A more recent article reviewed some thirteen studies that attempted to estimate economies of scale and economies of scope for credit unions, savings and loan associations, and commercial banks.48 Economies of scale are defined as those associated with firm size, whereas economies of scope relate to the joint production of two or more products. Economies of scale exist if per unit or average production costs decline as output rises. Economies of scope arise if two or more products can be jointly produced at a lower cost than is incurred in their independent production. Each study used a logarithmic function and employed similar measures of economies. The author summarized the results of these thirteen studies as follows: