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Suppose the price of an item is $P at two Ontario retail stores. One retailer tells...

Suppose the price of an item is $P at two Ontario retail stores. One retailer tells you he will knock 13% off the price as a discount. Another says she will give you a HST break instead (i.e., you do not pay the tax). Which retailer should you buy the item from? [Note: Do not substitute a numerical value for P. The answer is to be formulated, in general terms, in term of P – not in terms of a number.]

HST is a 13% tax

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Answer #1

In this case, the total cost from the first retailer should be equal to discounted price plus taxes. That is,

= (1 -0.13P) +0.13(1 -0.13)P

= (0.87P) (1.13)

=0.9831P

The total cost of retailer two is P only. So, the retailer 1 is cheaper.

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