Indifference curve

Preferencies

The consumer market is facing the choice of many different goods and services. However, to understand the problem choice we make the assumption that there are only two goods. It is unrealistic, but then the theory can be extended to the case of many goods.
Quantities of goods X and Y will be here denoted by x and y, respectively. On the plane, each set of (x; y) defines a point (Fig. 4.1). For example, if X - is an orange, and Y - cakes, then set a = (3, 2) contains 3 oranges and 2 cakes.

Fig. 4.1. Bundles of Goods

It is impossible to construct a theory of consumer choice, not making any assumptions about consumer behavior.
The axiom of completeness. For any two sets of products the consumer can definitely say that one of them is preferable to the other, or both sets for it are equivalent, i.e. for sets a and b, one of the following three relationships: " a preferably than b " or " b preferably than a " or "a and b are equivalent".
Violation of this axiom would mean that consumers behavior is unpredictable.
The axiom of transitivity. If "a is preferable to b" and "b is preferred to c", then it follows that "a is preferable to c".
Unless this condition is satisfied, then it is possible that "a is preferable to b" and "b is preferred to c" and "c is preferable to a". Consumers with these preferences would always want something else. His behavior is not rational.
The assumption of nonsatiation. If there are two different sets of items a = (x_a, y_a) and b = (x_b, y_b), and x_a ≥ x_b, y_a ≥ y_b, then "set a is prefertd to set b", i.e. it is preferable a set of larger amounts of its constituent products.
For example, when performing this assumption in Fig. 4.1 set c = (5, 4) is preferable to set a = (3, 2).
Hence, obviously more desirable points, located to the right or above and less preferred sets are located to the left or below.
The assumption of unsatiation is not called an axiom, since it can not be satisfied. This happens when at least one of the items is "harmful good. For example, fertilizer production also entails the elaboration of substances that pollute the environment.

Indifference curve

How can you describe the consumer preferences? You can use tables, but it is more convenient and intuitive way - it's graphic.
Indifference curve is called the line on which lie the various sets of items that are equivalent to each other.
When the condition of unsaturation is hold the indifference curve has a negative slope. Indeed, take an arbitrary point a on the indifference curve (Fig. 4.2).

Fig. 4.2. The slope of the indifference curve

If we assume that on the same indifference curve lies at a point located to the right or above, we obtain under the assumption of unsatiation, that "is preferable to a", ie "Dialing in is not equivalent to a set, and hence, the point can not belong to a given indifference curve.
Likewise, this indifference curve can not pass through point C, located to the left or below the point as well. Hence, the indifference curve can not go from point A to the right or left-up-down. Therefore, it can go only right and down or left-up, ie it has a negative slope.
In moving along the indifference curve of customer satisfaction remains unchanged. The slope of the indifference curve defines the relationship in which consumer can exchange one commodity for another, no winning or losing in a sense of his preferences (Fig. 4.3).
Marginal rate of substitution MRS of product Y on product X is the amount of product Y, from which a consumer would refuse to obtain an additional unit of a good X.

= . In limit =

Fig 4.3. Marginal rate of substitution

As the shift to the right along the indifference curve of the marginal rate of substitution MRS decreases, since for each additional unit of good X consumer agrees to give less good Y, than for the previous unit of good X. From a mathematical point of view the decreasing MRS means convexity of indifference curve.
Indifference curves do not intersect. Indeed, suppose that some two of them intersect at the point a.
Choose the first indifference curve at point b, and the second - a point c as it is indicated in Fig. 4.4. On the one hand, since the point c is to the right and above the point b, then c is preferably than b.

Fig. 4.4. The intersection of indifference curves

On the other hand, b is equivalent to a and a is equivalent to c. Hence, b is equivalent to c. Contradiction: the assumption about the possibility of intersection of the two indifference curves is incorrect.

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Fig. 4.5. Comparison of the indifference curves

Set of goods, located on the indifference curves farther from the origin is preferable than sets of goods that are closer to the origin.
On two different indifference curves are taken two points a, b, and then point c as it is shown in Fig. 4.5. We have that b the equivalent to c, and c preferably to a. Therefore, b preferable than a.
Consequently, any set on a higher indifference curve is preferable to any set on the lower indifference curve.
The collection of consumer indifference curves is called a chart of his indifference curves. It fully describes his preferences. The consumer seeks to achieve the highest possible indifference curve (the more distant from the origin).

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