What correctly defines change of inventories of a firm during a year?

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Step-by-step explanation:

1. Let $I_0$ = opening inventory, $P$ = production during the year, $S$ = sales during the year, and $I_1$ = closing inventory.
2. Inventory flow identity: $I_0 + P - S = I_1$.
3. Change in inventories = $I_1 - I_0 = (I_0 + P - S) - I_0 = P - S$.

Thus the change of inventories during the year is Production during the year minus Sales during the year, which corresponds to option (1).

FINAL_ANSWER: a

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