Marginal Cost and Supply in LONG run and imperfect market URGENT

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BrownieLover
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Please can you answer this URGENT questioniscuss whether there is a relationship between the marginal cost curve of the firm and the supply curve of the industry to which it belongs. I know that in the short run for a perfectly competitive firm, the supply curve is the portion of the MC curve that lies above the AVC. The firms' supply curves are added to form the market supply curve, which is upward sloping.
In the long run, the supply curve is the portion of the MC curve that lies above the ATC. However, I read that you cannot horizontally add all individual firms' supply curves to add the market supply curve in the long run. Why is this? How do we form the market supply curve?

I would also have to explain the lack of such a relationship in imperfect competition. But why is there a lack of this relationship - why can't we add the marginal cost curves of firms in imperfect markets to form the supply curve? What diagram would I draw to show the lack of this relationship?Thanks.
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