![]() They are more efficient than the best available processes for producing small levels of output.įor example, assume that we have three processes: ‘Mass- production’ methods (like the assembly line in the motor-car industry) are processes available only when the level of output is large. One of the basic characteristics of advanced industrial technology is the existence of ‘mass-production’ methods over large sections of manufacturing industry. Usually most processes can be duplicated, but it may not be possible to halve them. ![]() ![]() The increasing returns to scale are due to technical and/or managerial indivisibilities. When the technology shows increasing or decreasing returns to scale it may or may not imply a homogeneous production function. Homogeneity, however, is a special assumption, in some cases a very restrictive one. In most empirical studies of the laws of returns homogeneity is assumed in order to simplify the statistical work. The isoclines will be curves over the production surface and along each one of them the K/L ratio varies. With a non-homogeneous production function returns to scale may be increasing, constant or decreasing, but their measurement and graphical presentation is not as straightforward as in the case of the homogeneous production function. Production functions with varying returns to scale are difficult to handle and economists usually ignore them for the analysis of production. In figure 3.21 we see that up to the level of output 4X returns to scale are constant beyond that level of output returns to scale are decreasing. Over some range we may have constant returns to scale, while over another range we may have increasing or decreasing returns to scale. However, the technological conditions of production may be such that returns to scale may vary over different ranges of output. All processes are assumed to show the same returns over all ranges of output either constant returns everywhere, decreasing returns everywhere, or increasing returns everywhere. Returns to scale are usually assumed to be the same everywhere on the production surface, that is, the same along all the expansion-product lines. In figure 3.20 doubling K and L leads to point b’ which lies on an isoquant above the one denoting 2X. By doubling the inputs, output is more than doubled. The distance between consecutive multiple-isoquants decreases. In figure 3.19 the point a’, defined by 2K and 2L, lies on an isoquant below the one showing 2X. By doubling the inputs, output increases by less than twice its original level. The distance between consecutive multiple-isoquants increases. Doubling the factor inputs achieves double the level of the initial output trebling inputs achieves treble output, and so on (figure 3.18). The returns to scale may be shown graphically by the distance (on an isocline) between successive ‘multiple-level-of-output’ isoquants, that is, isoquants that show levels of output which are multiples of some base level of output, e.g., X, 2X, 3X, etc.Īlong any isocline the distance between successive multiple- isoquants is constant. The K/L ratio diminishes along the product line. If only one factor is variable (the other being kept constant) the product line is a straight line parallel to the axis of the variable factor (figure 3.15). The product curve passes through the origin if all factors are variable. What path will actually be chosen by the firm will depend on the prices of factors. The product line describes the technically possible alternative paths of expanding output. It does not imply any actual choice of expansion, which is based on the prices of factors and is shown by the expansion path. ![]() A product curve is drawn independently of the prices of factors of production. Instead of introducing a third dimension it is easier to show the change of output by shifts of the isoquant and use the concept of product lines to describe the expansion of output.Ī product line shows the (physical) movement from one isoquant to another as we change both factors or a single factor. To analyze the expansion of output we need a third dimension, since along the two- dimensional diagram we can depict only the isoquant along which the level of output is constant. Before explaining the graphical presentation of the returns to scale it is useful to introduce the concepts of product line and isocline. For a homogeneous production function the returns to scale may be represented graphically in an easy way. ![]()
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