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Explain why indifference curves are usually drawn convex to the origin, are downward sloping and do not cross each other. [12]

[CIE A level March 2019]

Tip : Provide a a clear analysis of ICs and consider all three parts of the question.Including diagrams will help in explanations.

Step ➊ : Define 'indifference curve' in the introduction.

An indifference curve shows all combinations of goods that provide an equal level of utility or satisfaction. Three important features of the indifference curves is that they are usually drawn convex to the origin, are downward sloping and do not cross each other.

Step ➋ : Explain why indifference curves are convex to the origin.

The indifference curve is convex to the origin due to the concept of the diminishing marginal rate of substitution between two goods. The marginal rate of substitution is the rate at which a consumer is willing to substitute one good for another.

In the diagram below, the indifference curve slope more steeply from left to right. This shows that when consuming large amounts of good A, the consumer is willing to give up rather more of this good when consumption of good B is small. The rate at which the consumer is willing to substitute one good for another in this way is known as the marginal rate of substitution

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

MRS = Mux / Muy

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Step ➌ : Explain why indifference curves do not cross each other
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It is impossible for two indifference curves to cross. To understand why this is the case, an example should be taken at what would happen if they did intersect.

In the diagram below, the two indifference curves IC1 and IC2 are cutting each other at point A. The combinations represented by points A and C given equal satisfaction to the consumer because both lie on the same indifference curve IC2. Similarly, the combinations show by points A and D on indifference curve IC1 give equal satisfaction to the consumer.

If combination C is equal to combination A in terms of satisfaction and combination D is equal to combination A in satisfaction, it follows that the combination C will be equivalent to D in terms of satisfaction. However, if we compare point D and point C, we can clearly see that point C offers more of good Y and good X, as compared to point D. Therefore it is impossible for both curves to provide the same level of satisfaction, which means they can never intersect.

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Step ➍ : Explain why indifference curves are downward sloping
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The law of diminishing marginal utility can be used to explain why indifference curves are downward sloping. The Law Of Diminishing Marginal Utility states that all else equal, as consumption increases the marginal utility derived from each additional unit declines. As consumption increases, there may actually come a point where marginal utility is negative, indicating dissatisfaction or disutility.

All indifference curves are downward sloping to indicate that a fall in the quantity consumed of one good is accompanied by an increase in consumption of the other good. If the level of satisfaction is high for the consumption of one good, it will be lower for the consumption of the second good. Thus, the curve must be downward sloping.

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Step ➎ : Conclude (summarise)
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To conclude, the indifference curve is convex to the origin due to the concept of the diminishing marginal rate of substitution between two goods. It is impossible for two indifference curves to cross is as it is impossible for both curves to provide the same level of satisfaction. All indifference curves are downward sloping to indicate that a fall in the quantity consumed of one good is accompanied by an increase in consumption of the other good.

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♕ Marking scheme
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Explanation of diminishing marginal utility, and how more of a good is preferred to less of a good so the curves cannot cross; they have an ‘indifferent’ response along them representing a constant level of utility.

L4 (9–12 marks): for a clear analysis of ICs and all three parts of the question.
L3 (7–8 marks): for a less competent explanation of at least two of the parts of the question or a weaker explanation of all three parts.
L2 (5–6 marks): for a competent explanation of one part or a weak explanation of two elements of the question.
L1 (1–4 marks): for an answer that has some basic correct facts but includes irrelevancies and errors of theory.

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♕ Examiner’s report
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This question asked about indifference curves. It was expected that candidates would give an explanation of the link between the construction of the indifference curve and how a consumer would have an ‘indifferent’ response along them representing a constant level of utility. The link between the downward slope and the principle of diminishing marginal utility, and how more of a good is preferred to less of a good so the curves cannot cross was also necessary. Many answers covered all three elements in the question. The weaker answers did not explain fully enough why the curves were downward sloping.

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