Question

if the price elasticity of demand for a good is about 1.3, then which of the following is consistent with a 7 percent increase in the quantity demanded of the good?

Answer 1

A 7 percent increase in the quantity demanded of the good is consistent with a price elasticity of demand of approximately 5.38.

Explanation:

The price elasticity of demand (Ed) is calculated using the formula Ed = (% change in quantity demanded) / (% change in price). In this case, Ed is given as 1.3, and the percentage increase in quantity demanded is 7 percent. To find the percentage change in price, we rearrange the formula to solve for it:

`\[ Ed = (\%\Delta QD)/(\%\Delta P) \]\\\`

`\[ 1.3 = (7)/(\%\Delta P) \]`

Solving for
`\%ΔP`, we get:

`\[ \% \Delta P = (7)/(1.3) \approx 5.38\% \]`

This means that for a 7 percent increase in quantity demanded, the price must decrease by approximately 5.38 percent to maintain a price elasticity of demand of 1.3.

The positive value of the price elasticity of demand indicates that the good is elastic, meaning the percentage change in quantity demanded is more responsive than the percentage change in price. Therefore, a decrease in price is associated with an increase in quantity demanded. In this specific scenario, a 5.38 percent decrease in price would result in a 7 percent increase in the quantity demanded, consistent with the given price elasticity of demand.

Answer 2

A 5.38% decrease in price would be consistent with a 7% increase in the quantity demanded given a price elasticity of demand of 1.3. This information would guide a company on pricing decisions: with an elasticity above 1, decreasing price can lead to higher revenue, as increased sales offset the lower price.

Step-by-step explanation:

If the price elasticity of demand for a good is about 1.3, then this suggests that the good is relatively elastic. As a result, the quantity demanded is responsive to changes in price. To understand the consequences of a 7 percent increase in quantity demanded, we should consider what change in price would lead to such an increase.

Using the formula for elasticity which is:

Price Elasticity of Demand (PED) = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)

We can plug in the known elasticity of 1.3 and the percentage change in quantity demanded of 7 percent to solve for the required percentage change in price. It follows that:

1.3 = (7%) / (Percentage Change in Price)

Therefore:

Percentage Change in Price = (7%) / 1.3

Percentage Change in Price ≈ 5.38%

A 5.38 percent decrease in price would be consistent with a 7 percent increase in the quantity demanded when the price elasticity of demand is 1.3.

In a practical sense, if a company had a product with a demand elasticity of 1.4, they would be advised to lower its price because the increase in the amount sold would compensate for the lower price, as compared to if the elasticity were 0.6, in which case they should increase the price because the increase in revenue from a higher price outweighs the loss from selling fewer units. If the elasticity were 1, they would maximize their total revenue by maintaining the current price.