Question

Two firms have the following cost functions (and the marginal cost functions in parentheses)
Firm 1: C₁ = 0.75q₁³ – 6q₁² + 180q₁ (MC₁ = 2.25q₁² – 12q₁ + 180)
Firm 2: C₂ = 0.5q₂³ – 20q₂² + 100q₂ (MC₂ = 1.5q₂² – 40q₂ + 100

At what output level is average cost minimized at each firm?
Firm 1:  
Firm 2:

If the 2 firms merged, they would have the following joint cost function:
C = 0.75q₁³ – 6q₁² + 180q₁ + 0.5q₂³ – 20q₂² + 100q₂ + 3q₁q₂

Assuming positive production of both goods, would the merger create economies of scope?  

Answer 1