In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.

In this paper, we analyse the company behaviour in duopoly taking into account the most common strategies, including dominant, reactive, cooperative and tit-for-tat strategies, since they account for most of the decisions made by companies. Dominant, reactive and cooperative strategies may lead to different outcomes, such as Stackelberg, Cournot, Cartel, Cartel with one cheater and Perfect competition equilibria, while the tit-for-tat strategy may lead to Cartel, Cournot or Perfect competition equilibria due to its retribution nature. However, we argue that these outcomes are mainly valid in the short-run since in the long-run the companies learn and adapt to the behavioural pattern of their peer, which leads them to evolve to a new way of thinking and strategic planning taking into account the long-run effects. Due to the long-term perspective, the outcome of the implementation of various strategies in duopoly may not be efficiently solved using simple game theory analysis. For that purpose, we propose the utilization of more complex analysis, an evolutionary game theory, which is based on the adaption of the company to the behaviour of other players in a duopoly. When the probability of choices is applied, new fitness equations are obtained which show the changing tendencies towards the companies' strategies that ensure payoffs above the average, in the long run, using a replicator dynamics concept. We analyse several scenarios, in which players choose among two, three or four strategies. Our results indicate that the long-run equilibrium and preferred options are significantly altered depending on the starting set of strategies.

Background: Our research assumes that the software quality affects the product validity. This assumption also refers to embedded software. Objectives: This paper analyses the Stackelberg equilibrium in which the consumer is the leader and the producer of embedded software is the follower. Methods/Approach: A comparative statics analysis of a producer's reaction is carried out and confirms our intuition that the product price is positively correlated to the number of employees and the software quality. Results: An increase in wage has an adverse effect on producer's reaction. Derived results are illustrated numerically and Stackelberg and cooperative equilibrium are compared. It is shown that the welfare loss is smaller with higher quality software for any number of employees. Conclusions: Although the equilibrium involves less employed workers, the optimal software quality is higher. The optimal product price is lower, which puts the consumer and the producer in a better position.

This paper examines a two-way relationship between convex analysis and microeconomic theory. Motivation for this paper are the observed similarities in the structure of the theory of consumer behavior and production theory. The fact that the behavior of variables is not determined by their nature but, rather, by their relationships is best illustrated and explained by using convex sets and convex analysis, which occupy central place in microeconomic theory. This paper is the result of efforts to make complex results of convex analysis and its application in microeconomic theory more transparent. Starting with the well-known economic phenomenon of profit maximization the authors derive in a novel way general results within the framework of convex analysis. From those results follow, directly and indirectly, the conclusions of the theory of consumer and producer behavior. The authors show that applying the Fundamental Theorems of Calculus opens up a new perspective in which the marginal cost curve can be interpreted as the marginal profit curve. This enables the derivation of Hotelling's lemma in a new way. Using the new interpretation of Hotelling's lemma, the authors reconstruct the cost function and confirm the Conjugate Duality Theorem of Legendre-Fenchel transformations. Relaxing the assumption of differentiability by describing the graph of the cost function as the envelope of its tangents, the authors rederive the properties of Legendre-Fenchel transformations and show that they hold in general. The path from the well-known economic facts to completely general conclusions of convex analysis is continued by applying the Conjugate Duality Theorem of Legendre-Fenchel transformations to the profit function. The essence of the dual characterization of technology by the profit function is illustrated by the graphical representation of linear homogeneity of the profit function. It results in the possibility to reconstruct the production function while using only the First Order Conditions to rederive Hotelling's lemma. It is this inductive-deductive approach used to examine the properties of Legendre-Fenchel trasformations and their application in the theory of consumer and producer behavior that establishes a two-way relationship between convex analysis and microeconomic theory.

Abstract. In line with global trends, the Croatian military is currently going through a transformation, but is being stifled by a long recession and negative demographic trends. The purpose of this article is to outline the possibilities of applying system dynamics models in testing the sustainability of the Croatian military forces (CMF) with respect to their size and composition. The article mainly focuses on the demographic trends and their implications on the CMF. After a brief exposition of the research done in this field to date, the article presents two developed models -a demographic model and a military recruitment model. The models were carefully tested using validation tests suitable for system dynamics modelling. Subsequent to validation, the models were merged into a single integral system dynamics model of the CMF. Three experiments were conducted based on different fertility values, and the impact of demographic trends, which emerge from the different fertility levels. The results of the simulation, based on demographic data from the 2011 Census, as well as estimated data, though not accessible at the time, suggest that the Croatian military will encounter difficulties in meeting its demands for recruits in the next 20-30 years. Further implications of current demographic trends on the CMF's sustainability are discussed towards the end of the paper. Since basic inputs for any organization are labor and capital, the problem is addressed from two complementary perspectives: a demographic and a financial perspective.