## Indifference Curve Analysis [Virtual Learning Arcade]

An introduction to indifference curve analysis as part of the labour market simulation in the Virtual Learning Arcade.

### Spotlight on the theory

Indifference Curve Analysis

The aim of indifference curve analysis is to analyse how a rational consumer chooses between two goods. In other words, how the change in the wage rate will affect the choice between leisure time and work time.

Indifference analysis combines two concepts; indifference curves and budget lines (constraints)

The indifference curve

An indifference curve is a line that shows all the possible combinations of two goods between which a person is indifferent. In other words, it is a line that shows the consumption of different combinations of two goods that will give the same utility (satisfaction) to the person.

For instance, in Figure 1 the indifference curve is I1. A person would receive the same utility (satisfaction) from consuming 4 hours of work and 6 hours of leisure, as they would if they consumed 7 hours of work and 3 hours of leisure.

Figure 1: An indifference curve for work and leisure

An important point is to remember that the use of an indifference curve does not try to put a physical measure onto how much utility a person receives.

The shape of the indifference curve

Figure 1 highlights that the shape of the indifference curve is not a straight line. It is conventional to draw the curve as bowed. This is due to the concept of the diminishing marginal rate of substitution between the two goods.

The marginal rate of substitution is the amount of one good (i.e. work) that has to be given up if the consumer is to obtain one extra unit of the other good (leisure).

The equation is below

The marginal rate of substitution (MRS) = change in good X / change in good Y

Using Figure 1, the marginal rate of substitution between point A and Point B is;

MRS = -3 / 3 = -1 = 1

Note, the convention is to ignore the sign.

The reason why the marginal rate of substitution diminishes is due to the principle of diminishing marginal utility. Where this principle states that the more units of a good are consumed, then additional units will provide less additional satisfaction than the previous units. Therefore, as a person consumes more of one good (i.e. work) then they will receive diminishing utility for that extra unit (satisfaction), hence, they will be willing to give up less of their leisure to obtain one more unit of work.

The relationship between marginal utility and the marginal rate of substitution is often summarised with the following equation;

MRS = Mux / Muy

It is possible to draw more than one indifference curve on the same diagram. If this occurs then it is termed an indifference curve map (Figure 2).

Figure 2: An indifference map

The general rule is that indifference curves further too the right (I4 and I5) show combinations of the two goods that yield a higher utility, while curves to the left (I2 and I1) show combinations that yield lower levels of utility.

A Budget Line (budget constraints)

The budget line is an important component when analysing consumer behaviour. The budget line illustrates all the possible combinations of two goods that can be purchased at given prices and for a given consumer budget. Remember, that the amount of a good that a person can buy will depend upon their income and the price of the good.

This discussion outlines the construction of a budget line and how the change in the determinants will affect the budget line.

Figure 3 constructs a budget line for a given budget of £60, £2 per unit of x and £1 per unit of y.

With a limited budget the consumer can only consume a limited combination of x and y (the maximum combinations are on the actual budget line).

A change in consumer income and the budget line

If consumer income increases then the consumer will be able to purchase higher combinations of goods. Hence an increase in consumer income will result in a shift in the budget line. This is illustrated in Figure 4. Note that the prices of the two goods have remained the same, therefore, the increase in income will result in a parallel shift in the budget line.

Assume consumer income increased to £90.

Figure 4: An increase in consumer income

If consumer income fell then there would be a corresponding parallel shift to the left to represent a fall in the potential combinations of the two goods that can be purchased.

A change in the price of a good and the budget line

If income is held constant, and the price of one of the goods changes then the slope of the curve will change. In other words, the curve will pivot. This is illustrated in Figure 5.

Figure 5: A change in price

The reduction of the price of good x from £2 to £1 means that on a fixed budget of £60, the consumer could purchase a maximum of 60 units, as opposed to 30. Note that the price of good y has remained fixed, hence the maximum point for good y will remain fixed.

Indifference analysis combines two concepts; indifference curves and budget lines (constraints)

The first stage is to impose the indifference curve and the budget line to identify the consumption point between two goods that a rational consumer with a given budget would purchase.

The optimum consumption point is illustrated on Figure 6.

Figure 6: The optimum consumption point

A rational, maximising consumer would prefer to be on the highest possible indifference curve given their budget constraint. This point occurs where the indifference curve touches (is tangential to) the budget line. In the case of Figure 6, the optimum consumption point occurs at point A on indifference curve I3.

Indifference analysis can be used to analyse how a consumer would change the combination of two goods for a given change in their income or the price of the good.

The next section looks at the income and substitution effects of a change in price.

If we assume that the good is normal, then the increase in price will result in a fall in the quantity demanded. This is for two reasons; the income effect (have a limited budget, therefore can purchase lower quantities of the good) and the substitution effect (swap with alternative goods that are cheaper).

These two processes can be visualised using indifference analysis (see Figure 7).

Figure 7: An increase in the price of good x (a normal good)

Due to the price of good x increasing, the budget line has pivoted from B1 to B2 and the consumption point has moved.

The decrease in the quantity demanded can be divided into two effects;

The substitution effect

• The substitution effect is when the consumer switches consumption patterns due to the price change alone but remains on the same indifference curve. To identify the substitution effect a new budget line needs to be constructed. The budget line B1* is added, this budget line needs to be parallel with the budget line B2 and tangential to I1.

Therefore, the movement from Q1 to Q2 is purely due to the substitution effect.

The income effect

• The income effect highlights how consumption will change due to the consumer having a change in purchasing power as a result of the price change. The higher price means the budget line is B2, hence the optimum consumption point is Q2. This point is on a lower indifference curve (I2).

Therefore, in the case of a normal good, the income and substitution effects work to reinforce each other.