Querying microeconomics

Thèmes abordés

Competitive Balance - microeconomics - competitive equilibrium - Pareto optimum - contract curve

Résumé du document

What is the relationship between Pareto Optimum and Competitive Balance?

Very briefly, the relationship between Pareto optimality and competitive equilibrium is an implication relation: z is a competitive equilibrium => z is Pareto optimal (note that the relation of implication does not apply in both directions).

This result is easy to show, since the condition for a Pareto optimum is only the tangency between the indifference curves of the two individuals (that is to say TMSA = TMSB), while a competitive equilibrium requires in addition, for each individual TMS is equal to the ratio of prices (ie, it must TMSA = TME = TMSB).

The contract curve is the set of points Pareto-optimal (in an Edgeworth box). Two things must be verified to Pareto-optimal point: first, this should be feasible (=> for each property, the sum of the amounts held by each individual = quantity of the good available in the economy). Secondo, the indifference curves of the two individuals must be tangent (=> their TMS must be equal). All this gives several equations that must be satisfied simultaneously for a Pareto-optimal point. The equation of the contract curve is the 'solution' to this system of equations.

Extraits

[...] The sum of the inputs, each multiplied by its price, provides the total cost. By cons, if the monopolist, the price depends on the amount he places on the market its total revenue function is q and not * as in the case perfect competition. So it changes the profit function maximized by the monopolist (compared to maximized by the firm in perfect competition), since the total revenue is directly involved in the profit function. NOTE: For the firm in perfect competition, the supply function specified the quantity placed on the market based on price. [...]

[...] Any solution (optimum amount) that falls outside the range for which the equation is valid request used, is eliminated. If several solutions are still possible after these eliminations, we must choose the one that gives the most profit. Voyer graphically what all this is. How to find equilibrium price and quantity when the monopolist faces several applications and can discriminate? The idea is of course always to maximize profit, but it will take a form other than in the case of non-discrimination. [...]

[...] Then, in order to know the price prevailing in each market, it suffices to introduce q1 and q2 respectively in the inverse demand functions p1 and p2 (q2). The solution to this problem is unique. DUOPOLY How to calculate the cooperative equilibrium? When firms cooperate, their objective is to maximize the joint profit, expressed as the difference between the Total Recipe cartel and Total Cost. The problem seems a priori very simple, except that in the general case, firms do not have the same cost function. [...]

[...] So it obviously takes into account when it chooses its production level. The resolution method is to calculate the reaction function of the follower and insert it into the profit function of the leader. The solution to this maximization problem gives the quantity produced by the leader, who introduced into the reaction function of the follower, given the quantity produced by the follower. The price is determined by the inverse demand function, assessed on the total amount. Another way to express what is happening in the Stackelberg duopoly is to say that the leader chooses the point on the reaction function of the follower that maximizes its own profit (compared with the case of Cournot duopoly where the solution is identified with the intersection of the two reaction functions). [...]

[...] This result is easy to show, since the condition for a Pareto optimum is only the tangency between the indifference curves of the two individuals (that is to say TMSA = TMSB), while a competitive equilibrium requires in addition, for each individual TMS is equal to the ratio of prices it must TMSA = TME = TMSB). How to find the equation of the contract curve? The contract curve is the set of points Pareto-optimal (in an Edgeworth box). Two things must be verified to Pareto-optimal point: first, this should be feasible for each property, the sum of the amounts held by each individual = quantity of the good available in the economy). Secondo, the indifference curves of the two individuals must be tangent their TMS must be equal). [...]