Use the image to answer the question.

Question

A demand curve is graphed. A line graph is titled Demand for Peanut Butter. The horizontal axis labeled Quantity goes from 0 to 600 in increments of 100. The vertical axis labeled Price goes from 0 to 2.00 dollars in increments of 0.40 dollars. A line segment passes through points (100, 2.00 dollars), (200, 1.60 dollars), (300, 1.20 dollars), (400, 0.80 dollars) and (500, 0.40 dollars).

What is the elasticity of demand for peanut butter when the price changes from $2.00 to $0.40 as shown by this supply and demand curve?
(1 point)
Responses

0.5
0.2
5
0.004

Answer 1

To calculate the elasticity of demand between two points on the demand curve, we use the formula for the price elasticity of demand (E):

\[ E = \frac{% \text{ change in quantity demanded}}{% \text{ change in price}} \]

1. Identify the initial and new values:

   • Initial Price (P1): $2.00
   • New Price (P2): $0.40
   • Initial Quantity (Q1): 100
   • New Quantity (Q2): 500

2. Calculate the changes:

   • Change in Price: \(P2 - P1 = 0.40 - 2.00 = -1.60\)
   • Change in Quantity: \(Q2 - Q1 = 500 - 100 = 400\)

3. Calculate the average price and average quantity:

   • Average Price = \(\frac{P1 + P2}{2}= \frac{2.00 + 0.40}{2} = 1.20\)
   • Average Quantity = \(\frac{Q1 + Q2}{2}= \frac{100 + 500}{2} = 300\)

4. Calculate the percentage changes:

   • Percentage change in Price: \[ \frac{\text{Change in Price}}{\text{Average Price}} = \frac{-1.60}{1.20} = -1.33 \text{ (or } -133% \text{)} \]
   • Percentage change in Quantity: \[ \frac{\text{Change in Quantity}}{\text{Average Quantity}} = \frac{400}{300} = 1.33 \text{ (or } 133% \text{)} \]

5. Calculate the elasticity:

   • E = \(\frac{1.33}{-1.33} = -1\)

However, we generally take the absolute value when discussing elasticity, which gives us:

\[ |E| \approx 1 \]

Since calculated elasticity values aren't matching your options, let's instead calculate the point elasticity using original values directly:

\[ E = \frac{\Delta Q / Q}{\Delta P / P} = \frac{(500 - 100) / 100}{(0.40 - 2.00) / 2.00} = \frac{400 / 100}{-1.60 / 2.00} = \frac{4}{-0.8} = -5 \]

The absolute value of elasticity is 5.

Thus, the answer is:

5