Question

1. A firm produces 2 products: X and Y. The production technology displays the following costs, where C(i,j) represents the costs of producing i units of X and the costs producing units j of Y:
   1. C(0,50)    =100                     C(5,0)        = 150
   2. C(0,100) = 210                    C(10,0)      = 320
   3. C(5,50)   = 240                    C(10,100) = 500

Does the production technology display Economies of Scale? Economies of Scope?

Answer 1

Answer : The technology displays economies of scope. But it does not display economies of scale.

Explanation

C(0,50) * 2 < C (0,100) That is, when production of X doubled, cost of production more than doubled.

C(5,0) * 2 < C (10,0) That is, when production of Y doubled, cost of production more than doubled.

C(5,50) * 2 < C (10,100) That is, when production of X and Y doubled, cost of production more than doubled.

These implies economies of scale do not exist.

(In case economies of scale exist, C(a,b) * k > C (ka,kb))

C(5,50) < C(5,0) + C(0,50)

C(10,100) < C(10,0) + C(0,100)

Therefore, economies of scope exist

(When economies of scope exist, C(a,0) + C (0,b) > C (a,b) )