We know this firm is operating in the shortrun as it has both variable and fixed costs. At a quantity of 4, what is the minimum price this firm must receive before it would shutdown.

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This question asks for the minimum price at which the firm would continue operating in the short run, given it has both fixed and variable costs and is producing a quantity of 4 units.

Key concept to apply: In the short run, a firm should continue producing as long as the price covers the average variable cost (AVC). If the market price falls below the minimum AVC, the firm will shut down and produce zero, since producing would only add variable costs without covering them.

Step-by-step analysis of the options:

Option 1: 37.5
- Without the underlying cost data (the total cost or the variable cost function at q = 4), we cannot determine the exact AVC or its minimum. If 37.5 were the price, the firm would continue operating only if AVC at q = 4 is at most 37.5. Since we don’t know AVC(4), this number could be either above or below the true minimum AVC, so we cannot judge definitively from this alone.

Option 2: 25
- Similar to option 1, this number could be above or below the minimum AVC. If AVC(4) minimum is less than or equal to 25, the firm would still operate at price 25; if the minimum AVC is greater than 25, the firm would shut down. Without the cost data, we cannot confirm.

Option 3: 12.5
- Again, this represents a potential shutdown threshold only if the minimum AVC at q = 4 equals 12.5 or higher. If the actual minimum AVC is above 12.5, the price would be insufficient to cover variable costs and the firm would shut down; if the minimum AVC is 12.5 or lower, the firm could continue producing.

Option 4: 40
- The same reasoning applies. If the minimum AVC at q = 4 is less than or equal to 40, price 40 would be sufficient to keep producing; if the minimum AVC exceeds 40, producing would be unprofitable relative to variable costs and the firm would shut down.

Overall, the central idea is that the critical threshold is the minimum average variable cost at the chosen output level (q = 4). Since the problem statement does not provide the cost data needed to compute AVC(4) or its minimum, we cannot determine exactly which option corresponds to the shutdown price.

If cost data were available, the typical approach would be:
- Compute AVC at q = 4: AVC(4) = VC(4) / 4, where VC is total variable cost.
- Determine the minimum of AVC over the relevant output levels (or specifically at q = 4 if that’s the only output level considered).
- The shutdown price is that minimum AVC. Any given option that is below this threshold would imply the firm should shut down, and any option at or above would allow production to continue.

ECON&201 15109 Applied Economics: Cost Curve Modeling

We know this firm is operating in the shortrun as it has both variable and fixed costs. At a quantity of 4, what is the minimum price this firm must receive before it would shutdown.

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