MyOpenMath Assessment

1. When the local grocery store puts laundry detergent on sale, reducing its price from $4.30 per item to $3.70 per item, the quantity sold increases from 220 per week to 240 per week. This response illustrates which of the following concepts?

income elasticity of demand
price elasticity of supply
cross-price elasticity of demand
price elasticity of demand

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2. What does this concept represent?

the percentage change in quantity demanded divided by the percentage change in income
the percentage change in quantity supplied divided by the percentage change in price
the percentage change in the quantity of good A that is demanded as a result of a percentage change in the price of good B
the percentage change in quantity demanded divided by the percentage change in price

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3. Let's look at the first part of the formula. How do we find the percentage change in quantity using the midpoint formula?

the average quantity divided by the change in quantity, multiplied by 2
the change in quantity multiplied by the average quantity
the change in quantity divided by the average quantity, multiplied by 100

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4. How do we express the percentage change in quantity using the variables Q₁ (original quantity) and Q₂ (new quantity)?

`\frac{Q_{1}-Q_{2}}{2}\times 100`
`\frac{Q_{2}-Q_{1}}{(Q_{2}+Q_{1})}\times 100`
`\frac{Q_{2}-Q_{1}}{(Q_{2}+Q_{1})\div 2}\times 100`

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5. Now calculate the percentage change in quantity demanded by plugging in the numbers for Q₁ and Q₂.

percentage change in quantity demanded =

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6. Now let's look at the second part of the formula. How do we find the percentage change in price using the midpoint formula?

the average price divided by the change in price, multiplied by 2
the change in price multiplied by the average price
the change in price divided by the average price, multiplied by 100

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7. How do we express this using the variables P₁ (original price) and P₂ (new price)?

`\frac{P_{1}-P_{2}}{2}\times 100`
`\frac{P_{2}-P_{1}}{(P_{2}+P_{1})}\times 100`
`\frac{P_{2}-P_{1}}{(P_{2}+P_{1})\div 2}\times 100`

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8. Now plug in the numbers for P1 and P2 to calculate the percentage change in price.

9. Finally, using the whole formula, calculate the value of the price elasticity of demand for laundry detergent.

price elasticity of demand =

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10. Explain what this result means in words. Then click 'Submit' to compare your answer to ours.

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