Question

The initial price of a good is 2.5X. A week later it drops 15%. A week later it drops another 20%. it still doesn't sell, so the manager marks it down an extra $10 in week 3. If you buy it for 30% of the original price, what was its price after the markdown in week 2?

Answer 1

Answer on Question #44765 – Economics – Macroeconomics

The initial price of a good is 2.5X. A week later it drops 15%. A week later it drops another 20%. it still doesn't sell, so the manager marks it down an extra $10 in week 3. If you buy it for 30% of the original price, what was its price after the markdown in week 2?

Solution

If the initial price is 2.5, then the price after the markdown in week 2 will be $2.5X*(1 - 0.15)*(1 - 0.2)$. And after the price is decreased by $10 and becomes 30% of the original price, so $2.5X*(1 - 0.15)*(1 - 0.2) - 10 = 0.3*2.5X$

$2.5X*0.68 - 10 = 0.3*2.5X$

$0.38*2.5X = 10$

$0.38X = 4$

$X = 4/0.38 = \$10.53$

So, the price after the markdown in week 2 will be $2.5*10.53*0.68 = \$17.9$

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