Partial and General Equilibrium

According to Prof. Stigler, a partial equilibrium is one which is based only on a restricted range of data.

A partial equilibrium analysis focuses on the equilibrium of only one economic unit or one part of the economy at a time—such as a single consumer, a single firm, a single industry, or a single market.
In partial equilibrium, we deliberately ignore interdependence with other markets. We treat the rest of the economy as given and constant while analyzing the unit of interest.

• "General equilibrium for the entire economy could exist only if all economic units were to achieve simultaneous partial equilibrium adjustment." - Leftwitch
• According to Stigler, theory of general equilibrium is the theory of inter-relationship of all units of economy. 

A general equilibrium refers to a situation in which all major economic units and markets in the economy are simultaneously in equilibrium.
In other words, every consumer, every firm, every factor market (like labour and capital), and every product market has reached an equilibrium position, and these equilibria are mutually consistent with one another.

There are two influential formal approaches:

1) Walrasian system of simultaneous equations

• Léon Walras developed a mathematical model in which all markets for goods and factors are represented by a system of simultaneous equations.
• Each equation describes the demand and supply for one good or factor; solving the system gives a set of prices and quantities at which all markets are in equilibrium at the same time.

2) Leontief’s input–output analysis

• Wassily Leontief studied interdependence among industries using input–output tables.
• Each industry uses outputs of other industries as inputs (for example, the steel industry uses coal, power, and machinery), and an input–output table shows these flows.
• By solving this system, we can see how a change in one industry’s output or demand affects other industries and whether the whole system can be in equilibrium.

Both approaches capture the idea that no market is isolated in reality.

a) Partial equilibrium example
Suppose we analyse only the market for school notebooks. We assume students’ incomes, prices of pens, and wages of paper mill workers remain unchanged. We derive the price and quantity where notebook demand equals notebook supply. This is partial equilibrium for the notebook market.

b) General equilibrium example
Now imagine a sharp increase in petrol prices. This change affects:

• Transport costs of goods (raising prices of food, clothing, etc.),
• Cost of commuting for workers,
• Wages they demand, and hence costs and prices in many industries.
  A general equilibrium analysis studies how all these markets (fuel, transport, food, labour, etc.) adjust together to reach a new set of prices and quantities that are mutually consistent.

• Equilibrium means a position of rest, with no tendency to change under existing conditions.
• Partial equilibrium looks at one unit or one market at a time, assuming all other things are constant.
• Consumer’s, producer’s, firm’s, and industry’s equilibria are all examples of partial equilibria.
• General equilibrium exists when all important markets and units in the economy reach equilibrium simultaneously, and their decisions are mutually consistent.
• Walras used a system of simultaneous equations to show general equilibrium for all markets, while Leontief used input–output analysis to trace interdependence among industries.