Now that we have categorized the long-run average total cost, we want to examine how these average costs change as the firm size grows. Because all inputs are variable in the long run, we can consider how per-unit costs are affected as the firm alters its scale of operation. In other words, what happens to the firm’s long-run average total cost as the firm increases all of its inputs by the same proportion?

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We talked about returns to scale in Chapter 6. Remember that a production technology has increasing returns to scale if doubling all inputs leads to more than a doubling of output. If doubling all inputs exactly doubles output, its returns to scale are constant. If output less than doubles, there are decreasing returns to scale.

Economies of scale are the cost-based flip-side of returns to scale. Instead of looking at the way output changes in proportion to inputs, economies of scale look at the way cost changes in proportion to output. If doubling output causes cost to less than double, a firm has economies of scale. If doubling output causes cost to more than double, a firm has diseconomies of scale. If doubling output causes cost to double, a firm has constant economies of scale.

Because economies of scale imply that total cost increases less than proportionately with output, they also imply that long-run average total cost falls as output grows. That is, the long-run average total cost curve is downward-sloping when there are economies of scale because total cost rises at a slower rate than quantity (remember, ATC = TC/Q). Similarly, diseconomies of scale imply an upward-sloping long-run average total cost curve because total cost rises more quickly than output. Constant economies of scale make the long-run average total cost curve flat.

Putting together these relationships, we can see what the typical U-shaped long-run average total cost curve implies about economies of scale. At low output levels (the left, downward-sloping part of the ATC curve), total cost rises more slowly than output does. As a result, average total cost falls, and the firm has economies of scale.

At the very bottom of the average total cost curve where it is flat, average cost does not change, total cost rises proportionally with output, and marginal cost equals ATC. Here, therefore, average total cost increases at the same rate that output increases, and there are constant economies of scale.

At higher output levels (the right upward-sloping part of the ATC curve where ATC is rising), marginal cost is above average total cost, causing total cost to rise more quickly than output does. As a result, there are diseconomies of scale.

Economies of scale and returns to scale are not the same thing. They are related—cost and the level of inputs move closely together—but there is a difference. Returns to scale describe how output changes when all inputs are increased by a common factor. But nothing says cost-minimizing firms must keep input ratios constant when they increase output. So, the measure of economies of scale, which is about how total costs change with output, does not impose constant input ratios the way returns to scale do.

Because a firm can only reduce its cost more if it is able to change its input ratios when output changes, it can have economies of scale if it has constant or even decreasing returns to scale. That is, even though the firm might have a production function in which doubling inputs would exactly double output, it might be able to double output without doubling its total cost by changing the proportion in which it uses inputs. Therefore, increasing returns to scale imply economies of scale, but not necessarily the reverse.3

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Many firms make more than one product. McDonald’s sells Big Macs, Quarter Pounders, Egg McMuffins, and french fries. Just as economies of scale indicate how firms’ costs vary with the quantity they produce, economies of scope indicate how firms’ costs change when they make more than one product. Economies of scope exist when a producer can simultaneously make multiple products at a lower cost than if it made each product separately and then added up the costs.

To be more explicit, let a firm’s cost of simultaneously producing Q₁ units of Good 1 and Q₂ units of Good 2 be equal to TC(Q₁, Q₂). If the firm produces Q₁ units of Good 1 and nothing of Good 2, its cost is TC(Q₁, 0). Similarly, if the firm produces Q₂ units of Good 2 and none of Good 1, its cost is TC(0, Q₂). Under these definitions, the firm is considered to have economies of scope if TC(Q₁, Q₂) < TC(Q₁, 0) + TC(0, Q₂). In other words, producing Q₁ and Q₂ together is cheaper than making each separately.

We can go beyond just knowing whether or not economies of scope exist, and actually quantify them in a way that allows us to compare scope economies across companies. We call this measure SCOPE, and it’s the difference between the total costs of single-good production [TC(Q₁, 0) + TC(0, Q₂)] and joint production [TC(Q₁, Q₂)] as a fraction of the total costs of joint production. That is,

If SCOPE > 0, the total cost of producing Goods 1 and 2 jointly is less than making the goods separately, so there are economies of scope. The greater SCOPE is, the larger are the firm’s cost savings from making multiple products. If SCOPE = 0, the costs are equivalent, and economies of scope are zero. And if SCOPE < 0, then it’s actually cheaper to produce Q₁ and Q₂ separately. In other words, there are diseconomies of scope.

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There are two important things to remember about economies of scope. First, they are defined for a particular level of output of each good. Economies of scope might exist at one set of output levels—for example, 100 units of Good 1 and 150 units of Good 2—but not at a different pair, like 200 units of each, for instance. (The specificity of economies of scope to particular output levels is shared with economies of scale. As we discussed earlier in this section, for example, a U-shaped average total cost curve embodies changing scale economies over different output levels—positive economies at low output levels, negative ones at higher output.) Second, economies of scope do not have to be related to economies of scale. A firm can have one without the other or both at the same time. In fact, it gets a bit difficult to even define economies of scale once there are multiple outputs. We don’t need to go into why this is so; it’s enough to recognize that scale and scope economies are different things.

There are many possible sources of scope economies. They depend on the flexibility of inputs and the inherent nature of the products.

A common source of economies of scope is when different parts of a common input can be applied to the production of the firm’s different products. Take a cereal company that makes two cereals, Bran Bricks and Flaky Wheat. The firm needs wheat to produce either cereal. For Bran Bricks, it needs mostly the bran, the fibrous outer covering of the wheat kernel, but for Flaky Wheat, the firm needs the rest of the kernel. Therefore, there are natural cost savings from producing both cereals together.

In oil refining, the inherent chemical properties of crude oil guarantee economies of scope. Crude oil is a collection of a number of very different hydrocarbon molecules; refining is the process of separating these molecules into useful products. It is physically impossible for a refining company to produce only gasoline (or kerosene, diesel, lubricants, or whatever petroleum product might be fetching the highest price at the time). While refiners have some limited ability to change the mix of products they can pull out of each barrel of crude oil, this comes at a loss of scope economies. That’s why refineries always produce a number of petroleum compounds simultaneously.

The common input that creates scope economies does not have to be raw materials. For example, Google employees might be more productive using their knowledge about information collection and dissemination to produce multiple products (e.g., Google Earth, Google Docs, and YouTube) than to produce just the main search engine.