A consumer is in equilibrium when he derives maximum satisfaction from the goods and is in no position to rearrange his purchases.
- There is a defined indifference map showing the consumer’s scale of preferences across different combinations of two goods X and Y.
- The consumer has a fixed money income and wants to spend it completely on the goods X and Y.
- The prices of the goods X and Y are fixed for the consumer.
- The goods are homogenous and divisible.
- The consumer acts rationally and maximizes his satisfaction.
In order to display the combination of two goods X and Y, that the consumer buys to be in equilibrium, let’s bring his indifference curves and budget line together.
We know that,
- Indifference Map: Shows the consumer’s preference scale between various combinations of two goods
- Budget Line: Depicts various combinations that he can afford to buy with his money income and prices of both the goods.
In the following figure, we depict an indifference map with 5 indifference curves – IC1, IC2, IC3, IC4, and IC5 along with the budget line PL for good X and good Y.
From the figure, we can see that the combinations R, S, Q, T, and H cost the same to the consumer. In order to maximize his level of satisfaction, the consumer will try to reach the highest indifference curve. Since we have assumed a budget constraint, he will be forced to remain on the budget line.
So, which combination will he choose?
Let’s say that he chooses the combination R. From Fig. 1, we can see that R lies on a lower indifference curve – IC1. He can easily afford the combinations S, Q, or T which lie on the higher ICs. Even if he chooses the combination H, the argument is similar since H lies on the curve IC1 too.
Next, let’s look at the combination S lying on the curve IC2. Here again, he can reach a higher level of satisfaction within his budget by choosing the combination Q lying on IC3 – higher indifference curve level. The argument is similar for the combination T since T lies on the curve IC2 too.
Therefore, we are left with the combination Q.
What happens if he chooses the combination Q?
This is the best choice since Q lies on his budget line and pts puts him on the highest possible indifference curve, IC3. While there are higher curves, IC4 and IC5, they are beyond his budget. Therefore, he reaches the equilibrium at point Q on curve IC3.
Notice that at this point, the budget line PL is tangential to the indifference curve IC3. Also, in this position, the consumer buys OM quantity of X and ON quantity of Y.
Since point Q is the tangent point, the slopes of line PL and curve IC3 are equal at this point. Further, the slope of the indifference curve shows a marginal rate of substitution of X for Y (MRSxy) equal to MUxMUy. Also, the slope of the price line (PL) indicates the ratio between the prices of X and Y and is equal to PxPy.
Hence, at the equilibrium point Q,
MRSxy = Mux/MUy = Px/Py
Therefore, we can say that consumers equilibrium is achieved when the price line is tangential to the indifference curve. Or, when the marginal rate of substitution of the goods X and Y is equal to the ratio between the prices of the two goods.