Question

A multiproduct firm's cost function is C(Q1,Q2)=50+0.2Q1^2+0.1Q2^2.

a) Are there economies of scope? Why?

b) Are there cost complementarities in producing products 1 and 2? Why?

Answer 1

a) Economies of scope exists when it is cheaper to produce two goods together than to produce them separately. The cost function has a fixed cost of f = 50 and coefficient of Q1Q2, designated as 'a' = 0. This is because the cost function does not have Q1Q2. Economies of scope exists if f - aQ1Q2 > 0. Here a is 0 so aQ1Q2 is also 0 but f is 50 so we have f - aQ1Q2 > 0. Hence there are economies of scope.

b) When the cost function has a < 0, it has cost complementarities. Now that a = 0 which means 'a' is not less than 0. Hence there are no cost complementarities