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The firm should continue to operate when

Marginal Revenue (MR) >= Variable Cost (VC = MC)

Because it is still making a structural profit per unit, which indicates an economic profit is being made. When making optimal production decisions, one should not include sunk costs, including plant investment, which cause TC >= VC. While the firm will be operating at a loss, it is still achieving a positive cost-benefit outcome.

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Q: Why should a firm continue to operate under a short-run period when TR is greater than VC but less than TC?
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