question_answer

Explain three properties of indifference curves.

Or

Explain the conditions of consumer's equilibrium under indifference curve approach.

 

Answer:

There are three properties of Indifference Curve.

1. Indifference curves are downward sloping to the right: Downward slope of the indifference curve to the right implies that a consumer cannot simultaneously have more of both the goods. An increase in the quantity of one good is associated with the decrease in the quantity of the other good. This is the accordance with the assumption of monotonic preferences.

2. Slope of IC: The Slope of an IC is given by the Marginal Rate of substitution (MRS). Marginal rate of substitution refers to the rate at which a consumer is willing to substitute one good for each additional unit of the other good.

At point A: Slope of Indifference Curve (MRS) \[=\Delta Y/\Delta X\]

i.e., MRS shows the rate at which the consumer is willing to sacrifice good Y for an additional unit of good X.

3. Shape of Indifference Curve: As we move down along the Indifference curve to the right, the slope of IC (MRS) decreases. This is because as the consumer consumes more and more of one good, the marginal utility of the good falls. On the other hand, the marginal utility of the good which is sacrificed rises. In other words, the consumer is willing to sacrifice less and less for each additional unit of the other good consumed. Thus, as we move down the ZC, MRS diminishes. This suggests the convex shape of indifference curve.

In the above figure, IC is the Indifference Curve.

At point A,         \[MR{{S}_{xy}}=\text{ }AD/DB\]

At point B,         \[MR{{S}_{xy}}=BE/EC\]

\[BE/EC<AD/DB\]

MRS at B < MRS at A, so MRS has fallen.

Or

As per the Indifference Curve Approach, a consumer attains equilibrium at the point where the budget line is tangent to the indifference curve and the IC is convex to the origin at the point of tangency. This optimum point is characterized by the following equality:

\[\left| \frac{-{{d}_{y}}}{{{d}_{x}}} \right|=\left| MRS \right|=\left| \frac{{{P}_{1}}}{{{P}_{2}}} \right|\]

It is, absolute value of the slope of the \[IC=\] Absolute value of the slope of the budget line.

In the above figure, point E depicts consumer?s equilibrium. At this point, the budget line is tangent to the Indifference curve\[I{{C}_{2}}\]. The optimum bundle is donated by \[(x_{1}^{*}\,\,x_{2}^{*})\]. This point is the optimum or the best possible consumption bundle, where the consumer is maximizing his satisfaction. All other point lying on the budget line (such as point B and point C) are inferior to \[(x_{1}^{*}\,\,x_{2}^{*})\] as they lie on a lower \[IC\] (i.e., \[I{{C}_{1}}\]). Thus, the consumer will rearrange his consumption and will attempt to reach the equilibrium point, where the marginal rate of substitution is equal to the price ratio.

Let?s suppose that instead of point E, the consumer is at point B. at this point, MRS is greater than the price ratio.\[\left[ i.e.,MRS>\frac{{{P}_{1}}}{{{P}_{2}}} \right].\] In the case, the consumer would tend to move towards point E by giving-up some amount of good 2 in order to consume more units of good 1. The consumer will reaches the point E, where, MRS becomes equal to the price ratio.

On the other hand, for all other points such as point C, MRS is lesser than the price ratio. \[\left[ i.e.,MRS<\frac{{{P}_{1}}}{{{P}_{2}}} \right].\] In this case, the consumer would tend to move towards point E by giving up some amount of good 1 to consume more units of good 2.

Thus, we can conclude that if the consumer is consuming any bundle other than the optimum one, than he would rearrange his consumption bundle in such a manner that the equality between the MRS and the price ratio is established and he attains the state of equilibrium.