Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 1

Suppose that a firm produces two different outputs, the quantities of which are represented by q1 and q2. In general, the firm's total costs can be represented by C ( q 1 , q 2 ). This function exhibits economies of scope if
for all output levels of either good.
a. Explain in words why this mathematical formulation implies that costs will be lower in this multiproduct firm than in two single-product firms producing each good separately.
b. If the two outputs are actually the same good, we can define total output as q = q 1 + q 2. Suppose that in this case average cost (= C/q) decreases as q increases. Show that this firm also enjoys economies of scope under the definition provided here.