Indifference Curve Analysis

# Indifference Curve Analysis

Indifference curve analysis is one of the two approaches to determining consumer equilibrium. This approach, in contrast to the marginal utility analysis, is based on the assumption that the amount of satisfaction derived from consumption cannot be measured or expressed in subjective units. The other name for this method is ordinal utility analysis. The consumer chooses the combination that yields the highest amount of satisfaction subject to income constraint. The indifference curve and the budget line are used to determine consumer equilibrium under this method.

Assumptions of indifference curve analysis

Rational consumers
The consumer is a rational being who always aims to maximise total utility from the combination of goods he or she consumes. We are dealing with a consumer that is armed with perfect knowledge and mental capacity to do all the computations necessary to ascertain all the benefits and costs associated with all products. These help in choosing a product that gives maximum satisfaction without restrictions.

Utility cannot be measured
Utility cannot be accurately measured. The goods can only be ordered. The consumer can only say he prefers good  X to good Y without the actual amount of utility derived. The consumer will have a scale of preference in which he places the most satisfying good in the first position, the send most satisfying is placed in the second position, and so on.

Preferences, habits and tastes remain unchanged
It is assumed that incomes, preferences and habits of the consumer are constant. This means that if he/she prefers good X to good Y, it will remain unchanged during the analysis.

More is preferred to less
The consumer would like to have more of a product than have less of it.

Diminishing marginal rate of substitution
The rate at which a consumer can replace one product with an additional unit of another good is the marginal rate of substitution. The consumer has to give up some units of one good in order to have an additional unit of another.  But he will be reluctant to give up more units of a product if he has less of it. So the rate at which the consumer is willing to replace one product with another falls with decreasing quantity of the product. In Table 1 below, 1 unit of good Y has to be sacrificed in order to produce 1 additional unit of good X when moving from A to B. 0.5 unit of good Y has to be given up to produce an extra unit of good X moving from B to C (6 more units of good X consumed to 3 units of Y given up is 3/6 which equals 0.5). 0.2 unit of good Y has to be foregone for every additional unit of good X produced from C to D (5 more units of good X consumed to 1 unit of Y given up is 1/5 which equals 0.2).

Table 1: A schedule showing the marginal rate of substitution

 Good X Good Y MRS A 0 20 – B 1 19 1 C 7 16 0.5 D 12 15 0.2

Indifference curve
It is a curve that joins the consumption bundles of two goods that yield the same amount of satisfaction to the consumer.

Indifference schedule

An indifference schedule is a list or table showing different consumption bundles of two goods that yield the same amount of satisfaction to the consumer.

Indifference map
It is a collection of two or more indifference curves. The higher-placed indifference curve joins the combinations that give the consumer a higher amount of utility or satisfaction while the lower-placed indifference curve gives lesser satisfaction.

Figure 1: An indifference map

Characteristics of indifference curve

Downward sloping
The indifference curve slopes from left to right, i.e. it is negatively sloped. The consumer has to make do with fewer amount of one good in order to obtain more units of another good.

The higher the indifference curve the higher the level of utility
Each indifference curve represents a different level of utility. Combinations on a higher indifference curve give more satisfaction than combinations on a lower indifference curve.

Indifference curves cannot cross each other
Each indifference curve connects the bundles that produce the same amount of satisfaction. If two indifference curve cross, it means that a point (point K in Figure 2 below) will be on both indifference curves. But it is impossible for a consumption bundle to give different amounts of satisfaction at the same time.

Figure 2: Two indifference cannot cross

Indifference curve is convex to the origin
It curves outward because, given two goods (good X and good Y), the quantity of good Y that can be replaced by good X falls as the consumer increases the amount of good  X. This is known as diminishing marginal rate of substitution.  The quantity of good Y that is given up declines as one moves from left to right on the indifference curve. If the marginal rate of substitution was increasing, the indifference curve would curve inward  (concave to the origin). This contradicts the assumption of diminishing marginal rate of substitution. Also, if the goods were perfect substitutes, the indifference curve would be a straight line with a constant marginal rate of substitution.

Budget line

A budget line shows the possible combinations of two goods that a consumer can buy with his income at given prices. It is a straight line that is drawn from left to right. The points on the budget line represent affordable combinations; points below the line show combinations that can be purchased if the consumer does not spend all its income, meaning he/she is not deriving maximum utility from his income; however, the consumer cannot afford the combinations above the budget line. The ratio of the prices of the two goods is the slope of the budget line.

A change in money income when prices are unhanged will lead to a parallel shift of the budget line to the right (increase in money income) or to the left (decrease in money income). A change in the price of one of the goods while money income remains unchanged will make the budget line to pivot or rotate clockwise (price increase) or anticlockwise (price decrease).

Figure 3: A budget line

Figure 4: Effect of a fall in money income on the budget line

Figure 5: Effect of a rise in money income on the budget line

Figure 6: Effect of a fall in  the price of good X on the budget line

Figure 7: Effect of a rise in  the price of good X on the budget line

Figure 8: Effect of a fall in  the price of good Y on the budget line

Figure 9: Effect of a rise in  the price of good Y on the budget line

Consumer equilibrium
A consumer will maximise utility by selecting the combination at the point where the budget line touches the indifference curve (point A in Figure 10 below). That is the combination that gives the consumer the highest amount of satisfaction given his income. Any other combination either yields less satisfaction or is unfordable. The slope of the indifference curve and that of the budget line are equal at equilibrium. Marginal rate of substitution (MRS) is the slope of the indifference curve while the slope of the budget line is the ratio of the two prices. Therefore, MRSxy = Px/Py at equilibrium.

Figure 10: Consumer equilibrium