Question

Let a two-output cost function be given by: C(y1, y2) = y1 + y2 + Y1Y2 – (y192)2 + y2. Assume that yı > 1, and y2 > 1. Does this cost function exhibit economies of scope?

Answer 1

Ans)- Economies of scope exist when the cost of producing two or more goods together is less than the cost of producing each good separately.

Economies of scope are determined with the following formula-

\

Ꮪ = Cy+ Cy2 - CyᎩ2 CyᎩ2

Where, C(y₁), C(y₂) are the cost of producing good y₁ and y₂ separately, and C(y₁,y₂) is the cost of producing both good together.

If Calculated ‘S’ is positive then the cost function exhibits economies of scope.

Given , cost function-

C(y₁,y₂) = y₁ +y₂ +y₁y₂ –(y₁y₂)² +y₂³

Put y₂ =0 to find C(y₁)

C(y₁) = y₁

Put y₁ =0 to find C(y₂)

C(y₂) = y₂ +y₂³

Hence,

Yı + y2 + y2 - [yı + y2 + yıyz - (yıy2)2 + y2] yı + y2 + yıyz - (yıy2)2 + y}

7ı + y2 + y2 – yı - Y2 – yıy2 + (yıyz)2 – y}] Yı + y2 + yıyz - (yıy2)2 + y}

S= (y_y2)2 – yıy2 yı + y2 + y2yz - (y.y2)2 + y; yuy2 (7172 - 1) Y. + y2 + yıy2 – (yıy2)2 + yz

Since, y₁y₂ >1 because y₁≥$1596134856571_blob.png$1 and y₂≥$1596134856860_blob.png$1

And also C(y₁,y₂) = y₁ +y₂ +y₁y₂ –(y₁y₂)² +y₂³≥$1596134856602_blob.png$0 (cost cannot be negative)

Thus

S= > 0 Yıyı (y1y2 - 1) Y1 + y2 + yıy2 - (7172)2 + y2 hence cost function exhibits economies of scale.