Question

Problem:

A discount shoe store always runs a ‘buy one, get one free (limit one free pair per customer)’ campaign. A customer asked a clerk, if he would sell her one pair for half price. The clerk answered, “I’m sorry, I can’t do that.” but when customer decided to leave the store, the clerk hastily offered, “However, I think I can give you a 40% 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:

a. Illustrate the consumer’s opportunity set with the “buy one, get one free” deal and with a 50 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) As the consumer has $200 to spend either on shoes(x) or on all other products (y) so in case of buy one, get one free the opportunity set consumer can buy 2 pair of shoes as the cost of each pair would be $100 which equals to $200 but as the scheme says buy one, get one free the consumer will finally own 3 pair of shoes as the limit of free pair of shoe per customer is only 1

while in case of 50% discount the cost of the shoe become $50 and consumer has $200 to spend which will benefit the consumer as now he can purchase and own 4 pair of shoes of $50 each.

b) Because if we se the deal of buy one, get one free implies 50% discount on the shoes which is more than the discount offered by the clerk of 40% but we must also notice that the free limit is upto one pair of shoe per customer and after that we have to pay the full price for the shoe but if we see from clerk point of view all the shoes are at 50% discount but by offering 40% discount clerk saves the 10% margin in discount which will increase the revenue comes from shoe.

c) The reason clerk is willing to offer buy one, get one free but unwilling to sell a pair of shoe on half price is same as discussed above as we said above the deal is applicable to only one pair of shoe per customer and afterwards customer would have to pay the full amount for the shoe but it's not same when he sells the pair of shoe on half price because in that case all the shoes have to be given at a 50% discount.