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The laws of returns to scale can also be explained in terms 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, output increases in exactly the same proportion, there are constant returns to scale. If in order to secure equal increases in output, both factors are increased in larger proportionate units, there are decreasing returns to scale. If in order to get equal increases in output, both factors are increased in smaller proportionate units, there are increasing returns to scale. The long-run production function of a firm involving the usage of two factors, say, capital and labour is represented by equal-product curve or isoquant.

The line CD represents the price ratio of capital and labour. After knowing the nature of isoquants which represent the output possibilities of a firm from a given combination of two inputs. We further extend it to the prices of the inputs as represented on the isoquant map by the iso-cost curves. This tendency of diminishing marginal substitutability of factors is apparent from Table 2 and Figure 11. If it is horizontal the quantity of labour increases, although the quantity of capital remains constant. When the amount of capital is increased, the level of output must increase.

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It is also called Leontief isoquant, after Leontief , who invented input-output analysis. In case of perfect complement factors, vertical portion of isoquant shows zero marginal product of capital while horizontal portion shows zero marginal product of labor. With the help of Isoquant diagram, we can draw the difference between returns to scale and returns to factor.

Isoquants are downward-sloping and convex like indifference curves. On isoquant Q1, the MRTS falls from 2 to 1 to 2/3 to 1/3. Isoquants are convex — the MRTS diminishes as we move down along an isoquant. Constant returns to scale takes place when output increases proportionately to the increase in input. There are constant returns to scale when output increases proportionately to the increase in input.

Hence, when there is an increase in scale of production by an increase of all inputs, the productivity of the large indivisible factors enhances manifold resulting in increasing returns to scale. This implies that the slope of the isoquant diminishes from left to right along the curve. This is because of the operation of the principle of diminishing marginal rate of technical substitution. An important feature of marginal rate of technical substitution is that it diminishes along isoquant, which is called principle of diminishing marginal rate of technical substitution. And, this principle of diminishing marginal rate of technical substitution imply that fewer and fewer amount of capital is needed to use one more additional unit of labor. The result states that marginal rate of technical substitution equals and inversely relates to the ratio of marginal products, or productivity, of two factors.

## What is Consumer equilibrium under the isoquant framework

The chapter examines the theory of production or how firms organize production i.e. how it combines resources or inputs to produce final commodities. Production theory is extended to deal with two variable inputs by the introduction of isoquants. From the theory of production where only one or two inputs are variable, we proceed to examine cases in which all inputs are variable. Factors having negative marginal product are called inferior factors, and we ruled out such inferior factors in production theory unless otherwise mentioned.

At some critical price ratio, the optimum input mix will shift from all input A to all input B and vice versa in response to a small change in relative prices. In economics, an isoquant curve or indifference curve represents a set of bundles that give a consumer the same utility level. The consumer has an equal preference for all bundles on the curve. It can be used to illustrate either attainable or optimal production possibilities in limited circumstances.

## Selection of the Optimum or Least Cost Combination:

Isoquant of a rational producer is convex towards the origin. Also, it shows decreasing MRTS as one factor is substituted for the other. The isoquant curve can present as an algebraic equation or as a schedule or as a graph. In the same manner, slop of iso-cost line will change when interest rate changes and it may become steeper or flatter. In the Figure 8.8 , the iso-cost line becomes flatter when interest rate increases and becomes steeper when the interest rate falls.

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At point B on IQ1, MPL is zero and beyond point B on IQ1, MPL is negative. An isoquant is the set of all possible combinations of the two inputs that yield the same maximum possible level of output. Each isoquant represents a particular level of output and is labelled with that amount of output. It is just an alternative way of representing the production function.

In this case, assume that the level of output and factor prices are given. Assume that producer is at point A on the isoquant curve, which produces q1 units by using the L1K1 input combination. Suppose that producer moves along the isoquant from A to B.

## Isoquant map

The use of sixth unit of labour does not add anything to the total production of the commodity . Hence, the marginal product of labour has fallen to zero. Beyond the use of the sixth unit of labour, total product diminishes and therefore marginal product of labour turns out to be negative. The average product of labour rises up to the use of third unit of labour and beyond unit of labour that it is Ming throughout. You can observe outlines of equal heights above KL plane corresponding to Q1 and Q2 level of outputs. These outlines are termed as isoelevation contours, and are as equal in height as corresponding Q1 and Q2 output levels.

To explain the law, capital is taken as a fixed factor and labour as a variable factor. The isoquants show different levels of output in the figure. ОС is the fixed quantity of capital which therefore forms a horizontal line CD.

One important thing to consider here is that, not every input combinations are economically feasible to use in production. Therefore, a rational producer will abandon those unfeasible input combinations unless she is compensated for the use of those input combinations. These unfeasible input combinations are represented by positively sloped portion of isoquant. As we move along these lines the amount of one input varies while of the other remains constant. Thus proportion between the two outputs undergoes a change.

## Properties of Iso-quant Curve

It has been already noted that isoquants are negatively sloped. But if it is specified that Marginal Rate of Technical Substitution is diminishing for a curve, it automatically implies that the curve is convex to the origin. Downward or negative slope of isoquant implies substitutability among factors of production. Any point on the isoquants outside the upper ridge line OR and the lower ridge line OL constitute uneconomic region of production. Note that the ridge lines separate the relevant (i.e., negatively sloped) from the irrelevant portions (i.e., positively or zero sloped) of the isoquants. Thus, points between A and B represent positive marginal productivities of both labour and capital.

We consider the production of a good, X, and suppose that only two factors of production— labour and capital—are employed. In principle, the marginal product of factor inputs assume any value positive, negative or zero. But, the rational producer does not employ an input when its marginal product is negative. An iso-cost line is drawn on two assumptions – First, at given total outlay of the firm and, second, at given factor prices. Thus, an iso-cost line will shift either because of a change in total outlay or a change in factor prices. This type of isoquant are depicted by a straight line sloping downward from left to right, as shown in Figure-8.6 .

- There comes a point, where employing more workers barely saves any capital at all.
- This indicates that one factor can be used a little more and other factor a little less, without changing the level of output.
- In addition, I request you to go through the concept of production function, which will presumably ease your learning journey ahead.
- For example, when labour is increased from 1 unit to 2 , output increases by 10.
- In Figure 24.3 combination В on IQ1 curve shows larger output than point A on the curve IQ.

Each isocost curve represents the different combinations of two inputs that a firm can buy for a given sum of money at the given price of each input. Marginal rate of technical substitution is a slope of isoquant which indicates the rate at which factor inputs can be substituted for so as to maintain the same level of output represented by isoquant. More specifically, marginal rate of technical substitution of labor for capital, MRTSL,K, is the rate at which one unit of labor substitutes for units of capital holding constant the level of output.

To circumvent this problem, another better measure of the slope of iso-quant explains substitution comes to play – which is elasticity of technical substitution, or simply elasticity of substitution. The line RP shows how larger quantities of labour can be employed to expand production. 3 shows that when the amount of labour is increased from OL to OL1, the amount of capital has to be decreased from OK to OK1, The iso-product curve is falling as shown in the figure. The iso-product map looks like the indifference of consumer behaviour analysis.

## Business Economics Tutorial

From the above schedule iso-product curve can be drawn with the help of a diagram. Equal product curve represents all those combinations of two inputs which are capable of producing the same level of output. 1 shows the various combinations of labour and capital which give the same amount of output.

That is, production function is of ‘variable proportion’ type rather than fixed proportion. MRTS is a rate at which units of two inputs are substituted with each other to maintain the same level of output. The Marginal Rate of Technical Substitution of K for L is defined as the amount of K, the producer can give up to get one more unit of L and maintain the same level of Output. The isoquant in which there can be only two possible combinations say A and B, except this the two factors of production are incapable of substituting each other. Property 5− The isoquant curve curve should not cross either the X-axis or the Yaxis of the graph in any way as the rate of technical substitution will be rendered null and invalid.

Normally, https://1investing.in/s are downward sloping from left to right. As we move from left to right along an isoquant, value of MRTS diminishes. Let us explain this point with the help of a diagram (see figure 8.6). The above table tells us that to produce 50 units of output, the producer can choose 1 unit of labour and 15 units of capital (i.e., combination A). However, if he chooses combination B or C or D or E, the same volume of output will be obtained.