*Economies of scope *exist when the cost of producing two or more goods together is less than the cost of producing each good separately. Economies of scope can result if two or more products share the same production facilities. For example, General Motors produces different car models that use the same engines and transmissions.

Economies of scope can also arise through marketing, such as Proctor and Gamble having a large number of home and beauty products that they market in similar ways. Thus, marketing strategies, product branding, and product design costs are spread over a large number of products. Finally, economies of scope arise from reduced distribution cost.

Economies of scope are determined with the following formula

In the formula, *C*(*q*_{a}) is the cost of producing the quantity *q*_{a} of good *a* separately, and *C*(*q*_{b}) is the cost of producing the quantity *q*_{b} of good *b* separately. The term *C*(*q*_{a} + *q*_{b}) is the cost of producing the same quantities of good *a* and good *b* together.

Economies of scope, *S*, measures the percentage cost saving that occurs when the goods *a* and *b* are produced together. Thus, *S* is greater than zero when economies of scope exist, and the larger the positive value for *S*, the greater the economies of scope.

Your firm produces both face cream and hand lotion. The cost of separately producing 2,000,000 jars of face cream is $0.75 each or $1.5 million. If 4,000,000 bottles of hand lotion are produced separately, the cost is $0.60 each or $2.4 million. If 2,000,000 jars of face cream and 4,000,000 bottles of hand lotion are produced together, the total cost is $3 million.

To determine the economies of scope, you take the following steps.

In the top of the equation, substitute $1.5 million for

*C*(*q*_{a}), $2.4 million for*C*(*q*_{b}), and $3 million for*C*(*q*_{a}+*q*_{b}).Remember that

*C*(*q*_{a}) is the cost of producing one product, face cream, separately;*C*(*q*_{b}) is the cost of producing the second product, hand lotion, separately; and*C*(*q*_{a}+*q*_{b}) is the cost of producing the two products together.In the bottom of the equation, substitute $3 million for

*C*(*q*_{a}+*q*_{b}).Calculate the value in the top of the equation.

Divide the top of the equation by the bottom of the equation and your economies of scope,

*S*, equals 0.3 or 30%.Thus the cost of producing face cream and hand lotion together is 30% less than the cost of producing them separately.