Final answer:
The statement is false. During a period of declining costs, FIFO, not LIFO, is generally preferred for a company aiming to maximize profits because it leads to lower cost of goods sold and higher gross profits.
Step-by-step explanation:
The statement that LIFO (Last-In, First-Out) Cost Flow is preferred to FIFO (First-In, First-Out) for a company wishing to maximize profits during a period of declining costs is false. When costs are declining, the FIFO method would report the lowest cost of goods sold, which means that older, higher-cost items are recognized first. This would lead to a higher gross profit. Conversely, LIFO would lead to a higher cost of goods sold since the more recent, lower-cost items would be recognized first, resulting in lower gross profits.
In the context given by the reference information, whether a firm should continue to produce or shut down depends on if the price exceeds the firm's average variable costs, not on the inventory accounting method. However, the long-run decisions would consider the most efficient production technology and may include adjustments to capital and labor factors based on cost changes.