(ii) Stable, Unstable and Neutral Equilibrium
Equilibrium, whether static or dynamic, may be stable, neutral or unstable. According to Schumpeter, “A stable equilibrium value is an equilibrium value that, if changed by a small amount, calls into action forces that will tend to reproduce the old value; neutral equilibrium is an equilibrium value that does not know any such forces; an unstable equilibrium is an equilibrium value, change in which calls forth forces which tend to move the system further and farther away from equilibrium value.” He gives the illustration of balls in bowl to distinguish the one from another.
He states, “A ball that rests at the bottom of a bowl illustrates the first case; a ball that rests on a billiard table, the second; and a ball that is perched on the top of an inverted bowl, the third case.” -History of Economic Analysis.
“A stable equilibrium” is defined by Ackley as the one to which “The system’s movements tend to approach or reach. If a stable equilibrium is disturbed, it will be re-established.” A stable equilibrium is one which, according to Marshall, “if displaced a little from it, will tend to return, as a pendulum oscillates about its lowest point.”
The following are the characteristics of a stable equilibrium:
(i) Demand price is greater than the supply price for amounts less than the equilibrium amount. In Fig, equilibrium is established at E. Equilibrium price is PE and equilibrium point is QE. Q1 is the amount less than the equilibrium amount QE. For this quantity Q1, E1Q1 is the demand price and P1Q1 is supply price such that E1Q1 is higher than P1Q1.
When the demand price is greater PE than the supply price, the amount produced tends to increase and returns to the equilibrium level.
(ii) Supply price exceeds demand of price for amounts greater than the equilibrium quantity as in the case quantity Q2. Excess supply is created in the market, as opposed to excess demand, in the case of demand price greater than the supply price. In this case supplies will lower price until supply and demand are equal again.
Fig is in a state of stable equilibrium. The property of this equilibrium is that the supply curve cuts the demand curve from below. Marshall says that equilibrium is stable or unstable according as the demand curve lies above or below the supply curve just to the left of the equilibrium point; or, the demand curve lies below or above the supply curve just to the right of that point.
Unstable equilibrium occurs if any divergence from the equilibrium position sets in motion forces which move the equilibrium point farther and farther away from it. In supply and demand analysis, this happens when both supply and demand curves are negatively sloped and the supply curve cuts the demand curve from above, as shown in Fig. In this figure, the equilibrium price OP is unstable equilibrium price. If for any reason, price rises to OP1, the quantity demand falls to OQ2 (= P1b), while quantity supplied declines to P1a.
It creates an excess demand of ‘ab’ which leads to a further rise in the price. If, on the other hand, price falls to OP2, demand declines to P2c but quantity supplies goes up to P2d creating an excess supply equal to ‘cd’. Excess supply leads to a further decline in price. It shows that in both the cases forces operate in such a way as to move to the equilibrium point farther either in the upward direction or in the downward direction.
An economy remains in neutral equilibrium when it, after being disturbed from its initial equilibrium position, rests in the new position and shows no tendency to return to the original position. It happens so because neither re-establishing forces nor further disturbing forces come into operation after being moved from its original position.
In Fig, the initial equilibrium point is a. The equilibrium, quantity is OQ1 and equilibrium price OP1. When price rises to OP2, b turns out to be new equilibrium position. The equilibrium quantity shows no change; it remains OQ1. The price range P1P2 or ‘ab’ is the region of neutral equilibrium.
Schumpeter, however, defines neutral equilibrium as one that does not experience the forces of change like a ball that rests on a billiard table. – History of Economic Analysis, p. 971.
(iii) Partial and General Equilibrium
Partial Analysis: Partial equilibrium analysis is the analysis of the determination of equilibrium positions for a small part of the economy. A single market is taken into consideration and the determination of its equilibrium position is examined. The basic assumption of partial equilibrium analysis is that the feedbacks on a sector are so small that they may be neglected.
So the interaction between the market under study and the rest of the economy is ignored as having little effect on the final result. “In effect, we make the other things equal assumption that the rest of the economy remains the same throughout the analysis of one market and so there are no ‘feedback effects’ on the single market under study”. (Penguin Dictionary of Economics). This method of analysis was characteristic of A. Marshall’s approach to economic theory.
Schumpeter says that when we observe small sectors of the economy, such as, individual households or firms, “we may assume that nothing that happens in these small sectors exerts any appreciable influence on the rest of the economy.” (History of Economic Analysis, p. 990.) From this assumption it should not be inferred that the rest of the economy remains unchanged, though the assumption of “other things equal”, i.e., ceteris paribus, means this.
It does, however, imply that “if some external influence be exerted upon the small sector under consideration, then this sector adjusts itself without exerting, in turn, more than a negligible effect on the rest of the economy or any element of it.” (Ibid). This has been shown ahead in Fig, and contrast it with Fig which is a case of general equilibrium analysis.
Partial equilibrium analysis, according to Schumpeter, has been used since the beginning of time. But it acquired a novel definiteness and an apparatus of its own at the hands of Cournot, Von Mangoldt and Marshall. Many economists are of the opinion that Marshall became and remained the master of partial analysis. This analysis has been and is being widely used; yet the fact is that it has also been condemned, especially by Walras and Pareto.
General Equilibrium Analysis: Baumol states that “General Equilibrium theory was developed to take account of a cardinal feature of the structure of our economy: The interdependence of its parts.” (Economic Theory and Operations Analysis, Second Edition, p. 338). The economy does not consist of a series of self-contained markets functioning in isolation; it is an interlocking system in which anything happening in one market greatly affects other markets, and could potentially affect every other market in the economy. This interaction is represented pictorially in Fig.
In the figure we start by considering some sector of the economy and we call this sector A. If there is some change in Sector A, this will cause changes in the rest of the economy, and these changes will, in turn, reflect back on Sector A, causing further changes in that sector. This reflection back is technically called, “Feedback.”
The distinction between partial and general equilibrium analysis lies in the assumption about the nature of the feedback. The basic assumption of partial equilibrium analysis is that the feedbacks on sector A are small enough that they may be neglected. General equilibrium analysis, on the other hand, allows that the feedbacks are quite large and so they cannot be neglected. This difference has been shown in Figures.
Traditionally two approaches have been adopted by economists to analyze economic systems. One is the partial equilibrium approach. It is a simpler approach associated with the name of Alfred Marshall. Here only a part of the system is examined, e.g. the market for apples on the assumption that conditions in the rest of the economy remains unchanged.
The second is the general equilibrium approach. It is a more difficult approach in conception and in the use of mathematical tools. It looks at the economic system as a whole and considers the simultaneous determination of all prices and quantities of all goods and services in the economic system. Walras is credited with being the founder of this approach.
Demand and supply curves are the tools of partial equilibrium analysis. Transformation and indifference curves are the tools of general equilibrium analysis. While demand and supply curves are based on ceteris paribus assumptions, transformation and indifference curves allow all quantities and prices to vary simultaneously.
Schumpeter says that there is no sharp dividing line between partial and general analyses. Partial analysis shades off into general analysis as its scope is extended. The best illustration of this is Marshall’s analysis of “General Relations of Demand, Supply and Value” in Book V of his ‘Principles of Economics’.
(iv) Single and Multiple Equilibrium
When there is only one point of equilibrium, it is known as single equilibrium, as shown in fig.
In the figure, only one point of equilibrium is at E where demand for X equals supply of X. If there is more than one set of price, output demanded and supplied, we get multiple equilibrium as at points A, E and B in Fig.
In the case of single equilibrium, also called unique equilibrium, there is only one set of quantities (variables) that satisfies equilibrium conditions. But there need not be only one set of values of variables satisfying the equilibrium conditions; “there may exist several such sets or an infinity of them”, observes Schumpeter. Where there are several such sets satisfying equilibrium conditions, we get multiple equilibria. Such equilibria are not of great practical importance. —Marshall, Principles, p. 391.
Multiple equilibria are not necessarily useless but, from the stand-point of any exact science, the existence of a single equilibrium, that is, a uniquely determined equilibrium is of utmost importance. In the theory of monopoly pricing, the concept of multiple equilibria was used by Robinson. Similarly, in his trade cycle theory, Kaldor has used this concept of equilibria.
Speaking generally, single equilibrium goes along with stable equilibrium. It is tacitly assumed, according to Marshall, “that there could be only one position of stable equilibrium in a market: yet in fact under certain conceivable, though rare, conditions there can be two or more positions of real equilibrium of demand and supply….. and any one of which if once reached would be stable, until some great disturbance occurred.”
(v) Short and Long-Period Equilibria
When the element of time is taken into consideration, equilibrium can be classified into short-period equilibrium and long-period equilibrium. In the short-run, a firm can vary its output but does not have time to vary the size of plant. Further, the number of firms in an industry is fixed because new firms do not have time to enter and existing firms do not have time to leave.
Change in output results from the use of larger quantity of variable factors by the fixed plant. Short-run equilibrium has been shown in Fig. In the figure DD is the market demand curve for the commodity, S is the short-run supply curve. OP1 is the short-run price. An increase in demand from DD to D’D’ increases the short-run equilibrium price to OP2.
In the long run a firm has time to alter its plant size; and there is ample time for new firms to enter into or for existing ones to leave the industry. Long-run equilibrium has been shown in Fig. Such an equilibrium implies that new firms have no incentive to enter the industry or existing firms to leave. This happens when the firms in the industry earn only normal profits, that is, profit which is just sufficient to induce the firm to remain in his present activity.
In Fig, DD is the market demand curve, while LS is the long-period supply curve which shows greater elasticity than the short-period supply curve SS because the firms get greater opportunity and time to adjust output to the conditions of demand. OP1 is the short-run and long-run price. An increase in demand to D’D’ raises the long-run equilibrium price to OP2 which is lower than the short-run equilibrium price OP3.