Sonnenschein—Mantel—Debreu theorem Although generally assuming convexity an equilibrium will exist and will be efficient, the conditions under which it will be unique are much stronger. While the issues are fairly technical the basic intuition is that the presence of wealth effects which is the feature that most clearly delineates general equilibrium analysis from partial equilibrium generates the possibility of multiple equilibria. When a price of a particular good changes there are two effects.
Property P1 is satisfied, because at the equilibrium price the amount supplied is equal to the amount demanded.
Property P2 is also satisfied. Demand is chosen to maximize utility given the market price: Likewise supply is An analysis of market equilibrum by firms maximizing their profits at the market price: Hence, agents on neither the demand side nor the supply side will have any incentive to alter their actions.
To see whether Property P3 is satisfied, consider what happens when the price is above the equilibrium. In this case there is an excess supply, with the quantity supplied exceeding that demanded. This will tend to put downward pressure on the price to make it return to equilibrium.
Likewise where the price is below the equilibrium point there is a shortage in supply leading to an increase in prices back to equilibrium.
Not all equilibria are "stable" in the sense of Equilibrium property P3. It is possible to have competitive equilibria that are unstable. However, if an equilibrium is unstable, it raises the question of how you might get there.
Even if it satisfies properties P1 and P2, the absence of P3 means that the market can only be in the unstable equilibrium if it starts off there.
In most simple microeconomic stories of supply and demand a static equilibrium is observed in a market; however, economic equilibrium can be also dynamic. Equilibrium may also be economy-wide or generalas opposed to the partial equilibrium of a single market.
Equilibrium can change if there is a change in demand or supply conditions. For example, an increase in supply will disrupt the equilibrium, leading to lower prices. Eventually, a new equilibrium will be attained in most markets. Then, there will be no change in price or the amount of output bought and sold — until there is an exogenous shift in supply or demand such as changes in technology or tastes.
That is, there are no endogenous forces leading to the price or the quantity.
Nash equilibrium[ edit ] Further information: Nash equilibrium and Cournot model Equilibrium quantities as a solution to two reaction functions in Cournot duopoly. The Cournot-Nash equilibrium occurs where the two reaction functions intersect and both firms are choosing the optimal output given the output of the other firm.
The Nash equilibrium is widely used in economics as the main alternative to competitive equilibrium. It is used whenever there is a strategic element to the behavior of agents and the "price taking" assumption of competitive equilibrium is inappropriate.
The first use of the Nash equilibrium was in the Cournot duopoly as developed by Antoine Augustin Cournot in his book. This determines the revenues of each firm the industry price times the quantity supplied by the firm. The profit of each firm is then this revenue minus the cost of producing the output.
Clearly, there is a strategic interdependence between the two firms. If one firm varies its output, this will in turn affect the market price and so the revenue and profits of the other firm. We can define the payoff function which gives the profit of each firm as a function of the two outputs chosen by the firms.
Cournot assumed that each firm chooses its own output to maximize its profits given the output of the other firm. The Nash equilibrium occurs when both firms are producing the outputs which maximize their own profit given the output of the other firm.
In terms of the equilibrium properties, we can see that P2 is satisfied: P1 is satisfied since the payoff function ensures that the market price is consistent with the outputs supplied and that each firms profits equal revenue minus cost at this output.
Is the equilibrium stable as required by P3? Cournot himself argued that it was stable using the stability concept implied by best response dynamics. The reaction function for each firm gives the output which maximizes profits best response in terms of output for a firm in terms of a given output of the other firm.
In the standard Cournot model this is downward sloping: Best response dynamics involves firms starting from some arbitrary position and then adjusting output to their best-response to the previous output of the other firm.
So long as the reaction functions have a slope of less than -1, this will converge to the Nash equilibrium.Equilibrium Analysis In many aspects of economic analysis, we tend to assume that a condition of equilibrium exists with respect to key economic variables.
Common examples include different models of market behavior known as Supply and Demand analysis. Market Equilibrium schwenkreis.com Slide-6 Market equilibrium is point where buyers and seller reach the compromise and settle down the price of the commodity.
At this price quantity demanded is equal to the quantity supplied. Market Equilibrium schwenkreis.com Slide-6 Market equilibrium is point where buyers and seller reach the compromise and settle down the price of the commodity.
At this price quantity demanded is equal to the quantity supplied. General equilibrium theory, or Walrasian general equilibrium, attempts to explain the functioning of the macroeconomy as a whole, rather than as collections of individual market phenomena.
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium.
Jan 02, · Equilibrium price and quantity for supply and demand Watch the next lesson: schwenkreis.com