Question

8. Economies of Scope

Definition:

Economies of scope exist when the total cost of producing two products within the same firm TC(Q1, Q2) is lower than when the products are produced by separate firms TC(Q1, 0) + TC(0, Q2). That is, when TC(Q1, 0) + TC(0, Q2) > TC(Q1, Q2)

A firm’s total cost function is TCQ1, Q2=100-14Q1Q2+Q12+(Q2)2 where Q1 and Q2 represent the number of units of goods 1 and 2, respectively.

A. If the firm produces 10 units of good 1 and 5 units of good 2, do economies of scope exist for this firm?

B. How will the firm’s total cost of production be affected if it decides to discontinue the production of good 2?

Answer 1

A.

Let the cost function be:

TC=100-14Q1Q2+Q1^2+(Q2)^2

Now in order to find the economies of scope, we need to find the following.

TC(Q1, 0) = 100 +Q1^2

As the firm produces 10 units of good 1, therefore,

TC (Q1, 0)= 100 + 100 = 200

Next,

TC (0, Q2) = 100 + Q2^2

As the firm produces 5 units of good 2, so,

TC (0, Q2) = 100 + 25 = 125

And

When the firm produces both good 1 and good 2, the total cost is

TC = 100-14*10*5+100+25 = 225 - 700 = -475

As TC(Q1, 0) + TC(0, Q2) > TC(Q1, Q2) holds, so we can say that economies of scope exist for this firm.

........

B.

If it discontinues the production of good 2, the total cost will increase to 200 and hence the firm will lose its economies of scope.