Marcin Jakubek

Division of the energy market into zones in variable weather conditions using Locational Marginal Prices

Adopting a zonal structure of electricity market requires specification of zones borders. One of the approaches to identify zones is based on clustering of Locational Marginal Prices (LMP). The purpose of the paper is twofold: (i) we extend the LMP methodology by taking into account variable weather conditions and (ii) we point out some weaknesses of the method and suggest their potential solutions. The offered extension comprises simulations based on the Optimal Power Flow (OPF) algorithm and twofold clustering method. First, LMP are calculated by OPF for each of scenario representing different weather conditions. Second, hierarchical clustering based on Wards criterion is used on each realization of the prices separately. Then, another clustering method, i.e. consensus clustering, is used to aggregate the results from all simulations and to find the global division into zones. The offered method of aggregation is not limited only to LMP methodology and is universal.

Integration as a catalyst for assimilation

We draw a distinction between the social integration and economic assimilation of migrants, and study an interaction between the two. We define social integration as blending into the host country’s society, and economic assimilation as acquisition of human capital that is specific to the host country’s labor market. We show that a non-integrated migrant finds it optimal to acquire a relatively limited quantity of human capital; with fellow migrants constituting his only comparison group, a non-integrated migrant does not have a relative-deprivation-based incentive to close the income gap with the natives. However, when a migrant is made to integrate, his social proximity to the natives exposes him to relative deprivation, which in turn prompts him to form more destination-specific human capital in order to increase his earnings and narrow the income gap with the natives. In this way, social integration becomes a catalyst for economic assimilation.

The Merger of Populations, the Incidence of Marriages, and Aggregate Unhappiness

Let a society’s unhappiness be measured by the aggregate of the levels of relative deprivation of its members. When two societies of equal size, F and M, merge, unhappiness in the merged society is shown to be higher than the sum of the levels of unhappiness in the constituent societies when apart; merger alone increases unhappiness. But when societies F and M merge and marriages are formed such that the number of households in the merged society is equal to the number of individuals in one of the constituent societies, unhappiness in the merged society is shown to be lower than the aggregate unhappiness in the two constituent societies when apart. This result obtains regardless of which individuals from one society form households with which individuals from the other, and even when the marriages have not (or not yet) led to income gains to the married couples from increased efficiency, scale economies, and the like. While there are various psychological reasons for people to become happier when they get married as opposed to staying single, the very formation of households reduces social distress even before any other happiness-generating factors kick in.

The scheme of a novel methodology for zonal division based on power transfer distribution factors

One of the methodologies that carry out the division of the electrical grid into zones is based on the aggregation of nodes characterized by similar Power Transfer Distribution Factors (PTDFs). Here, we point out that satisfactory clustering algorithm should take into account two aspects. First, nodes of similar impact on cross-border lines should be grouped together. Second, cross-border power flows should be relatively insensitive to differences between real and assumed Generation Shift Key matrices. We introduce a theoretical basis of a novel clustering algorithm (BubbleClust) that fulfills these requirements and we perform a case study to illustrate social welfare consequences of the division.

A bitter choice turned sweet: How acknowledging individuals’ concern at having a low relative income serves to align utilitarianism and egalitarianism

When individuals’ utility is a convex combination of their income and their concern at having a low relative income (the weights attached to income and to the concern at having a low relative income sum up to one), the maximization of aggregate utility yields an equal income distribution. This alignment of utilitarianism and egalitarianism is obtained for any number of individuals, and for general utility functions that are convex combinations of a power function of income and the concern at having a low relative income. The alignment can also hold when the weights sum up to a number different than one.

Market Coupling as the Universal Algorithm to Assess Zonal Divisions

Adopting a zonal structure of electricity market requires specification of zones borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational Marginal Prices (LMP) methodology presented in paper [1], which takes into account variable weather conditions. The offered method of assessment of a proposed division of market into zones is however not limited to LMP approach but can evaluate the social welfare of divisions obtained by any methodology.

Consensus income distribution

In determining the optimal redistribution of a given population’s income, we ask which factor is more important: the social planner’s aversion to inequality, embedded in an isoelastic social welfare function indexed by a parameter alpha, or the individuals’ concern at having a low relative income, indexed by a parameter beta in a utility function that is a convex combination of (absolute) income and low relative income. Assuming that the redistribution comes at a cost (because only a fraction of a taxed income can be transferred), we find that there exists a critical level of beta below which different isoelastic social planners choose different optimal allocations of incomes. However, if beta is above that critical level, all isoelastic social planners choose the same allocation of incomes because they then find that an equal distribution of incomes maximizes social welfare regardless of the magnitude of alpha.

The impact of the assimilation of migrants on the well-being of native inhabitants: A theory

We present a theory that systematically and causally links the well-being of native inhabitants with variation in the extent of the assimilation of migrants. Recent empirical findings are yielded as predictions of the theory.

Is Population Growth Conducive to the Sustainability of Cooperation

This paper asks whether population growth is conducive to the sustainability of cooperation. A simple model is developed in which farmers who live around a circular lake engage in trade with their adjacent neighbors. The payoffs from this activity are governed by a prisoners dilemma rule of engagement. Every farmer has one son when the population is not growing, or two sons when it is growing. In the former case, the son takes over the farm when his father dies. In the latter case, one son stays on his fathers farm, whereas the other son settles around another lake, along with the other sons of the other farmers. During his childhood, each son observes the strategies and the payoffs of his father and of the trading partners of his father, and imitates the most successful strategy when starting farming on his own. Then mutant defectors are introduced into an all-cooperator community. The defector strategy may spread. A comparison is drawn between the impact in terms of the sustainability of cooperation of the appearance of the mutants in a population that is not growing, and in one that is growing. It is shown that the ex-ante probability of sustaining the cooperation strategy is higher for a community that is growing than for a stagnant community.

An adverse social welfare consequence of a rich-to-poor income transfer: A relative deprivation approach

A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular - the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.