PARTIAL EQUILIBRIUM  and GENERAL EQUILIBRIUM APPROACH

Meaning and Definitions of Equilibrium

Concept of equilibrium, which forms the basis of various theories in different economic activities, is borrowed from Physics. Unlike its meaning in Physics i.e. an absence of activity, m economic sense it implies absence of tendency or urge to change. It thus means a state of balance.

“Equilibrium is a position from which there is no tendency to ‘move”. - Prof. Stigler

“Equilibrium denotes absence of change in the movement and not the absence of movement itself’. - Prof. J.K. Mehta “

A market or an economy or any other group of persons and firms is in equilibrium, when none of its members feels impelled to change his behaviour”. — Scitovsky

All the above definitions bring home the point that equilibrium in economic sense implies a position of rest. It does not imply absence of movement but suggests absence of change in the movement. Number of examples of equilibrium can be mentioned e.g. a firm is in equilibrium when it is maximising its profits; the consumer is in equilibrium when he maximises his level of satisfaction, within given constraints of his income and prices.

Types of Equilibrium

1. Stable — Unstable - Neutral Equilibrium

2. Static and Dynamic Equilibrium

3. Single and Multiple Equilibrium

4. Short Term and Long Term Equilibrium

5. Partial and General Equilibrium.

All these varieties are important in their own ways. However the concepts of Partial and General Equilibrium are of particular significance. 

An economy consists of various constituent segments which are interconnected and interdependent. The general equilibriurm approach recognises dependence of constituent parts of the economic system; it recognise inter relations of economic variables and seeks to answer the question how all the segments of the economy reach an equilibrium position simultaneously. General equilibriurn shows, by using the tools of partial equilibrium analysis how prices and outputs are simultaneously determined in all segments of the economy. In fact general equilibrium provides a link between microeconomics and microeconomics.

PARTIAL EQUILIBRIUM 

Partial Equilibrium analyses the position of rest i.e. equilibrium of an individual unit such as a consumer, a firm, an industry etc. It is thus a microeconomic concept. In order to analyze the position of equilibrium of an individual unit, it becomes necessary to assume that all other variables are constant. Thus if we intend to establish the conditions of equilibrium of an individual consumer, we have to ignore (assume to be constant) other forces that affect the behaviour of the said individual. Hence we ignore the changes in tastes and preferences of consumers, prices of other goods etc. while discussing the individual equilibrium. 

“A partial equilibrium is one which is based on only restricted range of data, a standard example is price of a single product; the prices of all other products being held fixed during the analysis’. It assumes ‘Ceteris Paribus’. Prof. Stigler In short Partial Equilibrium implies:

• Equilibrium of an individual or a single unit

• It isolates an individual unit from others

• It ignores the independence and hence is based on independence of individual units.

• It excludes other variables and relies on a restricted data.

• It assumes, ’Other things remaining the same’.

Subject Matter of Partial Equilibrium:

As mentioned above partial equilibrium explains how an individual consumption or production unit attains the position of equilibrium. Naturally, it deals with issues such as the following:

Equilibrium of Consumer : On the basis of income, prices and preferences of individual it determines the manner in which a consumer derives maximum satisfaction i.e. equilibrium.

Equilibrium of a firm : This implies determination of level of output that yields maximum profit. It reached when MR = MC. The position is arrived at on the basis of cost behaviour, prices, technique of production etc.

Industry Equilibrium : It occurs when number of firms in the industry remains constant i.e. there is neither entry nor exit of firms. This happens when all firms enjoy only normal profit i.e. AR = AC.

Factor Market : An individual factor reaches the position of equilibrium when it receives highest possible reward. Since the alternative reward is less he sticks to that employment.

Assumptions of Partial Equilibrium:

The Partial equilibrium isolates an individual unit from other influences. Naturally, it has to make a variety of assumptions many of which may be quite unrealistic. Following are assumed to exist.

1. Constancy of price of the product and income, habits etc. of consumer.

2. Prices of other goods are constant. For a firm prices and availability of resources is given and constant.

3. Perfect factor mobility.

4. Existence of perfect competition etc.

Partial equilibrium' in economics means a state of stability of individual segments of the economy by maximising their respective objective functions. The approach' ignores the interdependence of the segments of the economy. It isolates one segment of the study from the changes occuring  outside the area assumed to lemain constant even if incomes change in factor prices in f actor markets; prices of related goods arc assumed to remain constant even if they income change in factor prices in tactor markets; prices of related goods at assumed to rcmain constant even if they change due to change in demand and supply conditions, and the consumel.'s tastes and perlbmrances are assumed io be given even though they are not. The general equilibrium refbrs to a state in which all economic units maximise their respective objective functions and all prices are simultaneously in stability and all markets are cleared.

Significance of Partial Equilibrium

Although Partial equilibrium approach is exposed to number of limitations. Yet it has a considerable practical and theoretical significance.

1. Explanation of determination in product and factor prices.

2. Analysis of change in individual unit.

3. Explanation of consequences of change in behaviour of single unit

4. Description of effect of policy changes.

5. Help in solving economic problem.

6. Simplification of important issues.

7. Foundation of understanding interdependence.

8. Assistance in general equilibrium analysis.

Limitations of Partial Equilibrium

1. Narrow approach.

2. Limited applicability due to restrictive assumptions.

3. Neglect of interdependence among unit.

4. Inadequate

5. Inability to explain interdependence among units. 

GENERAL EQUILIBRIUM APPROACH

Above definition is self explanatory and fully reveals the meaning and nature of general equilibrium. It is obvious that this approach concentrates on the entire economy i.e. whole as against partial equilibrium analysis which deals with ‘a part’ or an individual unit. It is a macro approach undertaking extensive and comprehensive study of the different variables, their interrelations and inter-dependence, etc. It primarily tries to arrive at equilibrium of the entire system. A general equilibrium occurs when every individual unit attains equilibrium simultaneously. Thus what general equilibrium does is to bring out the link between different individual units in a system.

Subject Matter of General Equilibrium:

Since general equilibrium deals with the whole economy it has to explain how total demand and total supply are brought into equality both in the factor and product markets. This implies an in depth study of the factors forming total demand (Buyers) and total supply (Sellers) in both product as well as factor markets. The state of general equilibrium will be reached when the decisions of buyers and sellers regarding demand and supply in product and factor markets are in harmony.. Taking into account all these facts we can mention the subject matter of general equilibrium in the following manner.

Total Demand for product : Tastes, preferences, prices of complimentary and substitute products income i.e. rewards in factor market, etc.

Total Supply of product : Cost of different products, upon the reward of factors and their quantity prices of commodities in the product market, of production etc.

Total Demand for factor: Input productivity, the rewards of factors, quality and quantity of different factors of production etc.

Total Supply of factor : Rewards, availability, willingness to work, size and composition of population policy implications etc.

It is obvious that since general equilibrium approach deals with entire system in the context of equilibrium in product and factor markets, it has to properly analyze the interdependence among all the four aspects mentioned above. Study of consequences of change in one of the constituents on the different macro variables is also to be made. It can be observed that in any market the general equilibrium occurs at equality between total demand and total supply. In the product market the consumers are on demand side and the firms on the supply. In the factor market these roles are reversed. Two sets of conditions have to be fulfilled to achieve general equilibrium.

1. Subjective factors : Maximization of gains (satisfaction/profits) by each individual unit.

2. Objective factors : Demand — Supply equality in all markets.

Walras points out that : “General equilibrium occurs through the mutual interdependence between different markets and their constituents”. In his opinion, the trade in perfectly competitive market is similar to auction. The prices are raised when demand exceeds supply and lowered in the opposite situation. Raising and lowering continues till demand and supply become equal when we have the position of equilibrium. 

Assumptions of General Equilibrium

Following are the basic assumptions of general equilibrium analysis.

1. Existence of perfect competition in product and factor markets.

2. Perfect factor mobility

3. Identical cost conditions for all firms.

4. Homogeneity of productive resources.

5. Given and constant state of technology

6. Full employment of resources.

7. Constant Returns to scale.

Not all assumptions are true but are essential as they provide the framework for general equilibrium analysis. 

General equilibriurn approach explains how equilibrium can be attained simultaneously in the factor market and commodity market. It also explains that if the equilibrium is attained whether it is unchangeable in an intersectional manner. A simple case of: interdependence of markets is illustrated in figure in a simple model. Suppose demand for housing incrcases at some point of time in an economy. House rents go up, increasing the profitability of housing industry, Therefore the demand for intermediate goods like steel, cement, bricks and construction labour incrcases: The firms producing these intermediate goods increase their demand for factor input - land, labour, capital and organisation - and factor payments increases. Consequently, larger factor incomes flow to the households. When household income increases, demand for consumer goods and service increases and creates another chain of action and reaction between household and product rnarkets and factor markets: The whole economic system functions in a complex manner.

Let us consider a pure exchange model where no production takes place. Consumers have initial bundles of goods, initial endowments. They exchange with each other these goods according to their preferences. For example, you have quantities of apples and 1 have oranges. We enter into an exchange, your apple and my oranges. Note that the exchange to take, you must be willing to consume my oranges and 1 am willing to consume your apples. 4 
We can think of n consumers and k commodities in the economy. Each consumer has initial endowments and preferences. Whereas endowment refers to the commodity held by a consumer, her preferences are represented by a utility function y = u, (x,' ,x_I², x,^j, ...., x_i^k) where x, = x_i¹ , x_i² , x_i^j ,...., x_i^k) is the ith individual's consumption bundle. (' We introduce a price system P such that P = (P_I, P₂, ...., P_k). Note that the economy you are presented with, does required payment terms of money as people trade one good for another (exchange in barter system). But the price we intend to use is for the exchange rates. For example, the price of one unit of good X is one unit good Y. Such a price, therefore, can be called relative price of good X. If the price of Potato is Rs. 5 per kg and the price of apple is Rs. 2.5 per kg, then the relative price of Potato in terms of apple is 2 (i.e., each unit of Potato is worth 2 units of apple). Similarly, the relative price of apples in terms of Potato is 0.5 (i.e., one unit of apple is worth half unit of Potato). 
1 
Remember that we will use relative price in the following analysis. Imagine that the consumer i purchases x,' units of good j at price P_J. Then P_J.X, gives the amount of expenditure incurred by her and to that extent her income stands reduced. On the other hand, when she delivers goods of equal quantity, the income t',x,' is added to her income. 
To arrive at the equilibrium of the model, let us start with consumer's utility maximisation. See that the ith consumer maximises 
Ui(Xi) subject to her budget constraint PXi = PWi. Remember that solution to this problem yields the demand functions Xi = X,(P, PW_i), i =1,2,.. .n and demand for each commodity depends on all prices and the initial endowment. 

WALRASION EOUILIBRIUM 
A solution to consumer's utility maximisation problem when we take prices as given yields the demand function for a consumer. In the equilibrium the aggregate demand cannot exceed the endowment. The Walrasian Equilibrium refers to a pair of price and consumption bundle (P*, x*) such that 

If we assume that all markets are perfectly competitive and consumers participating there are price takers, then Walrasian equilibrium is called a competitive equilibrium.

Excess Demand Functions 
Define the excess demand function 

Xi's are demand functions for the ith individual. 
Making use of this notation, the equilibrium conditions can be written as 

This condition states that at the equilibrium prices, excess demand is to be equal to zero in all markets. Two interesting results immediately follow:

1) If there is equilibrium in the market for n-l ..... then in Walrasian equilibrium, the remaining market will also be in equilibrium. 
2) One can only solve for the relative prices in the model. Attempts to solve for absolute prices require adoption of normalisation. This would involve making additional assumption of one of the prices is equal to 1. Another form of commonly employed normalisation is to assume that 

Several interesting features emerge from such a formulation:

1) The aggregate excess demand functions (and demand functions) is homogenous of degree zero in all prices. That is to say, if all prices were to double, the quantity demanded of every good would remain unchanged.

2) Demand functions are continuous. If prices were to change by only a small amount, quantities demanded would change by only small amount.

3) n excess demand functions are not independent of one another and the equations are related by the formula, 

This formulation is called Walrus' Law. It states that the total value of excess demand is zero at any set of prices. There can be neither excess demand for all goods together nor excess supply. To prove this, take 

4) If for some price system P, we get all prices to be strictly positive and (k-1) markets clear, then the kth market also clears.

By Walras' law we have

5) If a commodity is in excess supply in Walrasian equilibrium, then its price must be zero in equilibrium.

That is, if (P*, x*) is a WE and ED,(P*)

Since (P*, x*) is a WE, ED(P*) L 0 and P* t 0, where 0 denotes the vector (0,0,0.. ..). \

Consequently, for P,*ED,(P*)

However, by Walras law, P*ED(P*) = 0. lf ED,(P*)o, then P;ED,(P*)

We will have P*ED(P*)

Example 1: , Suppose there are two people (A and B), two goods (F and S), with initial endowment (o: , w:),(oA ,&) .

A feasible allocation X = [(F,s,) F,, s,] . [f prices are PF and Ps, write the budget equations in terms of relative price. i 
The budgets are: 

 Existence of Equilibrium Prices

Existence of a set of equilibrium (relative) prices is tried to be seen by looking into the conditions that ensure the following: 

• Acertain that there exists at least one set of prices for which 

           a) individuals maximise their utilities subject to their budget constraints; and

           b) the demands are met by the existing stocks of the commodity in the hands of the consumers.

The idea then is to start with some initial arbitrary set of prices at which the economy is not in equilibrium. Some commodities may be in excess supply while others in excess demand. Some other market may be clearing at that price vector. Holding the other (n-1) prices constant, find the equilibrium price in the market for good.

I. Term this as provisional equilibrium price 4' . Keeping 4' and the other (n-2) prices constant, solve for the equilibrium price in the market good

2. Call this price P; . By changing P₂ from its initial position to P,' , you have disturbed the initial equilibrium price of market . Since the system of equations is Simultaneous, it is bound to happen. Using the provisional prices, 4' and Pi, solve per a provisional P,' and the proof proceeds until a complete set of provisional relative prices has been calculated.

       The phase of second interaction starts by holding   constant and calculating the new equilibrium price (P,') for the first good. Proceeding the same manner, we get an entire new set of provisional relative prices . The iteration goes on until a reasonable approximation to a set of equilibrium prices is achieve. 

Significance of General Equilibrium

The general equilibrium model of Walras has great utility in enhancing our understanding of the functioning of the whole system and in solving various problems faced by the entire economy. It rightly reveals the fact of inter-dependence between individual units and highlights the dangers in isolating them. The practical importance of this approach can be explained with reference to following

1. It provides a wide and comprehensive explanation of the inevitable mutual interdependence in a free enterprise economy.

2. This approach provides a thorough explanation of the functioning of the entire economy.

3. General equilibrium analysis simplifies the market complexities by revealing the inter-relations between individual units.

4.The approach clearly explains the role and functions of the market mechanism and reveals how economic decisions are arrived at.

5. The Input-Output analysis of Prof. Leontif is developed on the basis of general equilibrium analysis.

6. The Walrasian model provides the starting point for almost all economic theories. In almost every field of economic enquiry such as money, trade, welfare etc. the approach proves very useful. In brief General equilibrium model of Prof. Walras is useful in understanding the real issues of the economy as a whole. Thus Partial Equilibrium approach is based on the assumption, ‘other things remaining the same”. i.e. ‘ceteris paribus’: whereas the General Equilibrium approach assumes ‘everything depends on everything else”. Both the approaches, as we have seen, have their respective limitations and significance. 

 MECHANISM FOR ATTAINING WALRASIAN EOUILIBRIUM 

Under certain conditions, an equilibrium price,  can be found, for which demand is equal to supply. However, the underlying process through which the initial price P moves to P* is seen through various mechanisms. 
1) Tatonnemant Process: A fictitious auctioneer is put in charge with calling out a price vector and agents respond by providing information about their demands an supplies. Only when the auctioneer calls that price vector for which the quantity demanded is identical to that which is supplied, trading is permitted to take place. 
2) Provisional Contract: There could be recontracting in which buyers and sellers would enter into provisional contract before actual exchange goods takes place. Unless the agreed price vector is equilibrium one, provisional contracts remain unimplemented. 
3) Central Planning: A central authority is established to whom the consumers report their excess demands at all prices. You have to remember the planning processes of socialist economies to appreciate the notion of arriving at the equilibrium price. This was highlighted by Oskar Lange and Abba P. Lerner when they said that a socialist system can operate as efficiently as a capitalist one.

Limitations of General Equilibrium

1. Unrealistic Assumptions of this approach weaken its importance. The assumptions like perfect competition, full employment, perfect mobility etc. can hardly be experienced in practice.

2. Neglect of changing conditions is yet another defect of this approach. It assumes the constancy of most of the variables which in reality are frequently changing. Such a static model cannot effectively analyse the real dynamic scenerio. It is aptly remarked, “Since the given Wairasian conditions are continuously changing, the movement towards general equilibrium is ever thwarted and its attainment has ever remained wishful ideal’.

 3. Limited Validity is the fate of Walrasian general equilibrium model. They are applicable only when conditions are fulfilled i.e. assumptions are valid. This is true only in restricted situations. The validity depends upon proper solutions to various simultaneous equations.

In brief General equilibrium model of Prof. Walras is useful in understanding the real issues of the economy as a whole. Thus Partial Equilibrium approach is based on the assumption, ‘other things remaining the same”. i.e. ‘ceteris paribus’: whereas the General Equilibrium approach assumes ‘everything depends on everything else”. Both the approaches, as we have seen, have their respective limitations and significance.