Cash users withdraw money from automated teller machines (ATMs) to finance cash payments. However, most ATMs in the United States dispense only multiples of $20 bills. The paper first constructs a consumer's optimization model showing how the precise denomination of dollar bills available from...

Recent legislation and court settlements in the United States allow merchants to use price discounts to steer customers to pay with means of payment that are less costly to merchants. This paper suggests one method of calculating merchants' change in profit associated with giving price discounts...