Final answer:
The statement is false; costs do not always vary linearly with changes in facility size due to the presence of fixed, variable, economies of scale, and diseconomies of scale.
Step-by-step explanation:
The statement that costs always vary linearly with respect to different facility sizes is false. In the business world, a firm's costs can be split into fixed costs and variable costs. Fixed costs, such as rent or the cost to set up a website, do not change with the level of production, while variable costs change with the level of output. Different industries and businesses experience cost changes differently. Some may have a proportionate increase in costs as production increases, known as linear variablility, while others may experience economies of scale or diseconomies of scale, where the cost per unit can decrease or increase as production volume increases. For instance, a website providing medical advice may have high initial fixed costs but low variable costs, leading to a relatively flat total cost curve up to a certain level of output. On the other hand, a firm that needs to maintain equipment may see rising marginal costs as production intensifies. Therefore, costs do not always vary linearly with changes in the scale of production.