The SMC curve is a U-shaped curve due to the law of variable proportions or law diminishing returns. In order to understand the reason behind the U-shape of SMC, let us divide the SMC curve (UAB) into three different parts according to the law of variable proportions:
i. UA part corresponds to increasing returns to factor.
ii. Minimum point A corresponds to constant returns to factor.
iii. AB part corresponds to decreasing returns to factor. In the initial construction stages, the falling part of SMC (UA) is due to application of increasing returns to factor.
Then the SMC stops falling and reaches its minimum point 'A' due to the existence of constant returns to a factor. After the minimum point A, SMC starts rising (i.e. 'AB' part of SMC) due to the onset of decreasing returns of variable factors. This trend of SMC curve (initially falling, then becoming constant at its minimum point and then rising) makes it look like the English alphabet - 'U'.
In other words, Due to the operation of law of variable proportion, MP first rises, reaches its maximum point and then declines. Since increasing returns means diminishing costs and diminishing returns implies increasing cost, therefore, MC first falls because of increasing returns, reaches its minimum and then rises due to the operation of diminishing returns. As a result, the MC curve becomes U-shaped.