The price of strawberries falls from $1.50 to $1.00 per carton and the quantity demanded goes from 100,000 to 200,000 cartons. use the midpoint method to find the price elasticity of demand.

Answers

Answer 1
Final answer:

The price elasticity of demand, which measures the responsiveness in the quantity demanded due to a change in price, is -2. This is computed using the Midpoint Method, and indicates that the quantity demanded is highly responsive to changes in price.

Explanation:

The Price Elasticity of Demand (PED) measures how much the quantity demanded of a good responds to a change in its price. This can be calculated using the Midpoint Method, which is a more precise way of computing the elasticity when there is a change in both price and quantity.

The midpoint formula is given as: (Q2 - Q1) / ((Q2 + Q1)/2) / (P2 - P1) / ((P2 + P1)/2), where Q1 and P1 are the initial quantity and price, and Q2 and P2 are the final quantity and price.

Substituting in the given values in the problem: PED = (200,000 - 100,000) / ((200,000 + 100,000)/2) / ($1.00 - $1.50) / (($1.00 + $1.50)/2) = 666,666.67 x -1/-0.333 = -2. So the price elasticity of demand is -2. This indicates that the quantity demanded is very responsive to changes in price.

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Answer 2

The price elasticity of demand using the midpoint method is approximately -3.

To calculate the price elasticity of demand (PED) using the midpoint method, we use the following formula:

[tex]\[ PED = \frac{(Q_2 - Q_1) / ((Q_1 + Q_2) / 2)}{(P_2 - P_1) / ((P_1 + P_2) / 2)} \][/tex]

where [tex]\( Q_1 \) and \( Q_2 \)[/tex] are the original and new quantities demanded, and [tex]\( P_1 \) and \( P_2 \)[/tex] are the original and new prices.

Given:

- Original price [tex](\( P_1 \))[/tex] = $1.50

- New price [tex](\( P_2 \))[/tex] = $1.00

- Original quantity demanded [tex](\( Q_1 \))[/tex] = 100,000 cartons

- New quantity demanded [tex](\( Q_2 \))[/tex] = 200,000 cartons

First, we calculate the change in quantity demanded and the change in price:

[tex]\[ \Delta Q = Q_2 - Q_1 = 200,000 - 100,000 = 100,000 \text{ cartons} \][/tex]

[tex]\[ \Delta P = P_1 - P_2 = $1.50 - $1.00 = $0.50 \][/tex]

Next, we find the average quantity and average price:

[tex]\[ \text{Average quantity (AQ)} = \frac{Q_1 + Q_2}{2} = \frac{100,000 + 200,000}{2} = 150,000 \text{ cartons} \][/tex]

[tex]\[ \text{Average price (AP)} = \frac{P_1 + P_2}{2} = \frac{$1.50 + $1.00}{2} = $1.25 \][/tex]

Now we can calculate the price elasticity of demand:

[tex]\[ PED = \frac{\Delta Q / AQ}{\Delta P / AP} = \frac{100,000 / 150,000}{0.50 / 1.25} \][/tex]

[tex]\[ PED = \frac{2/3}{2/5} \][/tex]

[tex]\[ PED = \frac{2}{3} \times \frac{5}{2} \][/tex]

[tex]\[ PED = \frac{10}{6} \][/tex]

[tex]\[ PED = \frac{5}{3} \][/tex]

[tex]\[ PED \approx -3 \][/tex]

The negative sign indicates that the demand for strawberries is elastic; that is, the percentage change in quantity demanded is greater than the percentage change in price. The magnitude of the elasticity, approximately 3, suggests that for every 1% decrease in the price of strawberries, the quantity demanded increases by approximately 3%.


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