# Isoquants and MRTS: Solved Questions

#### 1- Explain and illustrate the concept of isoquant.

Ans: The term isoquant has been derived from Greek word ‘iso’ meaning equal and Latin word ‘quantus’ meaning quantity. The ‘isoquant curve’ is, therefore, also known as equal product curve and production indifference curve. In fact, an isoquant is the locus of all the combinations of two factors of production, say, capital and labor which yields equal levels of output to the producer. Since the isoquant represents an equal level of production, it is also called isoproduct curve.

#### Assumptions of isoquant:

1-There are only two inputs,, i.e. capital and labor.
2-There is an operation of law of diminishing marginal rate of technical substitution. (MRTS is the rate at which one input, say labor, is substituted for another input, say capital.)
3-Production function is continuous, inputs are divisible and substitutable to each other.
4-Producer has a production preference schedule.
5-The producer is rational.
6-Transitivity of choice, i.e. if A=B & B=C, A must be equal to C or (A=C)

The concept of isoquant is also illustrated by the help of the following production preference schedule.

 Combinations Capital (K) Labor (L) MRTS(KL)=L/K Output (Units) A 1 13 ..... 100 B 2 9 4 100 C 3 6 3 100 D 4 4 2 100 E 5 3 1 100

In the schedule, combination A consists of 1K+13L and yields 100 units of output. Similarly all other combinations B, C, D & E consisting 2K+9L, 3K+6L, 4K+4L & 5K+3L each produce the same level of output equal to100 units. Since, all combinations on an iso-quant yield equal level output for the producer, he is indifferent to any of combinations when it is the time to choose a combination.

The above production preference schedule is presented in a diagrammatic form to derive an isoquant curve as shown in the figure.
In the fig, IQ is the isoquant representing the combinations A, B, C, D & E containing different units of two factors of production, capital & labor which yield the same level of output to the producer equal to 100 units.

#### 2- What do you mean by isoquant? Explain the properties of isoquant.

Ans: To answer to the first part of the question, see the answer to the question number 1.

#### Properties of isoquant

There are various properties of Iso-quants as given below.

#### 1- Higher IQ represents higher level of output

Higher IQ represents higher level of output and lower IQ represents lower level of output. It is because each of the combinations on the upper IQ curve consists more of either K or L inputs or both.

In the above figure, combination B which lies on the upper IQ represents more of K & L inputs than combination A on lower IQ.

#### 2- IQs do not intersects each other

Each of the IQ represents a particular level of output so can not intersect each other. If it does, it violates the assumption of IQ as shown in the figure below.

In the above figure, A=B and A=C, So B should have been equal to C but it is not so. It shows B≠C because IQ2 has intersected IQ1 which is absurd.

#### 3-IQ is convex to the origin

An IQ is always convex to the origin due to diminishing marginal rate of technical substitution.  The MRTS of one input for another declines when more and more of one input is substituted for another. Only a convex IQ represents diminishing MRTS. So it is always convex to the origin as shown in the figure below.

When it is concave, it represents increasing MRTS which is absurd to the rule of IQ.

#### 4- IQ does not touch either axis.

An IQ never touches any of the axes. If it touches any of the axes as shown in the following figure, it will be the absurdity of IQ.

In the figure, on IQ1 at point A the producer is having OA of capital input but none of labor and at point B on IQ2, he is having OB of labor input but none of capital.

#### 5- IQ is sloping downward

An IQ is sloping downward from left to right because when the producer wants to have more than one input, the quantity of other input decreases so that he has the same level of output.  So IQ is neither vertical nor horizontal and nor sloping upward. It is sloping downward as shown in the following figure.

#### 3- What do you mean by isoquant map?

Ans: Isoquant map is a set or a collection of isoquant curves in which each of the curves representing different level of output. In the isoquant map a higher isoquant represent higher level of output because the higher isoquant contains more units of both inputs or more units of at least one input. On the contrary, a lower isoquant represent lower level of output because it contains only a few units of both inputs or a few units of at least on input. The following figure shows the isoquant map.

The above figure shows a set of isoquant in which there are three isoquants, IQ1, IQ2 and IQ3, each of them representing different level of output. Higher isoquant representing higher level of output whereas lower isoquant representing lower level of output.

#### 4- Explain the law of diminishing marginal rate technical substitution (MRTS).

Ans: The marginal rate of technical substitution is an important tool of producer’s indifference (IQ) curve analysis. MRTS is the rate at which units of two inputs are exchanged to or substituted for each other in such a way that the level of output remains the same. In other words, MRTS of capital K for labor L MRS_(KL) is the unit of L that will be given up for obtaining each additional unit of K.

Symbolically, it is expressed as;

MRTS_(KL)=-\frac{ΔL}{ΔK}

The concept of MRTS can be more clear by the help of the following schedule and diagram.

 Combinations Capital (K) Labor (L) MRTSKL= -L/K A 1 18 - B 2 13 -5 C 3 9 -4 D 4 6 -3 E 5 4 -2 F 6 3 -1

The initial combination of the inputs capital and labor is A, by which the producer can produce some certain amount of output. At combination B, the producer is ready to give up 5 units of L for obtaining an extra unit of K for the same level of output. The MRTSKL is -5. So the marginal rate of substitution is the number of the unit of K for which the number of L are given up. As the producer proceeds to have an additional unit of K, he wills to give away less and less units of L for the same level of output.This is why the MRTS falls from -5 to -4, and -4 to -3 and so on up to the sixth combination F as shown in the above schedule.

Diagrammatically,

In the above diagram, IQ curve is sloping downward. The substitution of labor for capital is diminishing.