Consumer equilibrium through indifference analysis

A consumer is in equilibrium when given his tastes, and price of the two goods , he spends a given money income on the purchase of two goods in such a way as to get the maximum satisfaction.

It shows a situation in which the consume purchases such a combination of the commodities that he gets the maximum satisfaction from his given income and with given prices of the commodities. The point of equilibrium is such that he does not want a change from it.

According to KOULSAYIANNIS, " The consumer is in equilibrium when he maximises his utility, given his income and the market prices ."

ASSUMPTIONS :-

1) The consumer indifference map for the two goods X and Y is based on his scale of preference for them which does not change at all in this analysis.

2) His money income is given and constant.

3) Prices of the two goods X and Y are also given and constant.

4) The goods X and Y are homogeneous and divisible.

5) There is no change in the tastes and habits of the consumer throughout the analysis.

6) There is perfect competition in the market from where he makes his purchases of the two goods.

7) The consumer is rational and thus maximises his satisfaction from the purchase of the two goods.

CONDITIONS FOR EQUILIBRIUM :-

There are three conditions for consumer's equilibrium :-

1) THE BUDGET LINE SHOULD BE TANGENT TO THE INDIFFERENCE CURVE :- given these assumptions, the consumer can buy 5 units of X by spending the entire sum of Rs. 10 on Good-X or on 10 units of Y. The table below illustrates some of the possible combinations on which Rs. 10 can be allocated.

***draw table

***draw diagram
The above figure shows these 7 possible combinations indicated by points P, R, K, S, T, N and Q. The line PQ shows combinations of Goods X and Y, given their prices, when he spends his income on them.This is because, algebraically,
                 I= Px*X + Py*Y
Where,
      I= consumer's income
      Px= prices of good-X
      Py=prices of good-Y

This budget equation is the equilibrium of the line connecting the points Q and P, where Q=I/Px and P=I/Py. Thus PQ is the budget line.
On this budget line, the consumer can have any combination out of the 7 possible combinations . Combination P or Q are out of question because in either case he would have only Y or only X. He would not take combination R or N on a lower IC I1 because combination K or T is also available to him on a higher IC I2. But there is another combination S which is on the highest IC I3. Since all other combinations lie onlower IC , they represent lower level of satisfaction than combination S which is the consumer equilibrium point.

Now going to the condition of consumer equilibrium we have :
The budget line PQ is tangent to curve I3 at S. At point S,  he is also satisfying the budget equation :
      I(rs.10)=OA*Px+OB*Py
                    = 2.5units of X*rs.2+ 5 units of Y*rs.1
                     = Rs. 5+ Rs. 5
                      =Rs. 10


2) AT THE POINT OF EQUILIBRIUM THE SLOPE OF INDIFFERENCE CURVE AND OF BUDGET LINE SHOULD BE THE SAME :- At S, the slope of indifference curve is, in fact, the MRS of X for Y and on the budget line it is the ratio of the price of X to the price of Y. The slope of the budget line :-
       PQ= I/Py / I/Px
             = I/Py * Px/I
              = Px/Py
We also know that MRSxy= Px/Py at point S. This is a necessary but not a sufficient condition for consumer equilibrium.

3) INDIFFERENCE CURVE SHOULD BE CONVEX TO THE ORIGIN :- The last condition is that at the point of equilibrium, the MRSxy must be falling for equilibrium to be stable. It means that the indifference curve must be convex to the origin at the point of equilibrium. If the IC is concave at point R, the MRSxy increases. The consumer is at the minimum point of satisfaction at R on the concave I1 curve. A movement away from point R towards either axis along PQ would lead him to higher IC. Point S on the curve I2 is, in fact,  the point of maximum satisfaction and of stable equilibrium. Thus for equilibrium to be stable at any point on an IC, the MRS between any 2 goods must be diminishing and be equal to their price ratio,that is,  MRSxy = Px / Py.
Therefore, the IC must be convex to the origin at the point of tangency with the budget line.

**draw diagram

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