We know that Ralph's price is greater than HP's.
Pr > Php
where Pr is Ralph's price, Php the Higgledy-Piggledgy's price.
But what matters is whether Ralph's COST (Cr) is great than HP's PRICE:
If and only if Cr > Php can you make both yourself and Ralph better
off by shopping at the HP.
For example, say cereal costs Ralph $4/box, but HP sells it for $3/box. And say Ralph sells cereal for $5/box, so that he makes $1 profit on each box. By buying at the HP, you save $2; give $1.50 of it to Ralph, and you're both better off.
On the other hand, say cereal costs Ralph $2.50,
but HP sells it for $3/box. And say Ralph sells cereal for $3.50/box
so that he makes $1 profit on each box, by buying at the HP, you save $.50,
but Ralph loses $1--you can't divvy up your fifty cent gain to make both
of you better off.
Of course, since Ralph could avoid this situation
and still make a profit by lowering his price to $3, it's hard to feel
much sympathy for him.
In general, when you buy at HP you save so much you
can compensate Ralph and leave both of you better off; i.e., you save more
Ralph loses when you but at HP--if and only if
Pr - Php > Pr - Cr
or Cr > Php.
Conversely, when you buy at HP you don't save
enough to compensate Ralph and leave both of you better off; i.e., you
save less than Ralph loses when you but at HP--if and only if
Pr - Php < Pr - Cr
or Cr < Php.
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This page maintained by Steven Blatt. Suggestions,
comments, questions, and corrections are welcome.