Economies of Scope
Economies of scope are said to be presented whenever it is less costly to produce a set of goods in one firm than it is to produce it in two or more firms. For the two-product case, this amounts to determining the sign of C(Q1,0) + C(0,Q2) – C(Q1,Q2). The first two terms in this equation are the total costs of producing product 1 in one firm and product 2 in another. The third term is the total cost of having these products produced by the same firm. If the difference is positive then economies of scope exist; if it is negative there are diseconomies of scope; and if it is zero then there are neither economies nor diseconomies of scope.
The degree of scope economies for the n-products case is given by the ratio below:
SC = [ C(Q1,0,0,…,0) + C(0,Q2,0,…,0) + … + C(0,0,0,…Qn) – C(Q1,Q2,Q3,…,Qn) ] / C(Q1,Q2,Q3,…,Qn)
Whenever SC exceeds zero, scope economies are present, which tell us that it is cheaper for one firm to produce both goods jointly.