Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRationality in the Theory of the Firm
131
0
0.0
(
0
)
Added by
Russell K. Standish
Publication date
2011
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We have previously presented a critique of the standard Marshallian theory of the firm, and developed an alternative formulation that better agreed with the results of simulation. An incorrect mathematical fact was used in our previous presentation. This paper deals with correcting the derivation of the Keen equilibrium, and generalising the result to the asymmetric case. As well, we discuss the notion of rationality employed, and how this plays out in a two player version of the game.
rate research
Read More
The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for its superiority. Many people, if given the choice to switch, think the chances are fifty-fifty between their options, but still strongly prefer to stay with their initial choice. Is there some sense behind these irrational feelings? We entertain the possibility that intuition solves the problem of how to behave in a real game show, not in the abstract textbook version of the Monty Hall problem. A real showmaster sometimes plays evil, either to make the show more interesting, to save money, or because he is in a bad mood. A moody showmaster erases any information advantage the guest could extract by him opening other doors which drives the chance of the car being behind the chosen door towards fifty percent. Furthermore, the showmaster could try to read or manipulate the guests strategy to the guests disadvantage. Given this, the preference to stay with the initial choice turns out to be a very rational defense strategy of the shows guest against the threat of being manipulated by its host. Thus, the intuitive feelings most people have about the Monty Hall problem coincide with what would be a rational strategy for a real-world game show. Although these investigations are mainly intended to be an entertaining mathematical commentary on an information-theoretic puzzle, they touch on interesting psychological questions.
Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the overall system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.
This is a small note meant to be published in a Conference Proceedings. We discuss elementary rationality questions in the Grothendieck ring of varieties for the quotient of a finite dimensional vector space over a characteristic 0 field by a finite group. Part of it reproduces the content of a letter dated September 27, 2008 addressed to Johannes Nicaise
The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $sigma(S) sim S^{-beta(S)}$ where $S$ is the firm size and $beta(S)approx 0.2$ is an exponent weakly dependent on $S$. Here we show how a model of proportional growth which treats firms as classes composed of various number of units of variable size, can explain this size-variance dependence. In general, the model predicts that $beta(S)$ must exhibit a crossover from $beta(0)=0$ to $beta(infty)=1/2$. For a realistic set of parameters, $beta(S)$ is approximately constant and can vary in the range from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry specific database in which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship.
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
