units of it

units of it. If the price of apple becomes much cheaper he may give up orange altogether.
On the other hand, if the price of apple becomes very high he may be forced by lack of means to give up apple. Between these two extremes he will purchase both apple and orange, but will vary the proportions according to relative prices so that he obtains the advantages of small price changes of either commodity. It follows, therefore, that there are more than one combinations of apple and orange which are equally satisfactory to him.
Suppose the following combinations are equivalent:
(a) 1 unit of apple and 4 units of orange
(b) 2 units of apple and 3 units of orange
(c) 3 units of apple and 2 units of orange
(d) 4 units of apple and 1 unit of orange
An Indifference Curve:
These combinations are represented by small circles in Fig. 4.7 where apple is measured on the horizontal axis and orange on the vertical axis. There may be many other such combinations. Let I be a continuous line joining the small circles and other similar points. The curve I1 is called an indifference curve.
Thus an indifference curve may be defined as a curve which shows combinations of goods which are equivalent to one another. It is a locus of points sharing alternative combinations of apple and orange which give the same satisfaction to the consumer. The consumer has no reason to prefer any of the combinations on the curve to any other on the same curve. He is indifferent as to which of these combinations he uses. Each indifference curve is an equal-utility curve.

Assumptions:

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The indifference curve approach is based upon the following assumptions:

1. Non-Satiety:
A rational person will prefer a larger quantity of a good than a smaller amount of it.
2. Transitivity:
The consumer is supposed to be consistent about his tastes and pre¬ference.
3. Diminishing Marginal Substitutability:
Suppose a consumer buys orange and apple. It can be assumed that as more and more of units of apple are substituted for orange, the consumer will be willing to give up fewer and fewer units of orange for additional units of apple. As the quantity of orange consumed increases, more of it will be required to compensate for loss of apple. This follows from the principle that as the consumption of orange increases the desire for it will fall and as the consumption of apple decreases the desire for it will increase.
Therefore, the marginal rate of substitution of orange for apple increases as the quantity of orange increases relatively to apple. Alternatively we can say that the marginal rate of substitution of orange for apple diminishes as the supply of apple diminishes. This is called the Principle of Diminishing Marginal Substitutability. It is assumed that the two goods are not perfect substitutes for one another and that want for the goods are not satiable.
Properties (Characteristics) of Indiffe¬rence Curves:

Indifference curves have the following four properties:

1. An indifference curve which lies above and to the right of another shows preferred combinations of the two commodities.

2. Indifference Curves Have a Negative Slope:
when the quantity of one commodity (A) in a combination of two goods increase, the quantity of the other commodity (O) must decline. Therefore, an indifference curve must slope downwards from left to right.
The Marginal Rate of Substitution:

Definition:
The slope of the indifference curve is called the MRS which is the ratio of the marginal utilities of the two commodities. This is expressed as
MRS x,y = – ?Y /?X = MUx/MUy

3. An Indifference Curve cannot Intersect or Touch Another Indifference Curve:
This can be proved by showing that if two indifference curves on the same indifference map intersect, there is logical contradiction (or inconsis¬tency). Suppose I1, and I2 intersect as in Fig 4.8, then from I1.

This explains why indifference curves cannot intersect.
… Transitivity implies that if A is preferred to B and B is preferred to C then A is preferred to C.

4. Indifference Curves are Convex to the Origin:

Conclusion:
Thus it is concluded that
(i) each indifference curve is a distinct line;
(ii) it slopes downwards from left to right and
(iii) it is convex to the origin.
There are, however, certain exceptions to rule 3. Under certain special circumstances an indifference curve may be a straight line or even concave to the origin.

ISOQUANT CURVE:
The term Iso-quant or Iso-product is composed of two words, Iso = equal, quant = quantity or product = output.
Thus it means equal quantity or equal product. Different factors are needed to produce a good. These factors may be substituted for one another.
A given quantity of output may be produced with different combinations of factors. Iso-quant curves are also known as Equal-product or Iso-product or Production Indifference curves. Since it is an extension of Indifference curve analysis from the theory of consumption to the theory of production.
Thus, an Iso-product or Iso-quant curve is that curve which shows the different combinations of two factors yielding the same total product. Like, indifference curves, Iso- quant curves also slope downward from left to right. The slope of an Iso-quant curve expresses the marginal rate of technical substitution (MRTS).
Definitions:
“The Iso-product curves show the different combinations of two resources with which a firm can produce equal amount of product.” Bilas
“Iso-product curve shows the different input combinations that will produce a given output.” Samuelson
“An Iso-quant curve may be defined as a curve showing the possible combinations of two variable factors that can be used to produce the same total product.” Peterson
“An Iso-quant is a curve showing all possible combinations of inputs physically capable of producing a given level of output.” Ferguson
Assumptions:
The main assumptions of Iso-quant curves are as follows:
1. Two Factors of Production:
Only two factors are used to produce a commodity.
2. Divisible Factor:
Factors of production can be divided into small parts.
3. Constant Technique:
Technique of production is constant or is known beforehand.
4. Possibility of Technical Substitution:
The substitution between the two factors is technically possible. That is, production function is of ‘variable proportion’ type rather than fixed proportion.
5. Efficient Combinations:
Under the given technique, factors of production can be used with maximum efficiency.
Properties of Iso-Product Curves:

The properties of Iso-product curves are summarized below:

1. Iso-Product Curves Slope Downward from Left to Right:
They slope downward because MTRS of labour for capital diminishes. When we increase labour, we have to decrease capital to produce a given level of output.
2. Isoquants are Convex to the Origin:
Like indifference curves, isoquants are convex to the origin. In order to understand this fact, we have to understand the concept of diminishing marginal rate of technical substitution (MRTS), because convexity of an isoquant implies that the MRTS diminishes along the isoquant. The marginal rate of technical substitution between L and K is defined as the quantity of K which can be given up in exchange for an additional unit of L. It can also be defined as the slope of an isoquant.
It can be expressed as:
MRTSLK = – ?K/?L = dK/ dL
Where ?K is the change in capital and AL is the change in labour.
Equation (1) states that for an increase in the use of labour, fewer units of capital will be used. In other words, a declining MRTS refers to the falling marginal product of labour in relation to capital. To put it differently, as more units of labour are used, and as certain units of capital are given up, the marginal productivity of labour in relation to capital will decline.
Thus it may be observed that due to falling MRTS, the isoquant is always convex to the origin.

3. Two Iso-Product Curves Never Cut Each Other:
As two indifference curves cannot cut each other, two iso-product curves cannot cut each other.. Therefore two curves which represent two levels of output cannot intersect each other.

4. Higher Iso-Product Curves Represent Higher Level of Output:

A higher iso-product curve represents a higher level of output

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