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.