Let S denote a measure of (local) economies of scale for a multiproduct firm. Define "strong" economies of scope as the savings in costs arising from the joint production of all products rather than producing each product separately. Define "incremental" economies of scope as the savings in costs arising from the joint production of all products rather than producing one of the products separately from the others. We show that these two concepts of economies of scope along with a measure of product- specific economies of scale, are sufficient to define S for the general case. For economies of scale it is important for "incremental" economies of scope to dominate "strong" economies of scope. To demonstrate this point, we provide an example in which diseconomies of scale may exist for the multiproduct firm despite the presence of both "strong" and "incremental" economies of scope and constant product specific returns to scale for each product.