To calculate the price elasticity of demand using the midpoint formula, we follow these steps:

1. Identify the initial and final prices and quantities.
- Initial price (P1) = $18
- Final price (P2) = $20
- Initial quantity demanded (Q1) = 17
- Final quantity demanded (Q2) = 12

2. Calculate the percentage change in quantity demanded.
$$
\text{Percentage change in quantity demanded} = \frac{Q2 - Q1}{\frac{Q2 + Q1}{2}} \times 100
$$
$$
= \frac{12 - 17}{\frac{12 + 17}{2}} \times 100
$$
$$
= \frac{-5}{14.5} \times 100
$$
$$
= -34.48\%
$$

3. Calculate the percentage change in price.
$$
\text{Percentage change in price} = \frac{P2 - P1}{\frac{P2 + P1}{2}} \times 100
$$
$$
= \frac{20 - 18}{\frac{20 + 18}{2}} \times 100
$$
$$
= \frac{2}{19} \times 100
$$
$$
= 10.53\%
$$

4. Calculate the price elasticity of demand using the midpoint formula.
$$
\text{Price elasticity of demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
$$
$$
= \frac{-34.48\%}{10.53\%}
$$
$$
= -3.27
$$

Given the options, the closest value to -3.27 is -3.29. Therefore, the price elasticity of demand when the price increases from $18 to $20 is:

-3.29.

Question

To calculate the price elasticity of demand using the midpoint formula, we follow these steps:

1. Identify the initial and final prices and quantities.
   - Initial price (P1) = $18
   - Final price (P2) = $20
   - Initial quantity demanded (Q1) = 17
   - Final quantity demanded (Q2) = 12

2. Calculate the percentage change in quantity demanded.
   $$
   \text{Percentage change in quantity demanded} = \frac{Q2 - Q1}{\frac{Q2 + Q1}{2}} \times 100
   $$
   $$
   = \frac{12 - 17}{\frac{12 + 17}{2}} \times 100
   $$
   $$
   = \frac{-5}{14.5} \times 100
   $$
   $$
   = -34.48\%
   $$

3. Calculate the percentage change in price.
   $$
   \text{Percentage change in price} = \frac{P2 - P1}{\frac{P2 + P1}{2}} \times 100
   $$
   $$
   = \frac{20 - 18}{\frac{20 + 18}{2}} \times 100
   $$
   $$
   = \frac{2}{19} \times 100
   $$
   $$
   = 10.53\%
   $$

4. Calculate the price elasticity of demand using the midpoint formula.
   $$
   \text{Price elasticity of demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
   $$
   $$
   = \frac{-34.48\%}{10.53\%}
   $$
   $$
   = -3.27
   $$

Given the options, the closest value to -3.27 is -3.29. Therefore, the price elasticity of demand when the price increases from $18 to $20 is:

-3.29.

Knowee AI · Accepted Answer

To calculate the price elasticity of demand using the midpoint formula, we follow these steps:

1. Identify the initial and final prices and quantities.
   - Initial price (P1) = $18
   - Final price (P2) = $20
   - Initial quantity demanded (Q1) = 17
   - Final quantity demanded (Q2) = 12

2. Calculate the percentage change in quantity demanded.
   $$
   \text{Percentage change in quantity demanded} = \frac{Q2 - Q1}{\frac{Q2 + Q1}{2}} \times 100
   $$
   $$
   = \frac{12 - 17}{\frac{12 + 17}{2}} \times 100
   $$
   $$
   = \frac{-5}{14.5} \times 100
   $$
   $$
   = -34.48\%
   $$

3. Calculate the percentage change in price.
   $$
   \text{Percentage change in price} = \frac{P2 - P1}{\frac{P2 + P1}{2}} \times 100
   $$
   $$
   = \frac{20 - 18}{\frac{20 + 18}{2}} \times 100
   $$
   $$
   = \frac{2}{19} \times 100
   $$
   $$
   = 10.53\%
   $$

4. Calculate the price elasticity of demand using the midpoint formula.
   $$
   \text{Price elasticity of demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
   $$
   $$
   = \frac{-34.48\%}{10.53\%}
   $$
   $$
   = -3.27
   $$

Given the options, the closest value to -3.27 is -3.29. Therefore, the price elasticity of demand when the price increases from $18 to $20 is:

-3.29.

Use the data in the table below to answer the following question. Price Quantity Demanded$20 1218 1716 2014 2412 3010 368 406 444 48 The price elasticity of demand (based on the midpoint formula) when price increases from $18 to $20 isMultiple Choice-3.29.-1.37.-1.-0.33.

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