on two models. In the first model the cartel faces j competitive firms and in the second model the cartel is the Stackelberg leader while the j-firms are Cournot followers. In the first model, the optimal number of cartel firms is always three irrespectively of the number of firms. In the second model, the number of k-firms is moderate higher, but lower than other studies find. In addition, there is no exact algebraic condition to determine the size of stable cartels. 

The size of imperfect cartels has been investigated by some researchers since early 1980s. Most papers have proposed various conditions to find the optimal number of cartel firms., while other researchers have conducted numerical simulations to determine the size of stable cartels. In this paper, I investigate two standard models, with additional parameters in demand and cost functions. In the first model the cartel faces j competitive firms, while in the second model the cartel is the Stackelberg leader and the j-firms are Cournot followers. In the second model, the entry to and exit from cartel are formulated as integer no-linear programming, using some parameter bounds. Contrary to other studies who relied on simplified demand and cost functions and found exact algebraic conditions, Mathematica fails to provide such conditions. It does provide though global numerical solutions. In the first model, irrespectively of the number of firms, the optimal number of k-firms is always three. In the second model, the number of k-firms is moderate higher, but lower than other studies found.

The Japanese system of lean production is the most efficient way for manufacturing cars argue Womack et al. in their MIT study The Machine that Changed the World (1990). They strongly recom- mend Western companies to learn and adapt to it, if they want to survive in the 1990s. This paper shows that lean production per se is not sufficient to explain the Japanese superiority unless favourable macroeconomic and microeconomic conditions prevail (precisely as for mass production). It also points to some methodological and analytical deficits in the MIT study.

This paper investigates if the value of the Swedish krona (SEK) against the US dollar ($) and the Euro (€) can be explained by some standard theories and fundamentals, such as the purchasing power parity, the interest rate parity, the debt-ratio and the trade balance ratio, using monthly data since February, 1993. All of them fail to explain why the SEK is so “weak”. The lower inflation rate in Sweden over the recent years has not strengthened the currency. Similarly, the theoretically stronger SEK implied by the lower interest rates in Sweden as the uncovered interest rate parity predicts, has not emerged yet. Finally, neither the persistent trade balance surpluses, nor the declining and very low debt ratio in Sweden has had any positive effects on the currency. It seems that the traders and investors ignore the fundamentals, speculate against the currency and keep it undervalued. Moreover, a number of simulated paths, predicted from various ARIMA-processes, based on the historic exchange rates, show that the worse exchange rates have already gone and by the end of 2020 the $ and the € will cost around 8 and 9.8 SEK respectively.

An incumbent is limit pricing if it produces more than its optimal quantity, so that there is not sufficient demand for a potential entrant. The lowest price that it sets is the "limit price" that excludes a profitable entry. [more] A numerical example (based on [1]) illustrates how the profits of both the incumbent and the entrant change with and without limit pricing, for various fixed costs common to both firms. Initially, in the absence of entrant, the incumbent is a monopolist and maximizes its profit (green rectangle). The entrant estimates the residual demand, optimizes its production level, and makes profit (blue rectangle), affecting the profits of the incumbent. To avoid entry, the incumbent must increase its production so that the entrant cannot make profits if it enters. In order to succeed with that, it needs to equate the slope of the residual demand with the slope of average costs. Notice that there are scale economies (decreasing average costs). Consequently, the incumbent's profit is reduced to the gray rectangle while the profits of entrant are zero. Finally, if the entrant exits due to the limit price, the incumbent makes a higher profit (yellow rectangle).

In a recent UEFA Champions League game between AC Milan and FC Barcelona, played in Italy (final score 2-3), the collected match statistics, classified into four offensive and two defensive strategies, were in favour of FC Barcelona (by 13 versus 8 points). The aim of this paper is to examine to what extent the optimal game strategies derived from some deterministic, possibilistic, stochastic and fuzzy LP models would improve the payoff of AC Milan at the cost of FC Barcelona.

In practice, all option strategies are decided in advance, given the investor’s belief of the stock price. In this paper, instead of deciding in advance the most appropriate hedging option strategy, an LP problem is formulated, by considering all significant Greek parameters of the Black-Scholes formula, such as delta, gamma, theta, rho and kappa. The optimal strategy to select will be simply decided by the solution of that model. The LP model is applied to Ericsson’s call and puts options.

The paper evaluates the Dayton Peace Agreement division of Bosnia. Based on Census data from 1991 and under plausible assumptions on all territories (pure ethnic and mixed as well), cooperative core allocations are applied to divide the country into its three parts. The highest share, which is received by the Serbs (the nucleolus solution), is 459 square km less than the respective Dayton share. Serbs, however, benefit from the goal programming implementation of that solution, since less of them are forced to leave their homes, compared to the Dayton division In general, the redrawn nucleolus map of Bosnia, is approximately 93% identical to the Dayton Peace Agreement map.

Using the classic Quadratic Assignment Problem or Facility Layout problem, this paper attempts to find the optimal formation of three midfielders and three forward football players on ground. Players are treated as “machines”, their positions as locations, and the flow of materials between machines as both “flow of passes” and “flow of markings”. Based on detailed statistics from four matches of AC Milan, and formulated the problem as minimum (quick strategy), maximum (slow strategy), and mixed or balanced strategies, a number of various layouts emerged. The efficiency time gains in the unconditioned layouts are between 3 - 6.8%. When the manager claims that his three forwards shouldn’t shift positions with the midfielders, the unrestricted optimal layouts deteriorate by 7´´ to 20´´, or about 1% of the team’s effective playing time.

The mass media, the football supporters and other experts in many countries are

often engaged in the ranking of football players. Given the heterogeneity of various

leagues or series in which players play, such a comparison is almost impossible. On

the other hand, the performance of players in international tournaments, like the

FIFA world cup at the national team level, or the UEFA Champions League at the

European Club level, can be measured, if we rely on “objective” measures and

statistics. Obviously, since various positions of players are evaluated by different

criteria, the heterogeneity is still apparent. In this paper we attempt to evaluate a

small subset of a team’s players, namely its scorers, using UEFA:s official match-play

statistics from the Champions League tournament 2006/07.

The classical Quadratic Programming (QP) formulation of the well-known portfolio selection problem has traditionally been regarded as cumbersome and time consuming. This paper formulates two additional models, (i) maximin, and (ii) minimization of mean absolute deviation. Data from 67 securities over 48 months are used to examine to what extent all three formulations provide similar portfolios. As expected, the maximin formulation yields the highest return and risk, while the QP formulation provides the lowest risk and return, which also creates the efficient frontier. The minimization of mean absolute deviation is close to the QP formulation. When the expected returns are confronted with the true ones at the end of a six months period, the maximin portfolios seem to be the most robust of all.