Difference between productive and allocative efficiency, Macroeconomics

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Explain the difference between productive and allocative ( economic ) efficiency.

Explanation of productive efficiency, e.g. output at AC minimum
Define to the effect that this shows that all factors (fixed and variable) are being utilised to the utmost efficiency when average costs are at the lowest point
Definition of allocative efficiency, e.g. P = MC
Explanation that allocative efficiency means that welfare is maximised - the firm is producing the last possible unit since the market price means that there is a demand for it at that price
illustrating both concepts using a unit cost picture (PCM)

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