Usually, when you purchase a lot in an auction, you pay not only your winning bid...
Usually, when you purchase a lot in an auction, you pay not only your winning bid price but also a buyer's premium. At one auction house, the buyer's premium is 21% of the winning bid price for purchases up to $60,000. For larger purchases, the buyer’s premium is 21% of the first $60,000 plus 7% of the purchase price above $60,000. Express the total purchase price of a lot at this auction house as a function of the final (winning) bid price. Sketch the graph of this function.
Homework Answers
Let us denote the final (winning) bid price by x. Then, if x<=$60,000 the total amount to be paid will be equal to:
=x + 21% of x
=x (1+0.21)
= 1.21x
similarly if x>60,000 the total amount to be paid will be equal to:
= x + 21% of 60,000 + 7% of (x-60,000)
= x + 12600 + 0.07*(x-60000)
= x + 12600 + 0.07x - 4200
= 1.07x + 8400
So we can write the purchase price as a function of x as
p(x)= 
The graph will look like as shown below:
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