Question

While at a discount shoe store, a customer asked a clerk, “I see that your shoes are ‘buy one, get one free- limit one free pair per customer.’ Will you sell me one pair for half-price?” The clerk answered, “I can’t do that.” When the customer started to leave the store, the clerk hastily offered, “However, I am authorized to give you a 40 percent discount on any pair in the store.” Assuming the consumer has $200 to spend on shoes (X) or all other goods (Y), and that shoes cost $100 per pair, answer the following questions:
a) Illustrate the consumer’s opportunity set under the “buy one, get one free” deal and under a 40 percent discount.
b) Why was the 40 percent discount offered only after the consumer rejected the “buy one, get one free” deal and started to leave the store?
c) Why was the clerk willing to offer a “buy one, get one free” deal, but unwilling to sell a pair of shoes for half-price?

Answer 1

a. Consumer opportunity set: The given income of consumer is $200 and the cost of the shoe is S100 per pair. Therefore, without any discount, consumer has the following options: Bundle A: spending all of the income on other goods, S200 value of other goods Bundle B: Spending all the income on shoes that means 2 pair of shoes The buy-one-get one has he following options: Bundle A: spending all of the income on other goods, S200 value of other goods. Bundle C: spending all the income on shoes that means 3 pair of shoes. b. If the consumer wants to purchase only a single pair, then buy-one-get-one offer is not preferred by the consumer because the utility of the second pair will be negligent. Therefore, the clerk will be ready to sell the shoe at 40% discount to crack the deal. This is because a 40% discount on shoes indicates the price of $60 per pair (100-40 . This is better than selling the shoe at $50 per pair (half of the price.)

Buy-one-get one offer as well as selling shoes at half price, both have the same result. However, the clerk is unwilling to sell a pair of shoes for half-price. The option buy one, get one will earn S100, whereas selling shoes at half price wl earn only S50. Thus, the first option entails a higher sale