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In welfare economics, the theory of the second best concerns the situation when one or more optimality conditions cannot be satisfied. [1] The economists Richard Lipsey and Kelvin Lancaster showed in 1956 that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the values that would ...
In chemistry, Le Chatelier's principle (pronounced UK: / l ə ʃ æ ˈ t ɛ l j eɪ / or US: / ˈ ʃ ɑː t əl j eɪ /) [1] is a principle used to predict the effect of a change in conditions on chemical equilibrium. [2] Other names include Chatelier's principle, Braun–Le Chatelier principle, Le Chatelier–Braun principle or the equilibrium ...
The principle of minimum energy is essentially a restatement of the second law of thermodynamics. It states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium. External parameters generally means the volume, but may include other parameters which ...
It can be shown that the other two equilibrium conditions imply the same equation. Together, the solutions of the three equilibrium equations imply sufficiency of Hardy's condition for equilibrium. Since the condition always holds for the second generation, all succeeding generations have the same proportions.
Le Châtelier's principle (1884) predicts the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S (to the chemical reaction above) from the outside will ...
Equilibrium in perfect competition is the point where market demands will be equal to market supply. A firm's price will be determined at this point. In the short run, equilibrium will be affected by demand. In the long run, both demand and supply of a product will affect the equilibrium in perfect competition.
The proportionality constant was called an affinity constant, k. The equilibrium condition for an "ideal" reaction was thus given the simplified form [] [] = ′ [′] [′] [A] eq, [B] eq etc. are the active masses at equilibrium. In terms of the initial amounts reagents p,q etc. this becomes
The second method, which is now referred to as the Lyapunov stability criterion or the Direct Method, makes use of a Lyapunov function V(x) which has an analogy to the potential function of classical dynamics. It is introduced as follows for a system ˙ = having a point of equilibrium at =.