Generally, isoquants generated by the production functions are negatively sloped, non intersecting and are convex to the origin. Further, higher isoquants represent higher level of production. In Fig. 7.8(a), the production functions are depicted in the form of a set of isoquants, which have positively sloped segments also.
Here, one factor has positive marginal product while the other factor has negative marginal product. The oval shape of isoquant means that beyond a certain point, employment of an additional unit of a factor will necessitate employing additional units of the other factor to produce the same level of output.
Consider isoquant IQ1 in this figure. Here, A1B1 segment of the isoquant has a negative slope. However, beyond points ‘A’ and ‘B’, this isoquant is positively sloped (either bends backwards or slopes upwards). At point A1, when the isoquant tends to be vertical, the marginal productivity of capital becomes zero.
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This implies that if the quantity of labour is held constant, with the quantity of capital added, output cannot expand. The additional units of capital become redundant here. A1 A3 and A4 are such other points, where the marginal productivity of capital becomes zero.
Here, capital has been substituted for labour to the maximum extent. The capital ridge line is formed by the locus of points (A1, A2, A3 and A4 in Fig. 7.8(a)) in an isoquant mapping, where the marginal productivity of capital is zero. Similarly, the labour ridge line is formed by the locus of points (B1, B2, B3 and B4 in Fig. 7.8) in an isoquant mapping, where the marginal productivity of labour is zero.
At points B1, B2, B3 and B4, the isoquants tend to be horizontal, parallel to the labour axes. On vertical stretches, labour input becomes redundant and makes no contribution to output. This implies that with quantity of capital held constant, an increase usage of labour would not increase output at all. Here, labour has been substituted for the capital to the maximum extent.
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Thus, the locus of points of isoquants where the marginal products of the factors are zero, form the ridge lines. At upper ridge line OA, the marginal product of capital is zero, while the lower ridge line OB implies that the marginal product of labour is zero. The production techniques are technically efficient only in the region inside the two ridge lines.
This region is also called as the viable or economic region of production. This region is associated with the second stage (stage of operation) discussed under ‘Law of Variable Proportions’ in the next chapter on Production Analysis. Here, the marginal products of factors are positive, but declining.
In this efficient range of production, the isoquants are normally shaped (convex to the origin). A profit maximising business firm (paying a positive price for the hired inputs) will definitely operate in the region lying between the two ridge lines. All least cost combinations and the expansion path, thus, necessarily falls between these two ridge lines. The inputs used here are assumed to be normal and essential for production.
The ridge lines OA and OB in Fig. 7.8(a) are isoclines, because along these lines, the marginal rate of technical substitution is constant. The marginal rate of technical substitution of capital for labour (MRTSK, L) is zero and hence MRTSL,K is undefined (infinity) along the ridge line OA (since, here, marginal product of capital is zero).
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Along this ridge line, the tangents to the isoquants are parallel to the vertical axis. Similarly, the marginal rate of technical substitution of labour for capital (MRTSL, K) is zero and hence MRTSK,L is undefined (infinity) along the ridge line OB (since, here, marginal product of labour is zero). Along this ridge line, the tangents to the isoquants are parallel to the horizontal axes.
Outside the ridge lines, the marginal products of factors are negative and the methods of production are inefficient, since, these require greater quantities of both the factors for producing the same level of output. The marginal product of capital becomes negative, if its application goes beyond its zero marginal products.
When the quantity of capital employed relative to the quantity of labour becomes too large, an increase in the quantity of capital with a fixed quantity of labour would result in a fall in the output level. Likewise, when the quantity of labour is increased (with a fixed quantity of capital), beyond its zero marginal product, the level of output will decline.
Therefore, no rational producer will choose a factor combination in the waste bearing segment lying outside the upper and lower ridge lines, even if the factors are available free of cost. Thus, only the ridge linies enclose the area of rational operation. The economic region of production for a homogenous production function (e.g., a Cobb Douglas Production Function) is cone shaped on a account of straight ridge lines (Fig. 7.8(b)).
