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The rule for this is that a plant (or any other sort of a business) should shut down in the short run if the price that it is getting for its product is lower than the average variable cost involved in making that product. The way to figure this out is to determine the average variable cost (AVC).
You might think that you should shut your plant down as long as the price you can sell for is lower than your average total cost (ATC). When the price is below the ATC, you lose money every time you well a unit of the product, so it seems like you should shut down. But that is not correct. If the price is below the ATC but above the AVC, you are losing money, but you are not losing as much money as you would if you closed down.
Why is this? If you shut down, you no longer have to pay variable costs, but you still have to pay fixed costs. If you sell at a point where the price is above the AVC but below the ATC, you can at least get some money that can go towards recouping your fixed costs.
So, to find your shutdown point, just find your AVC for the product. You shut down if your price is less than the AVC.
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