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Question

A consumer consumes only two goods. For the consumer to be in equilibrium why must Marginal Rate of Substitution between the two goods must be equal to the ratio of prices of these two goods? Is it enough to ensure equilibrium?

OR

A consumer consumes only two goods. Why is the consumer said to be in equilibrium when he buys only that combination of the two goods which lies at that point on the Indifference curve where the budget line is tangent to the indifference curve? Explain. Use diagram.

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Solution

Let the two goods be X and Y. MRSxy is the number of units of Y the consumer is willing to sacrifice to obtain one extra unit of X. The ratio of prices is Px/Py which also equals the ratio of the number of units of Y required to be sacrificed to obtain one extra unit of X in the market.

Initially when the consumer starts purchases, MRSxy is greater than Px/Py. It means that to obtain one extra unit of X the consumer is willing to sacrifice more than he has to sacrifice actually. The consumer gains. As he goes on obtaining more and more units of X, marginal utility of X goes on declining. Therefore the consumer is willing to sacrifice less and less of Y each time he obtains one extra unit of X. As a result MRSxy falls and ultimately becomes equal to Px/Py at some combination of X and Y. At this combination the consumer is in equilibrium.

If the consumer attempts to obtain more units of X beyond the equilibrium level, MRSxy will
become less than Px/Py and his total utility will start falling. So he will not try to obtain more of
X.

Let the two goods be X and Y as shown in the diagram. The tangency is at point E where:
Slope of indifference curve = Slope of budget line

Or MRSxy=PxPy
The equilibrium purchase is Ox of X and Oy of Y on the indifference curve l2

The consumer cannot get satisfaction level higher than I2 because his income does not permit him
to move above the budget line AB. The consumer will not like to purchase any other bundle on
the budget line AB, for example the bundle at C and D, because they all lie on the lower
indifference curve, and give him lower satisfaction. Therefore, the equilibrium choice is only at
the tangency point E.


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