Stanley Pope
11/19/2023 · Middle School

Exercise 10 Suppose a grocery store normally sells 100 cartons of milk per day and the price elasticity of demand for milk is 1.7. If the store lowers the price of milk by \( 10 \% \), about how many cartons of milk will it then sell per day?

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To determine how many cartons of milk the grocery store will sell after lowering the price, we can use the concept of price elasticity of demand. The price elasticity of demand (PED) is given by the formula: \[ \text{PED} = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}} \] In this case, we know: - The price elasticity of demand (PED) = 1.7 - The percentage change in price = -10% (since the price is lowered) We can rearrange the formula to find the percentage change in quantity demanded: \[ \%\text{ change in quantity demanded} = \text{PED} \times \%\text{ change in price} \] Substituting the known values: \[ \%\text{ change in quantity demanded} = 1.7 \times (-10\%) = -17\% \] This means that the quantity demanded will decrease by 17%. Now, we can calculate the new quantity demanded. The store normally sells 100 cartons of milk per day, so we can find the new quantity as follows: \[ \text{New quantity} = \text{Old quantity} + \left(\text{Old quantity} \times \frac{\%\text{ change in quantity demanded}}{100}\right) \] Calculating the decrease in quantity: \[ \text{Decrease in quantity} = 100 \times \left(-\frac{17}{100}\right) = -17 \] Now, we can find the new quantity: \[ \text{New quantity} = 100 - 17 = 83 \] Thus, after lowering the price of milk by 10%, the grocery store will sell approximately **83 cartons of milk per day**.

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After lowering the price by 10%, the store will sell about 83 cartons of milk per day.
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