Question

C(Q₁, Q₂) = 3,500 - 205Q₁Q₂ - (Q₁)² + (Q₂)²

A. What do you need to know from the equation above to see if there are Cost Complementarity? Are there Cost Complementarity?

B. What is MC₁(Q₁,Q₂) ?

C. What is MC₂(Q₁,Q₂) ?

D. Are there economies of scope? Explain.

E. What are the implications for a merger?

Answer 1

A) Cost Complementarities exists when marginal cost of one output decreases with there is increase of another output.

That is, [d MC(Q1) / dQ2 ] < 0

MC(Q1) = d C / d Q1

MC(Q1) = - 205Q2 - 2Q1

Now,

d MC(Q1) / d Q2 = - 205 < 0

Thus, cost complementarities exists.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

B) MC1(Q1,Q2) = - 205Q2 - 2Q1

C) And, MC2(Q1,Q2) = d C / d Q2 = - 205Q1 - 2Q2

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

D) If TC(q1,q2) < TC(Q1,0) + TC(0,Q2), then there is economies of scope

3500 - 205Q₁Q₂ - (Q₁)² + (Q₂)² < 3500 - (Q1)² + 3500 + (Q₂)²

3500 > - 205Q1Q2

Thus, there exists economies of scope.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

E) The firm can produce the two products jointly at a cheaper cost instead of producing them separately which incurs higher costs. Thus, by producing the two products jointly it can earn a higher profit and thus it is profitable for a merger to take place.