from a misunderstanding: it should be 'cheap at twice the price'. I suppose people have trouble with fractions. It's probably originally market trader talk or something like that.
�Cheap at half the price would make more sense if it were �cheap at double the price', as J says above. Market-traders/street-sellers, such as Del-Boy Trotter, might have cried:"This is worth �8.00 but I'm not asking for �8.00...I'm not even asking for �4.00...all I'm asking today is �2.00! Come on, ladies and gentlemen...it's cheap at half the price!" Another way of expressing it would be to think of "(This item is) cheap (today) at half the (normal) price."
No, no, it's just a boring joke. "Cheap at twice the price" was an (usually insincere) come-on to you to buy. Clever-dicks then took the mickey out of it by reversing it.