Theory of Consumer Choice
Topic Five

### The Ordinalist or Indifference Curve Approach

There are two main theories of consumer choice which are the ordinalist or indifference curve approach and the cardinalist or marginal utility approach.

The ordinalist or indifference curve approach to consumer theory requires the use of indifference curves and the budget constraints. An indifference curve is a graph that shows combinations of goods that give the consumer equal satisfaction or utility. That is, at each point on the curve, the consumer has no preference for one bundle or combination of goods over another. In other words, they are all equally preferred.

The characteristics or properties of indifference curves are as follows:

• Negatively sloped – this means that as quantity consumed of one good (X) increases, total satisfaction would increase with a fall in the quantity consumed of the other good (Y).
• Complete - all points on an indifference curve are ranked as equally preferred.
• Transitive - if each point on I2 is (strictly) preferred to each point on I1, and each point on I3 is preferred to each point on I2, then each point on I3 is preferred to each point on I1.
• Convex - more of one good will require less than another.

The indifference curve is combined with the budget line (which shows the budget constraint) to produce the optimum position of the consumer. The budget line shows the combination of goods that can be afforded with the current level of income.

In fact, where the indifference curve is tangent to the budget line constitutes the optimum position which is where the arrow is pointing at A in the following graph. Points under this point are attainable but will not result in the consumer maximizing his utility. Points above this optimum point cannot be attained because the consumer cannot afford such combinations of goods with his or her existing income. The consumer is constrained by the budget line which represents his maximum income. The budget line is derived as follows: If income is \$10.00 and there are two products for consumption (x and y), and if the price of x is \$1.00 and the price of y is \$2.00, when the consumer chooses to consume all of x and none of y, his point will be 10 units on the vertical axis. When the consumer consumes all of y and none of x, the budget constraint will be at 5 on the horizontal axis as can be seen in the following graph.

In order for the consumer to consume more of Y he must consume less of X. This is the change in Y divided by the change in X which is the marginal rate of substitution. As we move down the indifference curve, the slope decreases because more and more of Y will require less and less of X. This is what is referred to as diminishing marginal utility. We can also find the slope of the budget line from the equation of the budget line as is stated below:

BL = Px . X + Py . Y

ΔY/ΔX = - Px /Py

Px /Py is the opportunity cost of X in terms of Y.

### Changes in Income

In addition to the change in the price of one of the goods, another important factor that can change is the income of the consumer. As long as the prices remain constant, changing the income will create a parallel shift of the budget constraint. Increasing the income will shift the budget constraint to the right from BC1 to BC2 then to BC3 since more of both products can be bought as seen in the following graph.

### Change in Price

In the case above, we had the situation where income changed while holding the price of both Goods X and Y constant. We now turn to the situation where the price of Good Y changes while holding the price of X and income constant. If the price of Good Y falls from where it is at BC1, then the budget line pivots to BC2 and if price of Good Y further falls, then the budget line further pivots to BC3 because more of Y can now be afforded as can be seen in the following graph. To maximize the utility with the increased budget line, BC3, the consumer will re-allocate consumption to reach the highest available indifference curve which BC3 can touch. This indifference curve is I3, and therefore the amount of good Y bought will shift from Y1 to Y3. Equilibrium for the consumption of Good Y would have risen from e1 to e2 then to e3. The opposite effect will occur if the price of Y increases.

### Hicksian Substitution and Income Effects of Price Change

Every price change can be converted into an income effect and a substitution effect. The substitution effect is basically a price change that changes the slope of the budget constraint, but leaves the consumer on the same indifference curve. This effect will always cause the consumer to substitute away from the good that is becoming comparatively more expensive. The substitution effect can be separated from the income effect using two approaches: the Hicksian and the Slutsky approaches.

To illustrate the Hicksian approach (named after J R Hicks), we have two goods which are X and Y. Assume that the price of Good Y falls from \$2.00 to \$1.00. The budget line will shift from BC1 to BC2 – the consumer will be able to purchase more of Good Y. Resulting from this price fall of Good Y is a new indifference curve I2 and a new equilibrium point B. As a result of this price decline, quantity demanded of Good Y increases from Y1 to Y2 as can be seen in the following graph. This represents the total effect of the price change which is the substitution effect plus the income effect. The substitution effect is the change in consumption pattern of a good due to a change in the relative prices of goods. The income effect is the change in consumption patterns due to the change in purchasing power or real income when the price of one product falls while the price of other products and nominal income remain unchanged.

Now we need to separate these two effects. In order to do so, we need to keep the real income constant i.e., eliminating the income effect to calculate substitution effect. According to the Hicksian method of eliminating income effect, we just reduce consumer’s money income so that the consumer remains on his original indifference curve IC1, A reduction in consumer’s money income is done by drawing an imaginary budget line BC3. At the same time, the new parallel price line BC3 is tangent to the original indifference curve IC1 at point C. Hence, the consumer’s equilibrium changes from point A to point C. This means that an increase in quantity demanded of Good Y from Y1 to Y3 is purely because of the substitution effect. Therefore, the reason for drawing the imaginary line is to keep the consumer on his same level of income because the fall in the price of Good Y caused an increase in real income. In this case, the substitution effect from the fall in the price of Good Y is from A to C or from Y1 to Y3 and the income effect is from C to B or from Y3 to Y2. It must be remembered though that the separation of the substitution effect from the income effect assumes that nominal income and the price of the other good (Good X in our case) remain unchanged.

### Slutsky’s Substitution and Income Effects of Price Change

The Slutsky’s approach (named after Eugene Slutsky) is a bit different from the Hicksian approach to separating the substitution effect from the income effect. Again, we are assuming that the price of Good Y falls from \$2.00 to \$1.00 and income and the price of Good X remain unchanged. The initial budget line is BC1 and initial indifference curve I1. The consumer’s original equilibrium point (before price effect takes place) is A where the indifference curve I1 is tangent to the budget line BC1. Now if the price of Goof Y falls, the consumer will shift to another equilibrium point B where a new indifference curve I2 is tangent to the new budget line BC2. The movement from equilibrium point A to B means that purchases of Good Y has increased from Y1 to Y2. This is the total price effect caused by the decline in the price of Good Y. Now in order to isolate the substitution effect from the income effect, Slutsky suggests that consumer’s money income should be reduced in such a way that he returns to his original equilibrium point A even after the price change. This is so in order for the consumer to purchase at least his original consumption bundle, i.e., OA of quantity of Good X and OY1 of Good Y at the new price level as is seen in the following graph.

The separation of the substitution effect from the income effect is done by drawing a new budget line (an imaginary budget line) BC3 which passes through original equilibrium point A but is parallel to BC2. This means that the consumer’s money income has been reduced by the difference between BC2 to BC3 to eliminate the income effect. Therefore, the only possibility of price effect is the substitution effect. As a result of this substitution effect, the consumer moves from equilibrium point A to C or from Y1 to Y3 where indifference curve IC3 is tangent to the imaginary budget line BC3. This is the substitution effect. The income effect is from C to B or Y3 to Y2. In the Hicksian approach, there are two indifference curves but in the Slutsky approach, there are three indifference curves.

### Negative Income Effects

In some cases, both the substitution and income effects go in a positive direction. However, there can be cases where the income effect can be negative as can be seen in the following graph. In this case, the substitution effect goes in a positive direction from A to C or Y1 to Y3 but the income effect goes in a negative direction from C to B or Y3 to Y2. These resulted when the price of Good Y falling from \$2.00 to \$1.00. However, the positive substitution effect outweighs the negative income effect with the final result being an increase in the demand for Good Y. In this case, the good is a normal good.

There will even be cases where the negative income effect will outweigh the positive substitution effect and the overall effect will be a fall in quantity demanded of Good Y resulting from a fall in the price of Good Y as shown in the following graph. This will be the case for an inferior good where, as real income rises from the fall in the price of Good Y, meaning more can now be purchased from existing income, demand for Good Y will fall. In this case, the equilibrium point was at A on indifference curve I1 and budget line BC1 and level of output was Y1 before the fall in price of Good Y. After the fall in price of Good Y, the equilibrium point moves to point B on indifference curve I2. After adjusting for the consumer remaining at his original level of affordability, substitution effect is from A to C or from Y1 to Y3 and income effect from C to B or Y3 to Y2. Notice that the positive substitution effect which is from A to C or Y1 to Y3 is smaller than the negative income effect which is from C to B or Y3 to Y2; meaning that less of Good Y will be purchased when its price falls and real income increases which is the definition of an inferior good.

### Marginal Utility or Cardinalist Approach

Total utility refers to the total satisfaction that a customer receives from all units of a product consumed. Marginal utility refers to the change in satisfaction that the customer receives from consuming one more or less unit of that product. An important aspect of the marginal utility approach is that of the law of diminishing marginal utility. The law of diminishing marginal utility states that when more and more of a product is being consumed, the consumer will be getting. In marginal utility theory, the analysis can be conceptualized by obtaining the marginal utility to price ratio such as follows:

MUx/Px where

MUx = marginal utility of product X and,

Px = is the price of X

This ratio states the extra utility or satisfaction that a consumer gets from every dollar spent on this good which is Good X in this case. For example, if Good X costs \$5, and the marginal utility of consuming 5 units of Product X is 20, then the MUx/Px , will be: 20/5 = 4 utils per dollar. As a rule using the marginal utility approach, in order to maximize utility, the consumer must allocate his expenditures so that the marginal utility per dollar spent on Good X is equal to the marginal utility per dollar spent on Good Y. This can be stated as:

MUx/Px = MUy/Py

where

MUx = marginal utility of Good X and

Px = is the price of Good X

MUy = marginal utility of Good Y and

Py = is the price of Good Y.

Technically, the MUx/Px can assist consumers in choosing which goods to increase his or her consumption of or it can be used to assist consumers in ranking goods according to preference.

If MUx/Px > MUy/Py

then we know that Good X is preferred to Good Y because the former will be giving the consumer more utility or satisfaction. Therefore, Good X is preferred to Good Y. The opposite happens if

MUx/Px < MUy/Py

In this case, the consumer will prefer Good Y to Good X because he will be getting more utility from Good Y than from Good X.

The best position will be for the consumer to choose:

MUx/Px = MUy/Py

In this case, the consumer will not have any reason to consume more of either Good X or Good Y. Once one side of the equation is greater than the other, the consumer can arrange his expenses so that they become equal. For example, if a person’s utility of Good X is three times greater than his utility of Good Y, for that consumer to be maximizing his utility, he must increase his consumption of Good X by 1 unit and decrease consumption of Good Y by 1 unit. Due to the law of diminishing marginal utility, his utility for both Goods X and Y will now be equal at 2.