How the shape of the total variable cost curve (TVC) and total cost curve (TC) is related with the law of diminishing marginal returns in the short-run. Support your explanations with graphs and formula/equations.

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a) How the shape of the total variable cost curve (TVC) and total cost curve (TC) is related with the law of diminishing marginal returns in the short-run. Support your explanations with graphs and formula/equations.

b) Explain why the short-run marginal cost curve (MC) must intersect the average variable cost curve (AVC) at the minimum of the AVC. 

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