Question

Quantity Demanded Price $25 $15 Complete the following table by calculating the price elasticity of demand between specified points and indicating whether inelastic, or unit elastic. (Hint: Use the midpoints formula.) Interval From P - $20 to P - $25 From P - $20 to P - $15 Price Elasticity of Demand -1.40 Elastic, Inelastic, or Unit Elastic Elastic Elastic Inelastic From P - $15 to P - $20 From P - $15 to P - $10 Inelastic

Answer 1

Midpoint formula:

Price elasticity of demand = (Q2-Q1)/ (Q2+Q1)/2

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

Here “Q” stands for quantity and “P” stands for Price.

Let’s take an example of price change from $20 to $25 and quantity change from 40 to 20.

Step 1: Q1 = 40; Q2 = 20; P1 = $20; P2 = $25

Step 2: Average of quantity = (Q2+Q1)/2 = (20+40)/2 = 30

Step 3: Applying the midpoint formula for quantity;

               (20-40)/30^#= -0.67

^{# From step 2}

Step 4: Average of Price = (P2+P1)/2 = (20+25)/2 = 35

Step 3: Applying the midpoint formula for quantity;

               (25-20)/35^@= 0.22

^{@ From step 4}

Final answer = -0.6/0.143 = -3

Similarly,

Interval	Price elasticity of demand
From $20 to $25	-3
From $20 to $15	-1.4
From $15 to $20	-1.4
From $15 to $10	-0.714

Point Elasticity:

For the second part, you need to use the formula of point elasticity.

If it’s >1 its elastic, if its <1 it’s inelastic and if it’s equal to 1 its unit elastic.

Point elasticity = (new quantity- initial quantity)/ initial quantity

                              (Initial price – new price)/ initial price

From the above example = (20-40)/40

                                            (20-25)20

Elasticity = 2 (which is greater than 1, thus elastic)

Similarly,

Interval	Price elasticity of demand
From $20 to $25	2 = elastic
From $20 to $15	2 = elastic
From $15 to $20	1 = unit elastic
From $15 to $10	1 = unit elastic