Understanding economic equilibrium
An economic equilibrium is a situation when the economic agent cannot change the situation by adopting any strategy. To fully grasp the concept of economic equilibrium, it must be highlighted that it has been borrowed from the physical sciences. Take a system where physical forces are balanced for instance.This economically interpreted means no further change ensues.Properties of equilibrium
Three basic properties of equilibrium in general have been proposed by Huw Dixon. These are: Equilibrium property P1: The behavior of agents is consistent. Equilibrium property P2: No agent has an incentive to change its behavior. Equilibrium property P3: Equilibrium is the outcome of some dynamic process (stability).Example: competitive equilibrium
In a competitive equilibrium, supply equals demand. 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: no one on the demand side has any incentive to demand more or less at the prevailing price. Likewise supply is determined by firms maximizing their profits at the market price: no firm will want to supply any more or less at the equilibrium 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 reaching it. 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 alsoExample: monopolist equilibrium
In a monopoly, marginal revenue (MR) equals marginal cost (MC). The equilibrium quantity is obtained from where MR and MC intersect and the equilibrium price can be found on the demand curve where MR = MC. Property P1 is not satisfied because the amount demand and the amount supplied at the equilibrium price are not equal. Property P2 is not satisfied. Because the monopolist's profit-maximizing quantity is different from the socially-maximizing quantity, consumer's have an incentive to demand more at the equilibrium price. However, at the market price, monopolists maximize their profits so they have no incentive to change their price. Therefore, agents on the demand side have an incentive to alter their actions while the agents on the supply side do not have any incentive to alter their actions. In order to determine if Property P3 is satisfied, the same situations used to determine P3 in a competitive equilibrium can be used. When there is an excess in supply, monopolists will realize that the equilibrium is not at the profit-maximizing quantity and will put upward pressure on the price to make it return to equilibrium. This is the same case when the price is above the equilibrium and the shortage in supply leads the monopolist to decrease the supply to return to the profit-maximizing quantity. Therefore the equilibrium is the result of stability.Example: Nash equilibrium
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 1838 book. Both firms produce a homogenous product: given the total amount supplied by the two firms, the (single) industry price is determined using the demand curve. 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: in a Nash equilibrium, neither firm has an incentive to deviate from the Nash equilibrium given the output of the other firm. 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: if the other firm produces a higher output, the best response involves producing less. 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. However, this stability story is open to much criticism. As Dixon argues: "''The crucial weakness is that, at each step, the firms behave myopically: they choose their output to maximize their current profits given the output of the other firm, but ignore the fact that the process specifies that the other firm will adjust its output''...". There are other concepts of stability that have been put forward for the Nash equilibrium, evolutionary stability for example.Example: Walrasian equilibrium in a Power economy
Walrasian Equilibrium Prices A fictional auctioneer calls out prices. Consumers and firms report honestly their demands and supplies. When Net Demand = emand - Supply is zero, the auctioneer's job is done. The prices are market clearing prices. Special case: An island economy.Supply
Consumers a and b survive by consuming coconuts that fall from the palm trees, x, and crayfish, y, trapped in the lagoon. This yields 1 basketful per day of each commodity. Only the price ratio p = p1/p2 matters so the auctioneer only has to call out one price. There is one daily basketful of each commodity. Therefore the supply is 1=(1,1).Demand
The marginal rates of rates of substitution in Power σ economy are MRS(a)=(Ax(a)/y(a))1/σ and MRS(b)=(Bx(b)/y(b))1/σ (Pareto) Efficient Allocations The marginal rates of substitution are the same for an efficient allocation. So (Ax(a)/y(a))1/σ = (Bx(b)/y(b))1/σ. Therefore, for all Powers the condition for efficiency is Ax(a)/y(a) and MRS(b)=Bx(b)/y(b). This yields the first big result.Proposition: Efficiency in a Power Economy
If an allocation is (in)-efficient in any power economy, then it is (in)-efficient in all power economiesConsumer Choice
A consumer's choice is an allocation for which the consumer's marginal willingness to trade is equal to the price ratio.Market Clearing equations in a power σ economy
The marginal rates of substitution must be the same. Therefore, ''p'' =(Ax(a)/y(a)1/σ =(Bx(b)/y(b))1/σ. IT follows that ''μ'' = p''σ'' = Ax/y and ''p'' = B(1-x)/(1-y)) Key observation: The two market clearing equations are two equations for the three variables, x, y and σ''.'' Therefore, any one of the variables can be eliminated. The result is three equations for two variables. Let the difference in the parameters be D. Let the multiplication of the parameters be MDemand equations in a Power Economy
y(p) = (p1/σ - B)/(AD2) and x(p)= (1-(1/p1/σ))(M/D). where D=A-B and M=AB Demand Price Equations in a power economy: p1/σ = B - Dy and p1/σ = 1/(1-x(D/M)) The characteristic equation E(z)=z1z2 in a power economy This is a rectangular hyperbola Mutliplying the two demand price equations. The efficient allocations are on a level set of the following rectangular hyperbola E(x,y) = (x-AD)(y+B/D) = K, where D=A-B and M=AB If consumer a is allocated everything, this is efficient allocation. Any reallocation makes consumer a worse off. Therefore K=-AB.Market clearing prices
Most economists, for example Paul Samuelson, caution against attaching a normative meaning (value judgement) to the equilibrium price. For example, food markets may be in equilibrium at the same time that people are starving (because they cannot afford to pay the high equilibrium price). Indeed, this occurred during the Great Famine inInterpretations
In most interpretations, classical economists such as Adam Smith maintained that the free market would tend towards economic equilibrium through theSolving for the competitive equilibrium price
To find the equilibrium price, one must either plot the supply and demand curves, or solve for the expressions for supply and demand being equal. An example may be: : In the diagram, depicting simple set of supply and demand curves, the quantity demanded and supplied at price P are equal. At any price above P supply exceeds demand, while at a price below P the quantity demanded exceeds that supplied. In other words, prices where demand and supply are out of balance are termed points of disequilibrium, creating shortages and oversupply. Changes in the conditions of demand or supply will shift the demand or supply curves. This will cause changes in the equilibrium price and quantity in the market. Consider the following demand and supply schedule: * The equilibrium price in the market is $5.00 where demand and supply are equal at 12,000 units * If the current market price was $3.00 – there would be excess demand for 8,000 units, creating a shortage. * If the current market price was $8.00 – there would be excess supply of 12,000 units. When there is a shortage in the market we see that, to correct this disequilibrium, the price of the good will be increased back to a price of $5.00, thus lessening the quantity demanded and increasing the quantity supplied thus that the market is in balance. When there is an oversupply of a good, such as when price is above $6.00, then we see that producers will decrease the price to increase the quantity demanded for the good, thus eliminating the excess and taking the market back to equilibrium.Influences changing price
A change in equilibrium price may occur through a change in either the supply or demand schedules. For instance, starting from the above supply-demand configuration, an increased level of disposable income may produce a new demand schedule, such as the following: Here we see that an increase in disposable income would increase the quantity demanded of the good by 2,000 units at each price. This increase in demand would have the effect of shifting the demand curve rightward. The result is a change in the price at which quantity supplied equals quantity demanded. In this case we see that the two now equal each other at an increased price of $6.00. Note that a decrease in disposable income would have the exact opposite effect on the market equilibrium. We will also see similar behaviour in price when there is a change in the supply schedule, occurring through technological changes, or through changes in business costs. An increase in technological usage or know-how or a decrease in costs would have the effect of increasing the quantity supplied at each price, thus reducing the equilibrium price. On the other hand, a decrease in technology or increase in business costs will decrease the quantity supplied at each price, thus increasing equilibrium price. The process of comparing two static equilibria to each other, as in the above example, is known as comparative statics. For example, since a rise in consumers' income leads to a higher price (and a decline in consumers' income leads to a fall in the price — in each case the two things change in the same direction), we say that the comparative static effect of consumer income on the price is positive. This is another way of saying that the total derivative of price with respect to consumer income is greater than zero.Dynamic equilibrium
Whereas in a static equilibrium all quantities have unchanging values, in a dynamic equilibrium various quantities may all be growing at the same rate, leaving their ratios unchanging. For example, in the neoclassical growth model, the working population is growing at a rate which is exogenous (determined outside the model, by non-economic forces). In dynamic equilibrium, output and the physical capital stock also grow at that same rate, with output per worker and the capital stock per worker unchanging. Similarly, in models ofDisequilibrium
Disequilibrium characterizes a market that is not in equilibrium. Disequilibrium can occur extremely briefly or over an extended period of time. Typically in financial markets it either never occurs or only momentarily occurs, because trading takes place continuously and the prices ofSee also
* Exchange value * Labor theory of value * Law of value * Prices of production * Real prices and ideal prices * Asset pricing#General Equilibrium Asset PricingReferences
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