6 the average or unit cost of a payment. Up to some point, the larger is payment volume, the lower is the average cost of processing each payment.

Similarly, if the extra or marginal cost of processing one type of payment instrument is reduced as the volume of another payment instrument rises, then there will be economies of scope. When credit card payments over a network use the same terminals, communication links, or computers as debit card payments, the marginal cost of a credit card payment can fall as debit card volume rises (or vice versa). Similar economies of scope arise when ATM terminals use the same communication links as debit card transactions (as is more common). Scope economies exist when the total cost of processing two or more payment instruments together (jointly) is lower than the sum of the costs of processing the same volume of each instrument separately.6 (For a discussion of some empirical evidence of scope and scale economies see Annex 2).

# 4. **Demand for payment** services

The demand for a payment instrument is influenced by economic variables such as own price, the price and availability of substitutes, and user income. It is also influenced by such difficult to quantify influences as user convenience, acceptability by payees, and safety in use. For this and other reasons, the effect of price on the demand for payment instruments has been difficult to measure, although inferences can be made.

**_Substitution among payment instruments._** Due to a lack of extended time-series data within any one country, it has been necessary to infer the demand for and substitution among noncash payment instruments from pooled time-series cross-country analysis using data developed by the Bank for International Settlements. The relationships among the per person use of five non-cash payment instruments plus cash is illustrated in Table 1. Of the 15 pair-wise correlation coefficients, 11 are negative suggesting substitution.7 However, these substitution effects are weak since the largest negative correlation coefficient (or r) is -. 50.8

6 _Scope economies can have two sources. First, if excess capacity exists, the fixed costs associated with processing one type of payment instrument can be spread over processing other instruments as well. For example, if buildings and large computers have unused productive capacity, other types of payment instruments may be processed using these same facilities at low additional expense. Second, joint production costs can be lower when certain variable expenses can also be shared, as when credit and debit card payments use the same card terminals, communication links, or personnel._ 7 _The correlations relate the annual number of transactions per person across 14 developed countries in each year over 1987-93. Cash use reflects the real value of cash holdings per person, also across countries and for each year._ I _The strongest relationship is between checks and credit cards which, with an r of .81, suggests strong complementarity. When the U.S. (which uses the most checks and credit cards) is excluded, the complementarity between checks and credit cards is reduced but not eliminated Cr = .52). The complementarity of debit cards with both paper and electronic giro transactions reflects their positive cross-country and time-series association in various European countries while the complementarity between electronic giro use and cash reflects a positive association in Europe and Japan._