Static Profit Maximization Short Run Shut Down Decision

Question

In considering whether to stay open or shut down in the short run, a firm compares its revenues to its “avoidable costs”. We usually think of these avoidable costs as variable costs, but of course they could be fixed. This is where I have a thought experiment question:
Suppose we are looking at profit over a month. It is negative. You are considering if you are at least covering avoidable costs. How do we consider capital cost?
Case 1: You rent the factory and the lease is not flexible. This is a sunk cost.
Case 2: You own the factory. Your best alternative is to rent your factory out. If you shut down, you can easily find a replacement (assume no transaction cost). Then this foregone rent is an avoidable cost.
Case 3: This is where it gets tricky for me. You own the factory and no rental market exists. However, you can easily sell the factory if you shut down. So in my mind this is avoidable and the foregone rent (user cost of capital) is the relevant cost. But this doesn’t consider future profits unless we assume that the firm can buy back the factory in the following period when/if prices rise again. This seems incorrect.
That seems to be a downfall of static maximization. How would you propose thinking about this last scenario? Why don’t we consider dynamic profits when discussing shut down decisions?

RegressForward · Answer

In the short run, you cannot sell your capital. To do so would be a violation of "short run" and would instead be the "long run".
Case 3 (and I would also contest Case 2) are outright forbidden by the definition of short run.
I would note that your question has a lot of narrative to it - which is good in some cases, but you want to keep the literal definitions in mind, not all actions you describe are valid options in the parameters you've established. Optimization is, at its heart, a simple fact of math.

Static Profit Maximization Short Run Shut Down Decision

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