$1\mathrm{.}2\mathrm{.}3.$ What would be the profit$-$maximizing price$-$menu $($ph$,$ p$)$ if the seller offered

both versions of the product, and ph and p$$ were such that each version were the most

appealing one for the buyers of at least one type? Notice that there are three alternative ways in which a solution of this type can be implemented; these alternatives are

illustrated in Table $3.$

H$-$type M$-$type L$-$type

Version under alternative $1$ h h $$

Version under alternative $2$ h $$

Version under alternative $3$ h $$ n

Table $3.$ The alternative ways in which the solution in $1\mathrm{.}2\mathrm{.}3$ could

be implemented. The symbol n indicates that the given buyer type

would not purchase either version of the product.