Question

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? [5 pts.]

Answer 1

Producing separately,

C(q1) = 25+q1

C(q2) = 45+2q2

Q1 will cost $25 addition to the quantity produced. Q2 will cost $45 addition to the twice the quantity produced.

Lets consider, q1=75 and q2=50

C(q1) = 25+75 = 100

C(q2) = 45+(2*50) = 145

Lets consider q1=50 and q2 = 75

C(q1) = 75

C(q2) = 195

Combined, C(q1,q2) = 45+2q1+q2

C(q1,q2) = 45+(2*75)+50 = 245 (q1=75;q2=50)

C(q1,q2) = 45+(2*50)+75 = 220 (q1=50;q2=75)

Yes. There is economies of scope in this case when the q2 is to be produced more than the q1.