CONSUMER'S EQUILIBRIUM: MAXIMISING SATISFACTION

CONSUMER'S EQUILIBRIUM: MAXIMISING SATISFACTION

 

 A consumer is said to be in equilibrium when he is buying such a combination of goods as leaves him with no tendency to rearrange his purchases of goods. He is then in a position of balance in regard to the allocation of his money expenditure among various goods. In the indifference curve analysis it is assumed that the consumer tries to maximize his satisfaction.

 

We shall make the following assumptions to explain the equilibrium of the consumer:

 

(1) The consumer has a given indifference map exhibiting his scale of preferences for various combinations of two goods, X and Y

 

(2) He has a fixed amount of money to spend on the two goods. He has to spend whole of his given money on the two goods.

 

(3) Prices of the goods are given and constant for him. He cannot influence the prices of the goods by buying more or less of them.

 

(4) Goods are homogeneous and divisible.

 

(5) the consumer is assumed to be rational in the sense that he aims at maximizing his satisfaction.

 

It will be seen from Fig. below that the various combinations of the two goods lying on the budget line BL and which therefore he can afford to buy do not lie on the same indifference curve; they lie on different indifference curves. The consumer will choose that combination an the budget line BL which lies on the highest possible indifference curve. The highest indifference curve to which the consumer can reach is the indifference, curve to which the budget line BL is tangent. Any other possible combination of the two goods either would lie on a lower indifference curve and thus yield less satisfaction or would be unattainable.

 

Fig: 5 Consumer’s Equilibrium

 

 In Fig. 5 budget line BL is tangent to indifference curve IC3 at point Q. Since indif­ference curves are convex to the origin, all other points on the budget line BL, above or below the point Q, would lie on the lower indiffer­ence curves. Take point R which also lies on the budget line BL and which the consumer can afford to buy. Combination of goods represented by R costs him the same as the combination Q. But, as is evident, R lies on the lower indifference curve IC1, and will therefore yield less satisfaction than Q.

 

Likewise, point S also lies on the budget line BL but will be rejected in favor of y since S lies on the indifference curve IC2, which is also lower than IC3, on which Q lies. Similarly, Q will be preferred to all other points on the budget line BL which lies to the right of Q on the budget line, such as T and H. It is thus clear that of all possible combinations lying on BL, combination Q lies on the highest possible indifference curve and yields maximum possible satisfaction.

 

 Of course, combinations lying on indifference curves IC4, and IC5 will give greater satisfaction to the consumer than Q, but they are unattainable with the given money income and the given prices of the goods as represented by the budget line BL.

 

 It is therefore concluded that with the given money expenditure and the given prices of the goods as shown by BL the consumer will obtain maximum possible satisfaction and will therefore be in equilibrium position at point Q at which the budget line BL is tangent to the indifference curve IC3. In this equilibrium position at Q the consumer will buy OM amount of good X and ON amount of good Y.

 

Second Order Condition for Consumer Equilibrium

 

The tangency between the given budget and an indifference curve  is a necessary but not a sufficient condition for consumer's equilibrium. The second order condition must also be fulfilled. The second order condition is that at the point of equilibrium indiffer­ence curve must be convex to the origin., or to put it in another way, the marginal rate of substitution of X for Y must be falling at the point of equilibrium.

 

 It will be noticed from Fig. 5 above that the indifference curve IC3, is convex to the origin at Q. Thus at point Q both conditions of equilibrium are satisfied. Point Q in Fig.5 is the optimum or best choice for the consumer and he will therefore be in stable equilibrium at Q.

 

  But it may happen that while budget line is tangent to an indif­ference curve at a point but the indifference curve may be concave at that point. Take for instance, Fig. 6 where indifference curve IC1, is concave to the origin around the point J. Budget line BL is tangent to the indifference curve IC1, at point J But J cannot be a position of equilibrium because satisfaction would not be maximum there. Thus the consumer by moving along the given budget line BL can go to points such as U and obtain greater satisfaction than at J.

 

 

Fig:6 Second Order condition for Consumer’s Equilibrium

 

We therefore conclude that for the consumer to be in equilibrium, two conditions are required :

1. A given budget line must be tangent to an indifference curve, or marginal rate of substi­tution of X for Y (MRSxy.,) must be equal to the price ratio of the two goods .

 

2. Indifference curve must be convex to the origin at the point of tangency.