Why AC curve is downward sloping?

Dear student, 

The AC curve is u-shape . The reason behind the U-shape of AC curve is the Law of Variable Proportions. Accordng to this law in the initial stages of production the marginal product of labour rises as the fixed factors are not fully utilised. The rising marginal product of labour implies that more output can be produced by per additional unit of labour. So, cost of labour per unit of output falls. So, AVC falls and thereby, AC also falls. 
The AC continues to fall till it reaches the point of minimum. It becomes stable due to constant returns to scale. At this point the combination of labour and capital are optimally utilised. Beyond the minimum point the AVC starts rising due to overutilisation of capital. Therefore, marginal product starts fallling which implies higher AVC. The rise in AVC offsets the AFC, which pushes the AC curve to rise. 

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