Isoquant Curve

    By Aarti ECE  

An isoquant (derived from quantity and the Greek word iso, meaning equal) is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. While an indifference curve mapping helps to solve the utility-maximizing problem of consumers, the isoquant mapping deals with the cost-minimization problem of producers. Isoquants are typically drawn on capital-labor graphs, showing the technological tradeoff between capital and labor in the production function, and the decreasing marginal returns of both inputs. Adding one input while holding the other constant eventually leads to decreasing marginal output, and this is reflected in the shape of the isoquant. A family of isoquants can be represented by an isoquant map, a graph combining a number of isoquants, each representing a different quantity of output. Isoquants are also called equal product curves.

                      Production Isoquant/Isocost Curve

An isoquant shows the extent to which the firm in question has the ability to substitute between the two different inputs at will in order to produce the same level of output. An isoquant map can also indicate decreasing or increasing returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. Conversely, if the distance is decreasing as output increases, the firm is experiencing increasing returns to scale; doubling both inputs results in placement on an isoquant with more than twice the output of the original isoquant.

As with indifference curves, two isoquants can never cross. Also, every possible combination of inputs is on an isoquant. Finally, any combination of inputs above or to the right of an isoquant results in more output than any point on the isoquant. Although the marginal product of an input decreases as you increase the quantity of the input while holding all other inputs constant, the marginal product is never negative in the empirically observed range since a rational firm would never increase an input to decrease output.

                          SHAPE OF ISOQUANT                                                                                                                                                                                                                                                                                                     

If the two inputs are perfect substitutes, the resulting isoquant map generated is represented in fig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging rate. The perfect substitute inputs do not experience decreasing marginal rates of return when they are substituted for each other in the production function.

If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level of production Q3, input X and input Y can only be combined efficiently in the certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize profit.

Isoquants are typically combined with isocost lines in order to solve a cost-minimization problem for given level of output. In the typical case shown in the top figure, with smoothly curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear and downward sloped; any point of tangency between an isoquant and an isocost curve represents the cost-minimizing input combination for producing the output level associated with that isoquant. A line joining tangency points of isoquants and isocosts (with input prices held constant) is called the expansion path.^[

The only relevant portion of the isoquant is the one that is convex to the origin, part of the curve which is not convex to the origin implies negative marginal product for factors of production. Higher isoQuant higher the production.

                                                            An isoquant map where Q3 > Q2 > Q1. A typical choice of inputs would be labor for input X and capital for input Y. More of input X, input Y, or both is required to move from isoquant Q1 to Q2, or from Q2 to Q3                                                                              

                              

  A) Example of an isoquant map with two inputs that are perfect substitutes  M                                                                                       

   B) Example of an isoquant map with two inputs that are perfect complements

                                                                                                 

                                                                  Note                                                                                                         

 (1)         Thus we can say,isoquant curve is an extension of indifference curve analysis from the theory of consumption to the theory of production.these curve is a technical relation showing how inputs are converted in to output

(2)           A point on the isoquant curve is technically efficient.

 (3) MARGINAL RATE OF SUBSTITUTION-  (a)  The rate at which one factor must be added to compensate for the loss of another factor, to keep output constant  

(b) It is the slope of isoquant curve

(4) Isoquant curve is bowed inward because of the law of diminishing marginal productivity.                                                                       

Laws of Returns The Isoquant Isocost Approach

Isoquants

            An Isoquant is a curve on which the diverse mixtures of labour and capital prove the same productivity. As per Cohne and Cyret “An isoproduct curve is a curve along which the maximum achievable rate of production is constant.” It is also identified as a production indifference curve or a constant product curve. Just as an indifference curve representing the various mixtures of any two products that offer the consumer the same amount of satisfaction – iso utility, likewise an Isoquant designates the an assortment of mixtures of two aspects of production which offer the manufacturer the equal intensity of productivity per unit of time.

Isoquants Vs. Indifference Curve

            An Isoquant is equivalent to an indifference curve in a quantity of ways. In it, two factors (labour and capital) reinstate two articles of consumption. An Isoquant presents same amount of goods while in indifference curve gives same amount of contentment at all points. The properties of Isoquants as we are going to discuss are unerringly to those of indifference curves. Nevertheless there are definite differences amidst the two.

1. An indifference curve embodies contentment which cannot be calculated in physical units.

2. On an indifference sketch, one can only say that a higher indifference curve gives many contentment than a lower one, however it cannot be said how much more or less contentment is being derived from one indifference curve corresponding to the other whilst one can easily judge by how much productivity is greater on a higher Isoquant relating to a lower Isoquant.

Properties of Isoquant

1. Isoquants are negatively inclined – If they do not posses such a slope definite logical irrationality occurs. If the Isoquants inclines rising to the right, it entails that both capital and labour augment except they produce the same productivity.

2. An Isoquant lying above and to the right of one more stands for a advanced productivity level.

3. No Isoquants can intersect each other. In the illogical sense if they tend to intersect each other, those combinations cannot be both less and more productive at the same time. Therefore, two Isoquants cannot intersect each other at any point.

4. Isoquants need not be corresponding since the rate of substitution amidst two factors is not essentially the same in all Isoquant programmes.

5. Amidst two Isoquants there can be a number of Isoquants presenting diverse levels of productivity which the mixture of the two aspects can capitulate.

6. Units of productivity presented on Isoquants are random or any other variables can be presented.

7. No Isoquants can touch either axis – If it touches X axis, it would indicate that the product is being produced with the help of labour only devoid usage of capital. Hence this fact is logically incorrect and the actuality is they can touch the axis.

8. Each Isoquant is convex to the origin – As further units of labour are engaged, lesser and lesser units of capital are used. Thus the Isoquants are convex to the origin due to diminishing marginal rate of substitution.

9. Ridge Lines are the locus of the points of Isoquants where the marginal products of factors are nil. The top ridge line entails nil MP of capital while the lower, nought MP of labour. Manufacture methods are merely competent within the ridge lines. The marginal products of factors are negative and techniques of production are incompetent external the ridge lines. Thus ridge lines show the fiscal area of manufacture.

Isocost curves and Expansion Path

            After learning the nature of Isoquants that represents the possible productivity of a firm from a given combination of two contributions, we surpass the next aspect, prices of contributions that are represented on the Isoquant sketch by the Isocost curves. These curves are also acknowledged as cost lines, price lines, input price lines, factor cost lines, constant outlay lines etc. Each Isoquant curve corresponds to the diverse combinations of two inputs that a firm can purchase for a given sum of money at the given price of each input.

The principle of Marginal Rate of Technical Substitution

            The principle of marginal rate of technical substitution is based on the production function where two factors can be substituted in diverse magnitude in such a way as to manufacture a stable intensity of productivity. Salvatore defines as “The marginal rate of technical substitution is the amount of an output that a firm can give up by increasing the amount of the other input by one unit and still remain on the same Isoquant.”

The Law of Variable Proportions

            The performance of the law of variable proportions are of short run production function when one factor is invariable and the other variable, can also be explained in the terms of Isoquant analysis. For instance, capital is a fixed factor and labour is a variable factor. The portion of the Isoquant that lies outside the ridge lines, the marginal product of that factor is negative.

The Laws of Returns to Scale: Production Function with two variable inputs

The laws of returns to scale can also be elucidated in stipulations of the Isoquant approach. “The laws of returns to scale refer to the effects of a change in the scale of factors upon output in the long run when the combinations of factors are changed in some proportion.” If by increasing two factors say labour and capital in the same proportion, productivity augments in exactly the same proportion there are invariable returns to the scale.

Increasing Returns to Scale

1. There may be indivisibilities in machines, management, labour, finance etc. A little item of equipment or some activities have a minimum size and cannot be divided into smaller units.

2. Increasing returns to scale also result from specialisation and division of labour, when the scale of firm enlarges, there is a broader exposure for specialisation and division of labour.

3. As the firm enlarges, it enjoys internal economies of production. It may be able to install better machines, sell its products more easily, borrow money cheaply, procure the services of more efficient manager and workers etc.

Decreasing Returns to Scale

1. Indivisible factors may become incompetent and less productive.

2. The firm experiences internal diseconomies. Business may become unwieldy and produce problems of supervision and coordination. Large management creates complexities of control and rigidities.

3. To these internal diseconomies are additional external diseconomies of scale. These occur from higher factor price or from diminishing productivity of the factors.

Constant Returns to Scale

1. The returns to scale are invariable when internal economies enjoyed by a firm are neutralised by internal diseconomies so that productivity amplifies in the same ration.

2. One more reason is the balancing of external economies and external diseconomies.

3. Invariable returns to scale also result when factors of production are perfectly divisible, substitutable, standardised and their supplies are perfectly elastic at given prices.

That’s why in the case of invariable returns to scale, the production function is ‘homogeneous of degree one’.