Question

The firm is producing softball bats and baseball bats. let q1 denote the quantity of softball bats and q2 denote the baseball bats. The total cost function is C(q1,q2) = 860-0.25q1q2+ q1^2 + q2^2. The firm would like to produce 10 units of softballs and 14 units of baseball bats. Calculate the measure for scope economies. Do economies of scope exist?

Answer 1

Given

C(q1,q2)=860-0.25q1q2+q1^2+q2^2

First we estimate the cost of 10 units of q1 when q2=0 (i.e. without any production of baseball bats). Set q1=10 and q2=0

C(10,0)=C(q1=10)860-0.25*10*0+10^2+0^2=$960

Now we estimate the cost of 14 units of q2 when q1=0 (i.e. without any production of softball bats). Set q1=0 and q2=14

C(0,14)=C(q2=14)=860-0.25*0*14+0^2+14^2=$1056

Now, we estimate the cost if we produce 10 units of q1 and 14 units of q2 together

C(10,14)=860-0.25*10*14+10^2+14^2=$1121

Economies of scope=[C(q1)+C(q2)-C(q1,q2)]/C(q1,q2)

Economies of scope=(960+1056-1121)/1121=0.77

Since measure of economies of scale is positive, we can say that economies of score exists.