Question

Assume a company produces two products: x and y.     Assume the cost functions are as follows:

C(qx, 0) = 2qx^2

C(0, qy) = qy^2

C(qx, qy) = 2qx^2 + qy^2 + qxqy

A. Calculate the economies of scale meaure (S) for x

B. Does x exhibit economies of scale?

C. Calculate the economies of scale meaure (S) for y

D. Does y exhibit economies of scale?

E. Calculate the economies of scope meaure (SC)

F. Would it be better to produce x and y together or separately?

Answer 1

A. Calculate the economies of scale measure (S) for x

See that cost function is C = 2qx^2. The average cost AC is 4qx. Long run AC is the measure of economies of scale.

B. Does x exhibit economies of scale?

Now as qx rises, AC rises so there are diseconomies of scale.

C. Calculate the economies of scale measure (S) for y

See that cost function is C = qy^2. The average cost AC is 2qy. Long run AC is the measure of economies of scale.

D. Does y exhibit economies of scale?

No again, because as qy rises AC rises so there are diseconomies of scale.

E. Calculate the economies of scope measure (SC)

Economies of scope will be present when production cost together is less than the cost of producing the two goods separately. It is given by C(qx, 0) + C(0, qy) < C(qx, qy)

F. Would it be better to produce x and y together or separately?

Here see that cost of production separately is 2qx^2 + qy^2 and the cost of production jointly is 2qx^2 + qy^2 + qxqy. Hence there are no economies of scope and it would be better to produce x and y separately