MODULE 56: Long-Run Costs and Economies of Scale

Sunk Costs

To complete our discussion of costs, we need to include the concept of sunk costs. When making decisions, knowing what to ignore is important. Although we have devoted much attention to costs that should be taken into account when making a decision, some costs should be ignored when doing so. This section presents the kind of costs that people should ignore when making decisions—what economists call sunk costs—and explains why they should be ignored.

To gain some intuition, consider the following scenario. You own a car that is a few years old, and you have just replaced the brake pads at a cost of $250. But then you find out that the entire brake system is defective and also must be replaced. This will cost you an additional $1,500. Alternatively, you could sell the car and buy another of comparable quality, but with no brake defects, by spending an additional $1,600. What should you do: fix your old car, or sell it and buy another?

Some might say that you should take the latter option. After all, this line of reasoning goes, if you repair your car, you will end up having spent $1,750: $1,500 for the brake system and $250 for the brake pads. If you were instead to sell your old car and buy another, you would spend only $1,600.

However, this reasoning, although it sounds plausible, is wrong. It ignores the fact that you have already spent $250 on brake pads, and that $250 is nonrecoverable. That is, having already been spent, the $250 cannot be recouped. Therefore, it should be ignored and should have no effect on your decision whether to repair your car and keep it or not. From a rational viewpoint, the real cost at this time of repairing and keeping your car is $1,500, not $1,750. So the correct decision is to repair your car and keep it rather than spend $1,600 on a new car.

A sunk cost is a cost that has already been incurred and is nonrecoverable. A sunk cost should be ignored in a decision about future actions.

In this example, the $250 that has already been spent and cannot be recovered is what economists call a sunk cost. Sunk costs should be ignored in making decisions because they have no influence on future costs and benefits. It’s like the old saying, “There’s no use crying over spilled milk”: once something can’t be recovered, it is irrelevant in making decisions about what to do in the future. This applies equally to individuals, firms, and governments—regardless of how much has been spent on a project in the past, if the future costs exceed the future benefits, the project should not continue.

It is often psychologically hard to ignore sunk costs. And if, in fact, you haven’t yet incurred the costs, then you should take them into consideration. That is, if you had known at the beginning that it would cost $1,750 to repair your car, then the right choice at that time would have been to buy a new car for $1,600. But once you have already paid the $250 for brake pads, you should no longer include it in your decision making about your next actions. It may be hard to “let bygones be bygones,” but it is the right way to make a decision.

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There’s No Business Like Snow Business

Anyone who has lived both in a snowy city, like Chicago, and in a city that only occasionally experiences significant snowfall, like Washington, D.C., is aware of the differences in total cost that arise from making different choices about fixed cost.

In Washington, even a minor snowfall—say, an inch or two overnight—is enough to create chaos during the next morning’s commute. The same snowfall in Chicago has hardly any effect at all. The reason is not that Washingtonians are wimps and Chicagoans are made of sterner stuff; it is that Washington, where it rarely snows, has only a fraction as many snowplows and other snow-clearing equipment as cities where heavy snow is a fact of life.

In this sense Washington and Chicago are like two producers who expect to produce different levels of output, where the “output” is snow removal. Washington, which rarely has significant snow, has chosen a low level of fixed cost in the form of snow-clearing equipment. This makes sense under normal circumstances but leaves the city unprepared when major snow does fall. Chicago, which knows that it will face lots of snow, chooses to accept the higher fixed cost that leaves it in a position to respond effectively.

A lesson in returns to scale: cities with higher average annual snowfall maintain larger snowplow fleets.

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Summing Up Costs: The Short and Long of It

If a firm is to make the best decisions about how much to produce, it has to understand how its costs relate to the quantity of output it chooses to produce. Table 56.1 provides a quick summary of the concepts and measures of cost you have learned about.

Table 56.1Concepts and Measures of Cost

	Measurement	Definition	Mathematical term
Short run	Fixed cost	Cost that does not depend on the quantity of output produced	FC
	Average fixed cost	Fixed cost per unit of output	AFC = FC/Q
Short run and long run	Variable cost	Cost that depends on the quantity of output produced	VC
	Average variable cost	Variable cost per unit of output	AVC = VC/Q
	Total cost	The sum of fixed cost (short run) and variable cost	TC = FC (short run) + VC
	Average total cost (average cost)	Total cost per unit of output	ATC = TC/Q
	Marginal cost	The change in total cost generated by producing one more unit of output	MC = ΔTC/ΔQ
Long run	Long-run average total cost	Average total cost when fixed cost has been chosen to minimize average total cost for each level of output	LRATC

Table 56.1: Table 56.1 Concepts and Measures of Cost