Coupons and rebates
Coupons and rebates are marketing tools used to incentivize purchases and enhance brand visibility. Historically, the first known coupon dates back to 1894 when Coca-Cola issued handwritten tickets for product samples. By the 1930s, the use of coupons surged during the Great Depression as consumers sought ways to save money. Today, coupons come in various forms, including traditional paper coupons, digital codes, and discount cards. They offer small discounts at the time of purchase, whereas rebates can provide larger reimbursements, either instantaneously or after a mail-in process.
When using manufacturer coupons, customers pay tax on the full price before the discount is applied, while store coupons allow the tax to be calculated after the discount. Retailers also utilize loyalty cards to track purchases and offer tailored discounts, which may require an upfront fee. In addition to saving money, coupons and rebates can encourage consumers to try new products. However, economic studies suggest that rebates may not significantly boost consumer spending, as seen during various tax rebate initiatives. Overall, both coupons and rebates play a significant role in consumer behavior and retail marketing strategies.
Coupons and rebates
Summary: Mathematical differences between coupons and rebates provide different rewards to consumers.
Offering price reductions through coupons and rebates is a popular means of increasing the number of sales of a product, attracting customers to retail stores (both physical and online), and promoting public awareness of a brand name or product. One of the first known instances of a coupon was in 1894, when the Coca-Cola Company gave out handwritten tickets for samples of its new soft drink. The next year, Charles Post, of Post Cereal, started issuing coupons to help sell groceries. By the 1930s, these coupons were increasingly popular for saving money during the Great Depression. Some researchers claim that by the mid-1960s, half of American households used coupons.
In the twenty-first century, coupons are available on the Internet, or as permanent discount cards, in addition to their traditional paper form. In the age of online shopping, coupons for free shipping are cited by some as one of the most important factors in determining where to shop. For the customer, coupons and rebates bring savings on regularly purchased items and provide an incentive to try new products or services. In general, coupons are small discounts (a few dollars or cents) redeemed at the time of payment. The term “rebate” generally refers to larger reimbursements or discounts where the price reduction is either applied at the time of sale (an instant rebate) or reimbursed after required documents are mailed in by the customer. The specific type of coupon or rebate affects the calculation of both the discount and any applicable sales tax.
Coupons
Coupons may be issued by a product manufacturer or a store, and the redemption is somewhat different for the two types. When a customer presents a manufacturer coupon to a retailer, the customer pays any applicable tax on the full price of the item before the coupon is applied. For example, if a retailer charges $50 for a product with an 8% sales tax and a customer presents a manufacturer coupon for $10, then the cost to the customer at the time of purchase would be $44; that is, the original $50, plus sales tax of $4 ($50 × 0.08), minus the $10 coupon. Typically, the manufacturer reimburses the retailer for the amount of the coupon plus handling.
Sometimes a retailer like a grocery store, pizza restaurant, or automobile detailer will offer its own store coupons or rebates on its products or services. When a customer uses a store coupon, tax is computed on the balance after the coupon is deducted. If the $10 manufacturer’s coupon is replaced by a $10 store coupon, the cost to the customer would be less: $43.20 versus $44.00.
Many retailers issue plastic cards that customers present to take advantage of weekly card specials or to receive a certain percentage discount on purchases made with the card. These cards not only allow shoppers to save money, but also the data collected when these cards and the associated purchases are scanned allow stores to better track their sales and inventory, and sometimes offer additional discounts tailored to a specific buyer’s purchasing patterns. Sometimes these cards are free, but other times they require an initial or annual fee.
A retailer may offer a card at a cost of $10 that can be used for a 10% discount on all purchases at that store for one year. If a first-time customer checks out with a balance of $110 before tax, the customer can determine whether to purchase the card and take the 10% reduction. Although the card costs $10, the customer would save $11 on the initial balance (10% of the $110 total), resulting in a final cost of $109. The tax would be marginally less as well, since the total was reduced. Thus, the card would pay for itself at the first purchase, even before any other savings occur.
Another form of coupon is a card that is stamped each time the customer purchases a specified type of product, until a certain number of stamps are accrued. The customer then receives the next purchase of the specified product type free of charge, except for—possibly—sales tax. This form of coupon may be offered by certain restaurants, food markets, coffee shops, or bookstores.
Rebates
For a manufacturer rebate, an electronics retailer may sell a computer for $1,500, together with a free $100 printer after a mail-in rebate. The customer pays the tax on both the computer and the printer, and the manufacturer reimburses the customer $100 after the rebate is processed. With 8% sales tax, the cost to the customer after the rebate would be $1,628 (where the sales tax was 8% of $1,600, or $128).
Historically, economists have viewed consumer spending as a function of income. Politicians often cite this principle when pushing for tax rebates, believing they will increase consumption. However, there is little empirical evidence to support this notion, and in some cases there is contrary evidence. In 2001, the U.S. Congress enacted a tax rebate, giving $300 to anyone who had paid income taxes the previous year ($600 for couples). Economic indicators showed no associated increase in spending but rather a spike in saving. A survey of a sample of households that received a rebate reported that roughly one in five of those asked said they would spend the money. The Wall Street Journal ran the headline “Rebates Boost Incomes, But Not Spending.” A study of the 2008 rebate found similar results.
Coupon Collector’s Problem
There is a classic probability problem known as the Coupon Collector’s Problem, which has been explored by a number of mathematicians, including the prolific Paul Erdos. The problem supposes that there is some number of different coupons (n) a person needs to collect to win a prize and asks how many coupons will he or she have to acquire, one at a time, to get a complete set. Usually, the coupons are equally likely to be drawn, and getting one of the n coupons does not prevent another of the same type from being drawn. Solutions to the problem can be found in a number of ways, including harmonic numbers, probability generating functions, and simulation. Extensions of the Coupon Collector’s Problem are very useful in manufacturing quality control, for situations in which a number of product types must be sampled.
Bibliography
Better Business Bureau. “Mail-In Rebates: Now Available in Paper or Plastic.” http://www.bbb.org/us/article/mail-in-rebates-now-available-in-paper-or-plastic-13249.
Spencer, K., and S. Rose. How to Shop for Free: Shopping Secrets for Smart Women Who Love to Get Something for Nothing. Philadelphia: Da Capo Press, 2010.