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 with the "buy one, get one free" deal and with 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?