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I struggle to find formal mathematical expressions for long run average costs and long run marginal costs. All ressources I see take a finite number of short run average costs and draw the envelop curve to it. Is this really the right way to define it formally ? Since there is a finite number of curves, the envelop is not well-defined right ? So is it implicit that there are infinitely many short run average costs so that there is only one possible envelop curve : the LRAC ?

The LRMC is then the derivative of this curve. Is there a formal mathematical expression for theses curves ?

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