Find the price elasticity of demand between P = $35 and P = $30 and between P = $15 and P = $10

The price elasticity of demand formula can be summarized by taking the percentage change in quantity demanded divided by the percentage change in price.

In order to calculate the percentage change in quantity, we need to use the midpoint formula

(Q2 - Q1) / ((Q2 + Q1) / 2)

where Q2 is the new quantity demanded and Q1 is the previous quantity demanded.

In order to calculate the percentage change in price, we'll use the midpoint formula

(P2 - P1) / ((P2 + P1) / 2)

where P2 is the new price point and P1 is the previous price point.

First, we're tasked with finding the price elasticity of demand (PED) moving from P = $35 to P = $30.

To calculate the percentage change in quantity, we need to know that the quantity is increasing from 5 to 10, which makes sense since the price is falling from $35 to $30 (the law of demand tells us that quantity demanded increases as the price falls).

Putting this into the midpoint formula gives us Q2 = 10 and Q1 = 5.

Thus, (10 - 5) / ((10 + 5) / 2) = .67, which is the percentage change in quantity demanded.

In this scenario, P1 = $35 and P2 = $30.

Thus, (30 - 35) / ((30 + 35) / 2) = -.15, which is the percentage change in price.

Now, we can use our formula for PED and take the change in quantity / the change in price.

Thus, .67 / -.15 = -4.5.

Next, since the law of demand tells us that this number will be negative, we take the absolute value. That leaves us with 4.5. Since 4.5 is larger than 1, we know that the demand is elastic.

Moving on to finding the PED as it moves from P1 = $15 to P1 = $10. The chart tells us that Q1 = 25 and Q2 = 30.

The percentage change in quantity demanded = (30 - 25) / ((30 + 25) / 2) = .18.

The percentage change in the price = (10 - 15) / ((10 + 15) / 2) = -.4.

The price elasticity of demand = .18 / -.4 = -.45.

Taking the absolute value we end up with .45. Since .45 is less than 1, we know that the demand is inelastic.

Returning to our question, it asks in which price range the demand is more elastic. It would be more elastic between $35 and $30 than between $15 and $10 because the value for price elasticity of demand is larger (4.5 is greater than .45).