Let x and y represent output of two different but related products. C (Q, 0) denotes total cost associated with production of QX quantity of x alone and C (0, QY) stands for total cost of producing QY quantity of y alone. C (QX, QY) represents total cost of producing QX quantity of x and QY quantity of y by one firm. Mathematically, an economy of scope exists in a two-product firm if.
Source of economies of scope may be traced in spreading overhead activities like Reasearch & Development, advertising, distribution etc. over a range of products. Sometime, skills and experiences of existing management may be used for developing new similar products and thereby generating scope economies. Another source of economies of scope may lie in sharing the production process.
For related products, it is expected that processes of production are partially common. Good reputation of a firm also confers economies of scope when more new goods are added to its product line.
In case of related products (for an extension of the same product line), the same distribution network can be used. So, cost of distribution does not increase in proportion to the increase in number of products.
Economy of scope is measured by the formula:
Suppose, a firm has three options: Producing perfume only, producing only after-shave lotion and producing both the products. If the company prefers the first option, i.e., it produces perfume only and 1000 bottles of perfume costs Rs. 1, 00,000.
If the company produces only after-shave lotion, total cost of producing the same quantity of after-shave lotion is Rs. 50,000. Producing both perfume and after-shave lotion involves a cost of Rs. 1, 20,000 where 100 bottles of each product are produced. For this particular firm, economies of scope is calculated as
1, 00,000 + 50,000 – 1, 20, 000 1, 20,000/ 1, 20,000 = 0.25
Interpretation of the result is: if the company produces perfume and after-shave lotion, cost can be reduced by 25% as against separately producing both the products.