Final answer:
The correct statement about a firm that uses variable costing is that the operating income moves in the same direction as sales, due to only variable production costs being included in unit product cost.
Step-by-step explanation:
Among the statements provided about a firm that uses variable costing, it is true that operating income moves in the same direction as sales. This is because under variable costing, only the variable costs are included in the cost of goods sold and thus, they change with changes in production volume. Variable costs include both variable production costs and variable selling costs. However, only variable production costs are included in the unit product cost, not the variable selling costs.
It is also pertinent to note, the unit product cost does indeed change with changes in the number of units manufactured, as the total variable costs are divided by the total output to give the average variable cost. This calculation allows firms to understand if they are able to earn profits, given that their average variable cost is lower than the market price, excluding fixed costs. Long-term production and cost analysis further helps in making profit-maximizing decisions.