Stable Equilibrium
A stable equilibrium is a situation in which a system, when disturbed, tends to return to its original position, so that small deviations are self-correcting. In economics, a stable equilibrium is a state in which the forces acting on the system push it back toward equilibrium when it is perturbed, while an unstable equilibrium is one in which deviations are self-reinforcing and move the system away. Stability is a central property of economic models, and it determines whether the predicted equilibrium is a plausible outcome.
The concept
Stability concerns the response of a system to a deviation from equilibrium. If the system returns to equilibrium after a small disturbance, the equilibrium is stable; if it moves further away, it is unstable. A familiar example is a ball in a bowl, which returns to the bottom when displaced, compared with a ball on top of a hill, which rolls away when disturbed. The analogy illustrates that stability depends on the direction of the forces around the equilibrium.
In economics, stability is analysed by examining the forces that operate when the price or quantity deviates from the equilibrium. In a competitive market, if the price is above the equilibrium, quantity supplied exceeds quantity demanded, creating downward pressure on the price, and if the price is below the equilibrium, the opposite occurs. The market is stable when these forces push the price toward the equilibrium, which is the usual case under standard assumptions.
Types of stability
Several types of stability are distinguished. Local stability concerns the behaviour of the system in response to small deviations, while global stability concerns its behaviour in response to large deviations. A system may be locally stable but globally unstable, returning to equilibrium after small shocks but moving to a different equilibrium after large ones. The distinction matters for the analysis of shocks and of policy.
Static stability concerns the tendency to return to a given equilibrium, while dynamic stability concerns the path taken during the adjustment and the possibility of cycles or divergence. A system may converge to equilibrium smoothly, oscillate around it, or diverge, depending on the parameters. The analysis of dynamic stability, using differential equations or difference equations, examines the conditions under which the adjustment process converges.
Examples
Market equilibrium is stable under the usual assumptions of downward-sloping demand and upward-sloping supply, because excess demand or supply pushes the price toward the equilibrium. The stability of the foreign exchange market, of the labour market, and of other markets can be analysed in the same way, and the conditions for stability depend on the slopes of the relevant curves.
In macroeconomics, the stability of the economy around full employment, and of the debt ratio around a sustainable level, are analysed using stability concepts. The stability of a growth path, of a monetary policy rule, and of a financial system are all examined by considering whether the system returns to the desired state after a disturbance. In each case, the analysis identifies the conditions that ensure or undermine stability.
Significance
Stability is significant because it determines whether an equilibrium is a plausible prediction of a model. An equilibrium that is unstable may not be observed, because any small disturbance will move the system away, and the model's prediction may therefore be misleading. The analysis of stability is therefore part of the assessment of a model's usefulness and of the realism of its conclusions.
Stability also informs policy. Policies that affect the forces around an equilibrium can change its stability, and the design of policy must consider whether the target is stable and whether the policy itself contributes to stability. The stability of the financial system, of the public finances, and of the economy around full employment are central concerns, and the analysis of stability provides the framework for assessing resilience and for designing measures that reduce the risk of instability.
Stability in macroeconomic models
Stability is a central concern of macroeconomic analysis. The stability of the economy around full employment, of the price level, and of the debt ratio are all examined by considering whether deviations are self-correcting. In models with flexible prices, the economy tends toward full employment, and the equilibrium is stable; in models with rigidities, the adjustment may be slow or absent, and the economy may settle at a depressed level.
The stability of the economy under different policy rules is also analysed. A monetary policy rule that responds to inflation and output can stabilise the economy around the target, while a rule that is too passive or too aggressive may produce instability. The analysis of stability, known as the study of determinacy and of the Taylor principle, informs the design of policy rules and the assessment of their robustness.
Stability and multiplicity
Some models have multiple equilibria, some stable and some unstable, and the outcome depends on which equilibrium is selected. In models of financial crises, for example, an economy may have a good equilibrium with stable prices and a bad equilibrium with a crisis and a collapse, and a small shock can move the economy from one to the other. In such cases, the stability of the good equilibrium is fragile, and policy may be needed to sustain it.
The possibility of multiple equilibria has implications for policy. It means that expectations and confidence matter, and that policy can play a role in coordinating expectations on the good equilibrium. The analysis of self-fulfilling crises and of coordination failures informs the design of policy, including the provision of liquidity, the guarantee of deposits, and the communication of a clear framework, and it is central to the understanding of financial stability.
Stability and institutions
Institutions affect the stability of economic systems. Property rights, contract enforcement, and the rule of law support stable expectations and reduce the risk of disruptions. Central bank independence and credible fiscal rules support the stability of prices and of public finances. Regulatory frameworks for financial institutions support the stability of the financial system.
The design of institutions affects the resilience of the economy to shocks and the speed of adjustment. Institutions that facilitate adjustment, such as flexible labour and product markets and well-functioning financial systems, support stability, while institutions that impede adjustment can allow imbalances to persist and to grow. The analysis of stability therefore informs the design of institutions, and it links the study of economic dynamics to the broader analysis of institutions and policy.
Mathematical foundations
The analysis of stability draws on mathematics, particularly on the theory of dynamical systems. The behaviour of a system near an equilibrium is analysed by examining the eigenvalues of the linearised system, and the conditions for stability are that the eigenvalues have the appropriate properties. For differential equations, stability requires that the real parts of the eigenvalues be negative, and for difference equations, that the eigenvalues lie within the unit circle.
The mathematical analysis provides the conditions under which a system converges to equilibrium, oscillates, or diverges, and it informs the interpretation of the economic model. The application of these methods to economic models requires attention to the specification of the dynamics and to the interpretation of the parameters, and it provides a rigorous basis for the analysis of stability and of the effects of policy.