Tuesday, May 23, 2006

Product-Specific Economies of Scale based on a multiproduct environment

Suppose that instead of a C(q) cost function, we have a C(q1,q2) cost function. This new function represents the cost of a firm that produces q1 units of product 1 and q2 units of product 2.

The incremental costs of increasing product 2 from 0 to q2 holding product 1 constant is IC2 = C(q1,q2) – C(q1,0)

The average incremental costs of increasing product 2 from 0 to q2 holding product 1 constant is AIC2 = IC2/q2

So the product-specific economies of scale (PS2) of q2 holding the other output, q1, constant is: PS2=AIC2/MC2 , where MC2 is the marginal cost of product 2, which is the partial derivative of C(q1,q2) with respect to q2.

Note that in case with more than two products, we have PSi = AICi/MCi as before, but all outputs except qi must be held fixed (not only q1 as in the example above).

Tuesday, May 02, 2006

Single-Product Economies of Scale

The firm is said to have economies of scale if its average cost falls as output increases. But if average cost rises with output, the firm is said to have diseconomies of scale. Finally, if average cost does not vary with output, the firm has constant returns to scale.

There are a lot of reasons to expect a firm’s average cost to decline as its output increases (at least initially). Two of them are the followings: One is that fixed costs do not vary with output. Secondly, as output rises, a firm can use its labor in more specialized tasks (more efficient).

As I mentioned, scale economies exist if average costs (AC) falls as output expands. This can happen only if average cost (AC) is above marginal cost (AC > MC). This relationship suggest that a natural measure of scale economies (S) is the ratio of average to marginal cost (S=AC/MC). So economies of scale exist if S>1, diseconomies of scale exist if S<1 and constant returns to scale exist if S=1.