Consider a cereal manufacturer with two types of customer. Type 1 individuals have reservation price $4, and using a coupon costs them $1.25 (in terms of effort/time). Type 2 individuals have reservation price $3, and using a coupon does not cost them anything. It costs the manufacturer $2.50 to produce each box of cereal.
(a) What price should the manufacturer charge the type 1's? How large a discount could the coupons offer without tempting the type 1's to use them?
(b) At the above price, how large a discount would the coupons have to offer to induce the type 2's to buy cereal?
(c) What price and coupon discount should the manufacturer set? Calculate the profits he receives from each group. Would he still offer coupons if the manufacturing cost suddenly rose to $3?