Production with Two Outputs Economies of Scope

Many firms produce more than one product. Sometimes a firm's products are closely linked to one another-a chicken farm produces poultry and eggs, an automobile company produces automobiles and trucks, and a university produces teaching and research. Other times,firms produce products that are physically unrelated. In both cases, however, a firm is likely to enjoy production or cost advantages when it produces two or more products. These advantages could result from the joint use of inputs or production facilities, joint marketing programs, or possibly the cost savings of a common administration. In some cases, the production of one product gives an automatic and unavoidable by-product that is valuable to the firm. For example, sheet metal manufacturers produce scrap metal and shavings they can sell.

To study the economic advantages of joint production, let's consider an automobile company that produces two products, cars and tractors. Both products use capital (factories and machinery) and labor as inputs. Cars and tractors are not typically produced at the same plant, but they do share management resources, and both rely on similar machinery and skilled labor. The managers of the company must choose how much of each product to produce. Figure 7.10 shows two product transformation curves. Each curve shows the various combinations of cars and tractors that can be produced with a given input of labor and machinery. Curve Oi describes all combinations of the two outputs that can be produced with a relatively low level of inputs, and curve O2 describes the output combinations associated with twice the inputs.

Number of

Tractors

Number of

Tractors

FIGURE 7.10 Product Transformation Curve, me product transformation curve describes the different combinations of two outputs that can be produced with a fixed amount of production inputs. The product transformation curves Oi and O2 are bowed out (or concave) because there are economies of scope in production.

Number of Cars

FIGURE 7.10 Product Transformation Curve, me product transformation curve describes the different combinations of two outputs that can be produced with a fixed amount of production inputs. The product transformation curves Oi and O2 are bowed out (or concave) because there are economies of scope in production.

The product transformation curve has a negative slope because to get more of one output, the firm must give up some of the other output. For example, a firm that emphasizes car production will devote less of its resources to producing tractors. In this case, curve O2 lies twice as far from the origin as curve 01, signifying that this firm's production process exhibits constant returns to scale in the production of both commodities.10

If curve Ov were a straight line, joint production would entail no gains (or losses). One smaller company specializing in cars and another in tractors would generate the same output as the single company that produces both. However, the product transformation curve is bowed outward (or concave) because joint production usually has advantages that enable a single company to produce more cars and tractors with the same resources than would two companies producing each product separately. These production advantages involve the joint sharing of inputs. A single management is often able to schedule and organize production and to handle accounting and financial aspects more effectively than separate managements could.

Our discussion would be more complex if it incorporated the possibility of diseconomies or economies ofscale. For a more general analysis of economies of scope, see Elizabeth E. Bailey and Ann F. Fried-laender, "Market Structure and Multiproduct Industries: A Review Article," Journal of Economic Literature 20 (Sept. 1982): 1024-1048, or John C. Panzar and Robert D. Willig, "Economies of Scope," American Economic Revieiw 71 (May 1981): 268-272.

In general, economies of scope are present when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single product (with equivalent production inputs allocated between the two firms). If a firm's joint output is less than that which could be achieved by separate firms, then its production process involves diseconomies of scope. This could occur if the production of one product somehow conflicted with the production of the second product.

There is no direct relationship between economies of scale and economies of scope. A two-output firm can enjoy economies of scope even if its production process involves diseconomies of scale. Suppose, for example, that manufacturing flutes and piccolos jointly is cheaper than producing both separately. Yet the production process involves highly skilled labor and is most effective if undertaken on a small scale. Likewise, a joint-product firm can have economies of scale for each individual product, yet not enjoy economies of scope. Imagine, for example, a large conglomerate that owns several firms that produce efficiently on a large scale but that do not take advantage of economies of scope because they are administered separately.

The extent to which there are economies of scope can also be determined by studying a firm's costs. If a combination of inputs used by one firm generates more output than two independent firms would produce, then it costs less for a single firm to produce both products than it would cost the independent firms. To measure the degree to which there are economies of scope, we should ask what percentage of the cost of production is saved when two (or more) products are produced jointly rather than individually. Equation (7.8) gives the degree of economies of scope (SC) that measures this savings in cost:

C(Qi) represents the cost of producing output Qi, C{Qt) the cost of producing output Qi, and C(Qi, Q2) the joint cost of producing both outputs. (When the physical units of output can be added, as in the car-tractor example, the expression becomes C(Qi + Qi).) With economies of scope, the joint cost is less than the sum of the individual costs, so that SC is greater than 0. With diseconomies of scope, SC is negative. In general, the larger the value of SC, the greater the economies of scope.

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