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]]>The minimum price which can induce a firm to produce in the short-run is the one, which just equals AVC. It is also called the shut down point of the competitive firm. The competitive firm closes down the operation, if it is not in a position to cover AVC in the short-run.

When price = MC, the firm would decrease its profits, if, it either increased or decreased its output. For any point to the left of this equilibrium, price is greater than the marginal cost and it pays to increase output. Similarly, for any point to the right of this equilibrium, price is less than the marginal cost and it pays to reduce output.

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]]>Fig. 9.2: Total Fixed Cost, Total Variable Cost and Total Cost Curves

Total variable cost curve starts from the origin indicating that when output is zero, variable cost is nil. Further, the variable cost has a rising trend from left to right. Variable cost initially rises at decreasing rate, then, at increasing rate corresponding to the growth of total product (TP) at increasing rate and decreasing rate respectively. This is clear from the comparison of the shapes of TVC and TP curves.

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]]>Total fixed cost is a constant quantity. As the output increases, the total fixed cost spreads out over more and more units and therefore average fixed cost becomes lesser and lesser. When output becomes very large, average fixed cost approaches zero. Business Executives refer to it as ‘speeding the overheads’.

It will be seen that average fixed cost (AFC) falls continuously, as more units are being produced at the same fixed expenses. AFC corresponding to any point on the TFC curve is equal to the slope of the ray from origin to that point, i.e., perpendicular (total fixed cost) divided by base (total output) or tangent of the angle made by the ray with the X-axis.

Graphically, the average fixed cost curve is a downward sloping curve, since the slope of the ray from origin to any point on TFC curve decreases, as one move to the right. It will fall steeply in the beginning and will tend to touch X-axis, but will never become zero.

Similarly, AFC curve can never touch Y-axis. It is so, because, TFC is a positive value at zero output and any positive value divided by zero will provide infinite value. Thus, AFC curve Approaches both the axes asymptotically.

Further, the nature of AFC curve is rectangular hyperbola indicating that every rectangle (TFC = AFC x Q) will be equal to every other rectangle in area. When the output increases by a certain percentage, the average fixed cost decreases by the same percentage such that their product representing total fixed cost remains constant throughout.

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]]>The post What is the Relationship between Product and Cost? – Explained! appeared first on Villagefridays.com.

]]>=> AVC = N x P/Q = P. (1/AP)

Here, ‘P’ is the price per unit of the variable factor.

Substituting equation (9.1) in equation (9.2) we get

AVC=P. (1/AP)

Thus, average variable cost is equal to the price of the input multiplied by the reciprocal of its average product. Given the price of the variable input (P), the average variable cost is equal to the reciprocal of the average product.

In other words, the average variable cost and average product vary inversely with each other. When average product rises in the beginning (as more variable inputs are employed), the average variable cost must be falling. The level of output at-which the average product is maximum, the average variable cost is minimum.

Further, when the average product of the variable input falls, the average variable cost must be rising. The average variable cost (AVC) curve looks like the average product (AP) curve turned upside down with minimum point of the AVC curve corresponding to the maximum point of AP curve.

Likewise, the marginal cost curve in the short run is a mirror image of the marginal product curve, expressed in monetary terms. To prove it, assume that price of the variable input is constant. Now, the change in total variable cost will occur only due to the change in the amount of the variable input.

Therefore,

Thus, marginal cost of production is equal to the price multiplied by the reciprocal of the marginal product of the variable input. Given price of the variable input, marginal cost varies inversely with the marginal product of the variable input.

The fact that marginal product rises initially, reaches a maximum and then falls ensures that the marginal cost curve of a firm first declines, then reaches a minimum and finally rises. The maximum of marginal product corresponds to minimum of marginal cost. The relation between marginal product and marginal cost is quite similar to the relationship between average product and average cost.

The relationship between product curves (average product curve and marginal product curve) and cost curves (average cost curve and marginal cost curve) is graphically shown in Fig. 9.9. While the marginal product intersects average product from above at its maximum point (if AP rises, MP is greater than AP; if AP falls, MP is less than AP and when AP is at its maximum, MP is equal to AP), the marginal cost intersects average cost from below at its minimum point. Average cost and marginal cost are simply the transformation of average product and marginal product respectively from physical terms into money terms.

Fig. 9.9: Relationship between Product and Cost

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]]>The post Useful Notes on the Effect of Change in Factor Prices and Factor Combinations on the Productions appeared first on Villagefridays.com.

]]>By joining various points of equilibrium like ‘E’, ‘F’ and ‘G’ in Fig. 7.14, we get a curve called price factor curve (PFC). The price factor curve may slope upwards or downwards to the right depending upon whether fall (or rise) in the price of factor ‘X’ causes increased (or decreased) purchase of the factor ‘X’ and decreased (or increased) purchase of factor ‘Y’ in the two cases respectively and vice-versa.

The analysis of the distribution of the two effects, i.e., output effect and technical substitution effect is quite analogous to the distribution of price effect under indifference curve analysis between income and substitution effects.

In Fig. 7.15, the total effect of a fall in the price of factor ‘X’ is shown by a movement from point ‘E’ to point ‘F’ which has caused a rise in the employment of factor ‘X’ and an uncertain rise in the employment of factor ‘Y’.

If output is held constant at the original level by nullifying the output effect through an appropriate decline in outlay, the producer would reach at point ‘G’. Now, the movement from point ‘E’ to point ‘G’ is called the technical substitution effect, while the movement from point ‘G’ to point ‘F’ is called the output effect.

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]]>The post What is the Concept of Elasticity of Factor Substitution? – Explained! appeared first on Villagefridays.com.

]]>On the other hand, if wages (price of labour) fall, the producer will use relatively more labour than capital. The manner and the rate at which the two factors will be substituted for each other will depend upon the marginal rate of technical substitution between the factors and change in their relative prices.

Elasticity of factor substitution is defined as the proportionate change in the factor- proportions to the proportionate change in the marginal rate of technical substitution, so that the output remains the same (one moves along an isoquant. It measures the strength of substitution effect. Therefore,

Intuitively, elasticity of factor substitution can also be thought of as a measure of the degree of ease with which one factor is substituted for the other. It can also be conceived as a measure of similarity of factors of production from a technological point of view.

In equilibrium position, the marginal rate of technical substitution in the formula of ‘a’ will be replaced by the ratio of factor prices. Thus, in equilibrium

In practical life, replacement of marginal rate of technical substitution by factor price ratio is helpful, as information regarding latter is easily available. Moreover, changes in factor proportions in which factors are used are generally influenced by relative factor prices only.

Thus, when exogenous input price ratio (PK/PL) change, we expect a simultaneous change in optimal input ratio (L/K) in the reverse direction. The reason is simple. We always substitute relatively cheaper factor for the dearer one. That is, the direction of change is clear, but the extent of input substitution will be measured by the above formula of elasticity of substitution.

Elasticity of factor substitution can take any value from zero to infinity, always being positive. If marginal rate of technical substitution declines slowly, elasticity of substitution between the two factors will be high. If, on the other hand, it declines rapidly, elasticity of substitution will be low. Elasticity of factor substitution is zero for Leontief function, one for Cobb Douglas function and constant for linear and CES function.

The shape of the isoquant is related to its elasticity of substitution. The magnitude of the elasticity of substitution can be assessed by looking at the curvature of isoquants. The greater the convexity of isoquants, the smaller would be the elasticity of substitution.

In the extreme case, when the two factors of production are perfect substitutes, production can be carried through both the factors or through any one of them. Here, both the factors are identical for all purposes. Hence, increase in one factor will be accompanied by a constant decrease in the other factor.

Thus, the marginal rate of technical substitution will be constant and uniform. Further, ?MRTSK, I = 0 or L/K = 0. The isoquants between them will be straight lines. Therefore, a fall in the price of one factor will induce the producer to replace the costly factor completely by the cheaper one. In such a case, the elasticity of substitution between the two factors is infinite.

On the other extreme, suppose the two factors are perfect complements in the sense that both have to be combined in fixed proportions to produce a given output, i.e., ? (K/L) = 0. The marginal rate of technical substitution between such factors will be infinite or zero, as output will not increase by substitution of one factor by the other.

Hence, one and only one combination of inputs can produce specified output. Here, change in the relative price of a factor cannot lead to any substitution and therefore, elasticity of factor substitution is zero and the isoquants will be right angled in such case. Here, MPK = 0 along vertical stretch and MPL = 0 along horizontal stretch of the isoquant.

The elasticity of substitution between factors is simply the ratio of proportionate change in the slopes of two rays from the origin to two points on an isoquant to the proportionate change in the slopes of isoquants at these points (Fig. 7.16).

Therefore, elasticity of substitution

Substitution curve can be plotted (Fig. 7.17) by taking K/L ratio on the X-axis and MRTS on Y-axis. Where the substitution curve AB is steep (above point ‘A’), the elasticity of factor substitution is low. Capital and labour are not good substitutes here.

On the other hand, the elasticity of factor substitution is high in the flat portion of substitution curve (below point ‘B’). In this case, capital and labour are good substitutes. The substitution curve becomes vertical at point ‘C’. Here, a given percentage changes in MRTS fails to bring in change in the capital labour ratio.

Hence, the elasticity of factor substitution becomes zero. On the other extreme, at point ‘D’, the substitution curve becomes horizontal. Here, even no change in MRTS brings an infinitely large change in the capital-labour ratio. Hence, the elasticity of factor substitution is equal to infinity.

Somewhere between points ‘A’ and ‘B’, a given percentage change in MRTS brings an equal change in capital-labour ratio making the elasticity of factor substitution equal to unity. Thus, it is clear that the elasticity of factor substitution increases from zero to infinity, as one move downwards along a substitution curve (Fig. 7.17).

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]]>The post What is the Concept of Elasticity of Factor Substitution? – Explained! appeared first on Villagefridays.com.

]]>On the other hand, if wages (price of labour) fall, the producer will use relatively more labour than capital. The manner and the rate at which the two factors will be substituted for each other will depend upon the marginal rate of technical substitution between the factors and change in their relative prices.

Elasticity of factor substitution is defined as the proportionate change in the factor- proportions to the proportionate change in the marginal rate of technical substitution, so that the output remains the same (one moves along an isoquant. It measures the strength of substitution effect. Therefore,

Intuitively, elasticity of factor substitution can also be thought of as a measure of the degree of ease with which one factor is substituted for the other. It can also be conceived as a measure of similarity of factors of production from a technological point of view.

In equilibrium position, the marginal rate of technical substitution in the formula of ‘a’ will be replaced by the ratio of factor prices. Thus, in equilibrium

In practical life, replacement of marginal rate of technical substitution by factor price ratio is helpful, as information regarding latter is easily available. Moreover, changes in factor proportions in which factors are used are generally influenced by relative factor prices only.

Thus, when exogenous input price ratio (PK/PL) change, we expect a simultaneous change in optimal input ratio (L/K) in the reverse direction. The reason is simple. We always substitute relatively cheaper factor for the dearer one. That is, the direction of change is clear, but the extent of input substitution will be measured by the above formula of elasticity of substitution.

Elasticity of factor substitution can take any value from zero to infinity, always being positive. If marginal rate of technical substitution declines slowly, elasticity of substitution between the two factors will be high. If, on the other hand, it declines rapidly, elasticity of substitution will be low. Elasticity of factor substitution is zero for Leontief function, one for Cobb Douglas function and constant for linear and CES function.

The shape of the isoquant is related to its elasticity of substitution. The magnitude of the elasticity of substitution can be assessed by looking at the curvature of isoquants. The greater the convexity of isoquants, the smaller would be the elasticity of substitution.

In the extreme case, when the two factors of production are perfect substitutes, production can be carried through both the factors or through any one of them. Here, both the factors are identical for all purposes. Hence, increase in one factor will be accompanied by a constant decrease in the other factor.

Thus, the marginal rate of technical substitution will be constant and uniform. Further, ?MRTSK, I = 0 or L/K = 0. The isoquants between them will be straight lines. Therefore, a fall in the price of one factor will induce the producer to replace the costly factor completely by the cheaper one. In such a case, the elasticity of substitution between the two factors is infinite.

On the other extreme, suppose the two factors are perfect complements in the sense that both have to be combined in fixed proportions to produce a given output, i.e., ? (K/L) = 0. The marginal rate of technical substitution between such factors will be infinite or zero, as output will not increase by substitution of one factor by the other.

Hence, one and only one combination of inputs can produce specified output. Here, change in the relative price of a factor cannot lead to any substitution and therefore, elasticity of factor substitution is zero and the isoquants will be right angled in such case. Here, MPK = 0 along vertical stretch and MPL = 0 along horizontal stretch of the isoquant.

The elasticity of substitution between factors is simply the ratio of proportionate change in the slopes of two rays from the origin to two points on an isoquant to the proportionate change in the slopes of isoquants at these points (Fig. 7.16).

Therefore, elasticity of substitution

Substitution curve can be plotted (Fig. 7.17) by taking K/L ratio on the X-axis and MRTS on Y-axis. Where the substitution curve AB is steep (above point ‘A’), the elasticity of factor substitution is low. Capital and labour are not good substitutes here.

On the other hand, the elasticity of factor substitution is high in the flat portion of substitution curve (below point ‘B’). In this case, capital and labour are good substitutes. The substitution curve becomes vertical at point ‘C’. Here, a given percentage changes in MRTS fails to bring in change in the capital labour ratio.

Hence, the elasticity of factor substitution becomes zero. On the other extreme, at point ‘D’, the substitution curve becomes horizontal. Here, even no change in MRTS brings an infinitely large change in the capital-labour ratio. Hence, the elasticity of factor substitution is equal to infinity.

Somewhere between points ‘A’ and ‘B’, a given percentage change in MRTS brings an equal change in capital-labour ratio making the elasticity of factor substitution equal to unity. Thus, it is clear that the elasticity of factor substitution increases from zero to infinity, as one move downwards along a substitution curve (Fig. 7.17).

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]]>In this stage, total product increases at an increasing rate from origin till point ‘C’. It is clear from the Fig. 8.2, where the slope of the total product curve (TP) increases upto point ‘C’ (TP curve is concave upwards upto this point).

Thus, marginal product rises upto point ‘D’ vertically downwards to point ‘C’. This shows that the firm is moving towards optimum combination. Rising marginal product also pulls up the average product. From point ‘C’ onwards during the stage I, the total product continues to rise, but, at a diminishing rate (total product is concave downwards), i.e., marginal product falls, but, is positive.

The point ‘C’ where the total product stops rising at a diminishing rate is called the point of inflexion. The average product, however, will continue to rise even after the point of inflexion, as marginal product (though falling) exceeds its average product.

Rising average product indicates increase in the efficiency of labour. The marginal product of the variable factor is equal to the average product of the factor at point ‘E’.

The stage I end, where the average product reaches its highest point. So, here, efficiency of labour is maximum. This stage is known as the stage of increasing returns, as average product of the variable factor rises throughout the stage and marginal product of the variable factor rises in a significant part of this stage.

In stage I, total product is not fully utilized. The quantity of the fixed factor is too much relative to quantity of variable factor so that if some of the fixed factors are withdrawn, the total product would increase.

Thus, in the first stage, marginal product of the fixed factor is negative. No rational producer will choose to produce in this stage even if the fixed factor costs nothing (in which case, he will stop at the end of first stage, i.e., at point ‘A’). Producer can expand production by increasing quantity of the variable factor and make efficient use of the fixed factor.

In stage II, the total product continues to increase at a diminishing rate, until it reaches the maximum point ‘F’ where the second stage ends. In this stage, both the average product and marginal product of the variable factor are diminishing (but not negative), the latter falling at faster rate.

That is why; this stage is known as the stage of diminishing returns. With falling average product curve, efficiency of variable factor decreases and that of fixed factor continues to rise. The average product of the variable factor exceeds the marginal product of the factor throughout this stage.

At the end of second stage, i.e., at point ‘B’, marginal product of the variable factor is zero (corresponding to the highest point ‘F’ of the TP curve). This stage is very crucial. It is the stage of operation. A rational producer will always seek to produce in this stage, where both the average and marginal product are falling.

In the words of Joan Robinson, “The Law of Diminishing Returns as it is usually formulated, states that with a fixed amount of any factor of production, successive increases in the amounts of other factors will, after a point, yield diminishing increments of output”.

In stage III, total product declines. So, marginal product of the variable factor becomes negative and falls below the X-axis. This stage is called the stage of negative returns, as total product, average product and marginal product fall during this stage and the average product of the variable factor is non-negative. In this stage, efficiency of variable as well as fixed factor declines and factor ratio is highly sub-optimal. Producer should reduce the amounts of variable factor.

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]]>However, if capital were kept constant at ‘K’ and labour were doubled to ‘2L’; we would reach point ‘C’, which lies on a lower isoquant. Thus, doubling labour (L), with capital constant, less than doubles output. To double the output, more than double units of labour would be required. Therefore, constant returns to scale in the long run are compatible with diminishing returns in the short run.

It can also be simply understood with the help of Fig. 8.5 that in case, the long run production function exhibits diminishing returns to scale (doubling both factors less than doubles output), the short run production function will too exhibit diminishing returns to variable factor.

If, however, the long run production function shows increasing returns to scale, the short run production function may exhibit increasing, constant or diminishing returns, depending upon the relative strength of the increasing (positive) returns to scale vis-a-vis diminishing marginal productivity of the variable factor.

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]]>Hence, the optimal proportion of the inputs will remain unchanged. It is also known as scale-line, as it shows how the producer will change the quantities of the two factors, when it raises the scale of production.

The expansion path may have different shapes and slopes depending upon the relative prices of the factors used and shape of the isoquant. In case of constant returns to scale (homogenous production function), the expansion path will be a straight line through the origin, indicating constancy of the optimal proportion of the inputs of the firm, even with changes in the size of the firm’s input budget. (Fig. 7.12 (b)). In short-run, however, the expansion path will be parallel to X-axis (when capital is hold constant at K shown in Fig. 7.12 (b)).

As expansion path depicts least cost combinations for different levels of output, it shows the cheapest way of producing each output, given the relative prices of the factors. It is difficult to tell precisely the particular point of expansion path at which the producer in fact be producing, unless one knows the output which he wants to produce or the size of the cost or outlay it wants to incur.

But, this much is certain that though for a given isoquant map, there can be different expansion paths for different relative prices of the factors. Yet, when prices of the variable factors are given, a rational producer will always try to produce at one or the other point of the expansion path.

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