The short run marginal cost (SMC) curve is 'U'-shaped because it initially falls as output increases, reaches a minimum point, and then rises with further increase in output.

In the short run, the SMC curve shows a specific relationship with average variable cost (AVC) and short run average cost (SAC) curves, which are also 'U'-shaped. The SMC curve cuts both the AVC and SAC curves from below at their respective minimum points.

To the left of the minimum point of AVC, the AVC is falling and SMC is less than AVC. To the right of this minimum point, AVC is rising and SMC is greater than AVC. Similarly, to the left of the minimum point of SAC, SAC is falling and SMC is less than SAC. To the right of this point, SAC is rising and SMC is greater than SAC.

This U-shaped pattern indicates that marginal cost first decreases with increase in output, reaches a minimum, and then starts increasing. The area under the SMC curve up to any level of output gives us the total variable cost at that level.

Thus, the 'U'-shape of the SMC curve reflects the inverse relationship between marginal cost and average costs at different levels of output in the short run.