Question

1. Two firms currently produce the goods q1 and q2 separately. Their cost functions are C(q1) = 25 + q1, and C(q2) = 45 + 2q2. If the two firms merge, it is estimated that the merged firm can produce the two goods jointly with costs described by the function C(q1, q2) = 45 + 2q1 + q2. Are there scope economies in this case that would justify the merger?

Answer 1

Total cost when produced separately =   25 + q1 + 45 + 2q2 = 70 + q1 + 2q2
Total cost when produced together = 45 + 2q1 + q2

Economies of scope means that total cost of producing two goods together is less than producing them separately.

Here, producing them together reduces the fixed costs from 70 to 45.
However, for economies of scope to exist it must be that 70 + q1 + 2q2 >  45 + 2q1 + q2
which hold true when 25 + q2 > q1

Hence, economies of scope exists only when 25 + q2 > q1