Q3. Explain how a product would reach equilibrium position with the help of ISO – Quants and ISO-Cost curve

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ISO-Quants an

ISO-Quants and ISO-Costs

The prime concern of a firm is to workout the cheapest factor combinations to produce a given quantity of output. There are a large number of alternative combinations of factor inputs which can produce a given quantity of output for a given amount of investment. [ad#l]Hence, a producer has to select the most economical combination out of them. Iso-product curve is a technique developed in recent years to show the equilibrium of a producer with two variable factor inputs. It is a parallel concept to the indifference curve in the theory of consumption.

Meaning and Definitions

The term “Iso – Quant” has been derived from ‘Iso’ meaning equal and ‘Quant’ meaning quantity. Hence, Iso – Quant is also called Equal Product Curve or Product Indifference Curve or Constant Product Curve. An Iso – product curve represents all the possible combinations of two factor inputs which are capable of producing the same level of output. It may be defined as – “ a curve which shows the different combinations of the two inputs producing the same level of output .”

Each Iso – Quant curve represents only one particular level of output. If there are different Iso–Quant curves, they represent different levels of output. Any point on an Iso – Quant curve represents same level of output. Since each point indicates equal level of output, the producer becomes indifferent with respect to any one of the combinations.

Equal Product Combination 

Combinations Factor X (Labor) Factor Y Capital Total Output in units
A 12 1 100
B 8 2 100
C 5 3 100
D 3 4 100
E 2 5 100

In the above schedule, all the five factor combinations will produce the equal level of output, i.e.100 units. Hence, the producer is indifferent with respect to any one of the combinations mentioned above.

Graphic Representation
In the diagram, if we join points ABCDE (which represents different combinations of factor x and y) we get an Iso-quant curve IQ. This curve represents 100 units of output that may be produced by employing any one of the combinations of two factor inputs mentioned above. It is to be noted that an Iso-Product Curve shows the exact physical units of output that can be produced by alternative combinations of two factor inputs. Hence, absolute measurement of output is possible.

Iso – Quant Map

A catalogue of different combinations of inputs with different levels of output can be indicated in a graph which is called equal product map or Iso-quant map. In other words, a number of Iso Quants representing different amount of out put are known as Iso-quant map.

 

Marginal Rate of Technical Substitution (MRTS)

It may be defined as the rate at which a factor of production can be substituted for another at the margin without affecting any change in the quantity of output. For example, MRTS of X for Y is the number of units of factor Y that can be replaced by one unit of factor X quantity of output remaining the same.

Combinations Factor X Factor Y MRTS of
x for y
A 12 1 Nil
B 8 2 4:1
C 5 3 3:1
D 3 4 2:1
E 2 5 1:1

In the above example, we can notice that in the second combination the producer is substituting 4 units of X for 1 unit of Y. Hence, in this case MRTS of Y for X is 4:1.

Generally speaking, the MRTS will be diminishing. In the above table, we can observe that as the quantity of factor Y is increased relative to the quantity of X, the number of units of X that will be required to be replaced by one unit of factor Y will diminish, quantity of output remaining the same. This is known as the law of Diminishing Marginal Rate of Technical Substitution (DMRTS).

ISO-Cost Line or Curve

It is a parallel concept to the budget or price line of the consumer. It indicates the different combinations of the two inputs which the firm can purchase at given prices with a given outlay. It shows two things (a) prices of two inputs (b) total outlay of the firm. Each Iso-cost line will show various combinations of two factors which can be purchased with a given amount of money at the given price of each input. We can draw the Iso-cost line on the basis of an imaginary example.

Let us suppose that a producer wants to spend Rs. 3,000 to purchase factor X and Y. If the price of X per unit Rs. 100 he can purchase 30 units of X. Similarly if the price of factor Y is Rs. 50 then he can purchase 60 units of Y.

When 30 units of factor X are represented on OY – axis and 60 units of factor Y are represented on OX- axis, we get two points A & B. If we join these two points A and B, then we get the Iso-Cost line AB. This line represents the different combinations of factor X and Y that can be purchased with Rs. 3,000.

 

The Iso-Cost line will shift to the right if the producer increase his outlay from Rs. 3,000 to Rs. 4,000. On the contrary, if his outlay decreases to
Rs. 2,000, there will be a backward shift in the position of Iso-cost line.

The slope of the Iso-cost line represents the ratio of the price of a unit of factor X to the price of a unit of factor Y. In case, the price of any one of them changes there would be a corresponding change in the slope and position of Iso-cost line.

 

 

PRODUCERS EQUILIBRIUM (Optimum factor combination or least cost combination).

The optimal combination of factor inputs may help in either minimizing cost for a given level of output or maximizing output with a given amount of investment expenditure. In order to explain producer’s equilibrium, we have to integrate Iso-quant curve with that of Iso-cost line. Iso-product curve represent different alternative possible combinations of two factor inputs with the help of which a given level of output can be produced. On the other hand, Iso-cost line shows the total outlay of the producer and the prices of factors of production.

The intention of the producer is to maximize his profits. Profits can be maximized when he is producing maximum output with minimum production cost. Hence, the producer selects the least cost combination of the factor inputs. Maximum output with minimum cost is possible only when he reaches the position of equilibrium. The position of equilibrium is indicated at the point where Iso-Quant curve is tangential to Iso-Cost line. The following diagram explains how the producer reaches the position of equilibrium.

 

It is quite clear from the diagram that the producer will reach the position of equilibrium at the point E where the Iso-quant curve IQ and Iso-cost line AB is tangent to each other. With a given total out lay of Rs. 5,000 the producer will be producing the highest output, i.e. 500 units by employing 25 units of factors X and 50 units of factor Y. (assuming Rs. 2,500 each is spent on X and Y)

The price of one unit of factor X is Rs.100-00 and that of Y is Rs. 50-00.. Rs.100 x 25 units of 2500 – 00 and Rs. 50 x 50 units of Y = 2500 – 00. He will not reach the position of equilibrium either at the point E1 and E2 because they are on a higher Iso-cost line. Similarly, he cannot move to the left side of E, because they are on a lower Iso-Cost line and he will not be able to produce 500 units of output by any combinations which lie to the left of E.

Thus, the point at which the Iso-Quant is tangent to the Iso-Cost line represents the minimum cost or optimum factor combination for producing a given level of output. At this point, MRTS between the two points is equal to the ratio between the prices of the inputs.

d ISO-Costs The prime concern of a firm is to workout the cheapest factor combinations to produce a given quantity of output. There are a large number of alternative combinations of factor inputs which can produce a given quantity of output for a given amount of investment. Hence, a producer has to select the most economical combination out of them. Iso-product curve is a technique developed in recent years to show the equilibrium of a producer with two variable factor inputs. It is a parallel concept to the indifference curve in the theory of consumption. Meaning and Definitions The term “Iso – Quant” has been derived from ‘Iso’ meaning equal and ‘Quant’ meaning quantity. Hence, Iso – Quant is also called Equal Product Curve or Product Indifference Curve or Constant Product Curve. An Iso – product curve represents all the possible combinations of two factor inputs which are capable of producing the same level of output. It may be defined as – “ a curve which shows the different combinations of the two inputs producing the same level of output .” Each Iso – Quant curve represents only one particular level of output. If there are different Iso–Quant curves, they represent different levels of output. Any point on an Iso – Quant curve represents same level of output. Since each point indicates equal level of output, the producer becomes indifferent with respect to any one of the combinations. Equal Product Combination Combinations Factor X (Labor) Factor Y Capital Total Output in units A 12 1 100 B 8 2 100 C 5 3 100 D 3 4 100 E 2 5 100 In the above schedule, all the five factor combinations will produce the equal level of output, i.e.100 units. Hence, the producer is indifferent with respect to any one of the combinations mentioned above. Graphic Representation In the diagram, if we join points ABCDE (which represents different combinations of factor x and y) we get an Iso-quant curve IQ. This curve represents 100 units of output that may be produced by employing any one of the combinations of two factor inputs mentioned above. It is to be noted that an Iso-Product Curve shows the exact physical units of output that can be produced by alternative combinations of two factor inputs. Hence, absolute measurement of output is possible. Iso – Quant Map A catalogue of different combinations of inputs with different levels of output can be indicated in a graph which is called equal product map or Iso-quant map. In other words, a number of Iso Quants representing different amount of out put are known as Iso-quant map. Marginal Rate of Technical Substitution (MRTS) It may be defined as the rate at which a factor of production can be substituted for another at the margin without affecting any change in the quantity of output. For example, MRTS of X for Y is the number of units of factor Y that can be replaced by one unit of factor X quantity of output remaining the same. Combinations Factor X Factor Y MRTS of x for y A 12 1 Nil B 8 2 4:1 C 5 3 3:1 D 3 4 2:1 E 2 5 1:1 In the above example, we can notice that in the second combination the producer is substituting 4 units of X for 1 unit of Y. Hence, in this case MRTS of Y for X is 4:1. Generally speaking, the MRTS will be diminishing. In the above table, we can observe that as the quantity of factor Y is increased relative to the quantity of X, the number of units of X that will be required to be replaced by one unit of factor Y will diminish, quantity of output remaining the same. This is known as the law of Diminishing Marginal Rate of Technical Substitution (DMRTS). ISO-Cost Line or Curve It is a parallel concept to the budget or price line of the consumer. It indicates the different combinations of the two inputs which the firm can purchase at given prices with a given outlay. It shows two things (a) prices of two inputs (b) total outlay of the firm. Each Iso-cost line will show various combinations of two factors which can be purchased with a given amount of money at the given price of each input. We can draw the Iso-cost line on the basis of an imaginary example. Let us suppose that a producer wants to spend Rs. 3,000 to purchase factor X and Y. If the price of X per unit Rs. 100 he can purchase 30 units of X. Similarly if the price of factor Y is Rs. 50 then he can purchase 60 units of Y. When 30 units of factor X are represented on OY – axis and 60 units of factor Y are represented on OX- axis, we get two points A & B. If we join these two points A and B, then we get the Iso-Cost line AB. This line represents the different combinations of factor X and Y that can be purchased with Rs. 3,000. The Iso-Cost line will shift to the right if the producer increase his outlay from Rs. 3,000 to Rs. 4,000. On the contrary, if his outlay decreases to Rs. 2,000, there will be a backward shift in the position of Iso-cost line. The slope of the Iso-cost line represents the ratio of the price of a unit of factor X to the price of a unit of factor Y. In case, the price of any one of them changes there would be a corresponding change in the slope and position of Iso-cost line. PRODUCERS EQUILIBRIUM (Optimum factor combination or least cost combination). The optimal combination of factor inputs may help in either minimizing cost for a given level of output or maximizing output with a given amount of investment expenditure. In order to explain producer’s equilibrium, we have to integrate Iso-quant curve with that of Iso-cost line. Iso-product curve represent different alternative possible combinations of two factor inputs with the help of which a given level of output can be produced. On the other hand, Iso-cost line shows the total outlay of the producer and the prices of factors of production. The intention of the producer is to maximize his profits. Profits can be maximized when he is producing maximum output with minimum production cost. Hence, the producer selects the least cost combination of the factor inputs. Maximum output with minimum cost is possible only when he reaches the position of equilibrium. The position of equilibrium is indicated at the point where Iso-Quant curve is tangential to Iso-Cost line. The following diagram explains how the producer reaches the position of equilibrium. It is quite clear from the diagram that the producer will reach the position of equilibrium at the point E where the Iso-quant curve IQ and Iso-cost line AB is tangent to each other. With a given total out lay of Rs. 5,000 the producer will be producing the highest output, i.e. 500 units by employing 25 units of factors X and 50 units of factor Y. (assuming Rs. 2,500 each is spent on X and Y) The price of one unit of factor X is Rs.100-00 and that of Y is Rs. 50-00.. Rs.100 x 25 units of 2500 – 00 and Rs. 50 x 50 units of Y = 2500 – 00. He will not reach the position of equilibrium either at the point E1 and E2 because they are on a higher Iso-cost line. Similarly, he cannot move to the left side of E, because they are on a lower Iso-Cost line and he will not be able to produce 500 units of output by any combinations which lie to the left of E. Thus, the point at which the Iso-Quant is tangent to the Iso-Cost line represents the minimum cost or optimum factor combination for producing a given level of output. At this point, MRTS between the two points is equal to the ratio between the prices of the inputs.

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