Let the two goods consumed be X and Y. A consumer attains equilibrium when :
(i) MRSXY = Px/Py
(ii) MRSXY must be decreasing due to the assumption of diminishing marginal rate of substitution to ensure,
MRSXY = Px/Py
Explanation to the conditions of consumer'* equilibrium:
Condition 1: Suppose MRSXY >Px/Py
It means that the consumer is willing to sacrifice more of Good Y than he needs to give up actually in the market for an extra unit of Good X.
The consumer gains and increases consumption of good X.
As consumption of good X increases, satisfaction derived from Good X falls and satisfaction derived from Good Y rises. Thus, MRSXY falls till MRSXY = Px/Py
Condition 2: Unless MRSXY is declining consumer may not be able to attain equilibrium.
Detailed Answer:
Consumers Equilibrium through Indifference Curve Approach.
According to Indifference Curve approach, consumers equilibrium is determined if the following two conditions are satisfied :
(i) MRSxy = Px/Py
(ii) MRSxy is declining.
MRSxy is the rate at which the consumer is willing to sacrifice Y to obtain one more unit of X.
Thus, we can say that A consumer is in equilibrium at a point where budget line is tangent to Indifference Curve".
Slope of Indifference Curve = Slope of budget line i.e.
MRSxy =Px/Py
In the diagram, equilibrium is at point E, where the budget line touches the highest attainable indifference curve IC2 within consumer'* budget.
Bundles on the Indifference Curve IC3 are not affordable within budget.
Bundles on the Indifference Curve IC1 (i.e. points F and G) are lying on a lower Indifference Curve i.e. will have lower utility levels as compared to the tangency point E. Therefore, the consumer will choose only the tangency point on the budget line.
Therefore, E is a point of consumer'* equilibrium where he maximizes his satisfaction. Point E is also called the"Optimum Consumption Point" where he consumes OX1 of X and OY1 of Y.
If MRSxy > MRE it implies that the consumer is willing to sacrifice more unit of Y than what market requires. This induces the consumer to buy more of X. When he buys more of X, utility derived from X falls and he is willing to sacrifice less of Y. Thus MRSxy starts declining. He continues to consume more of X, till MRSxy=MRE=Px/Py.
If MRSxy < MRE, it implies consumer is willing to sacrifice fewer units of Y than what the market requires. He decreases the consumption of X. Due to this MRSxy began to rise, he continues to decrease the consumption of X till MRSxy = MRE.
