No, this firm is not natural monopoly, bcoz natural monopoly is a firm is that has so large economies of scale that a single form can supply the entire market at a lower average cost than two or more firms
For natural economy, average cost should continuously fall over a large range of output such that Economics of scale are generated.
Also MC is always lower than AC
Now AC falls continuously till Q = 2, after that it increases.
Also As TC = Q* AC
TC = 12 + Q2+Q3/2
So MC = 2Q + 3Q2/2
Now MC is continuously rising
So it is not natural monopoly
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