The firm is producing softball bats and baseball bats. let q1 denote the quantity of softball...

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?

Solutions

Expert Solution

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.

Rahul Sunny answered 2 years ago

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