As isoquant map may be used to show the two laws of production explained in this chapter. The physical movement from one isoquant to another, as we change only one factor of production (the law of variable proportions) can be shown by a proportion line parallel to the axis of the variable factor.
It shows changing proportion of labour with fixed quantity of capital. On the other hand, when all the factors are variable, the scale line passes through the origin. It shows expansion in scale of production along with a fixed ratio between capital and labour.
If the homogenous production function shows constant returns (or diminishing returns) to scale in the long run, the returns to the variable factor in the short run will be diminishing. This is explained below.
In Fig. 8.5, ‘L’ units of labour and ‘K’ units of capital are needed to produce (say) 100 units of output. If both the factors of production were doubled to ‘2 L’ and ‘2K’, output is doubled to 200 units”. Thus, the production function shows constant returns to scale.
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.