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Dimensions of 100 randomly selected wheat seeds of the Smuglyanka variety, rye seeds of the Puhovchanka variety and barley seeds of the Pejas variety were determined by measuring their length (l), width (b) and thickness (h). Results of the measurements were processed by the methods of mathematical statistics; parameters of distributions of individual sizes as random variables were calculated. On the basis of values of variation coefficient, the density function of normal distribution (Gaussian distribution) was taken as a model of individual sizes of seeds. Models of two-dimensional distributions of seed sizes as independent random variables were presented. Correlation coefficients between geometric sizes of seeds were calculated. Obtained values of the correlation coefficients indicate that the geometric sizes of seeds should be considered as dependent random variables. Mathematical models of geometric sizes of studied cereal crops’ seeds as dependent random variables in the form of density functions of their normal distribution were proposed. By values of the sums of squared deviations as a fitting criterion, it was established that the mathematical models of geometric sizes of seeds as dependent random variables in the form of density functions of their normal distribution provide better data approximation than the mathematical models of geometric sizes of some cereal crops’ seeds as independent random variables.

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Many economic interactions rely on trust and trust violations can have serious economic consequences. Simple minimum standard rules are attractive because they prevent egregious trust violations. However, they may undermine more trusting and reciprocal (trustworthy) behavior that otherwise would have occurred, leading to worse outcomes. In an experimental trust game, we test the efficacy of exogenously imposed minimum standard rules. Rules damage trust and reciprocity, reducing economic welfare. While sufficiently restrictive rules restore welfare, trust and reciprocity never return. Results indicate that participants are concerned about payoffs while also using the game to learn about trust and trustworthiness of others. (JEL C72, C90, D63, D64, L51), I. INTRODUCTION Relationships based on trust are critical because most social and economic situations are not explicitly contracted with behavior regulated by enforceable rules (Davis 1992; Glaeser et al. 2000). [...]

Recognizing donors by revealing their identities is important for increasing charitable giving. Using a framed field experiment, we show that all forms of recognition that we examine increase donations relative to the baseline treatment, and recognizing only the highest or only the lowest donors has the strongest and significant effect. We argue that selective recognition creates tournament-like incentives. Recognizing the highest donors activates the desire to seek a 'positive prize' of prestige, while recognizing the lowest donors activates the desire to avoid a 'negative prize ' of shame. We discuss how selective recognition can be used by charities to increase donations. (JEL C93, D64), I. INTRODUCTION Positive recognition hits long been a trusted way of raising money on college campuses, where buildings, benches, and even the insides of library books bear the names of [...]