Using the data under D1 and D2, calculate the cross elasticity of Lorena’s demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.)


Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.
Cross elasticity of Lorena’s demand at the price of $55 =


Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.

Cross elasticity of Lorena’s demand at the price of $40 =


Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.

Cross elasticity of Lorena’s demand at the price of $25 =


Is the cross elasticity the same at all three prices?

no

To calculate the cross elasticity of demand using the midpoints approach, we need to use the following formula:

Cross elasticity = ((Qd2 - Qd1) / ((Qd2 + Qd1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

Let's calculate the cross elasticity of demand at each price point:

1. Cross elasticity at the price of $55:
Using the data provided, we have:
Qd1 = 100
Qd2 = 80
P1 = $60
P2 = $55

Cross elasticity = ((80 - 100) / ((80 + 100) / 2)) / (($55 - $60) / (($55 + $60) / 2))
Cross elasticity ≈ ((-20) / (180 / 2)) / (-$5 / ($115 / 2))
Cross elasticity ≈ ((-20) / 90) / (-$5 / 57.5)
Cross elasticity ≈ (-0.2222) / (-0.0869)
Cross elasticity ≈ 2.5593

Therefore, the cross elasticity of Lorena's demand at the price of $55 is approximately 2.56.

2. Cross elasticity at the price of $40:
Using the data provided, we have:
Qd1 = 100
Qd2 = 120
P1 = $60
P2 = $40

Cross elasticity = ((120 - 100) / ((120 + 100) / 2) / (($40 - $60) / (($40 + $60) / 2))
Cross elasticity ≈ ((20) / (220 / 2)) / (-$20 / ($100 / 2))
Cross elasticity ≈ ((20) / 110) / (-$20 / 50)
Cross elasticity ≈ 0.1818 / (-0.4)
Cross elasticity ≈ -0.4545

Therefore, the cross elasticity of Lorena's demand at the price of $40 is approximately -0.45.

3. Cross elasticity at the price of $25:
Using the data provided, we have:
Qd1 = 100
Qd2 = 200
P1 = $60
P2 = $25

Cross elasticity = ((200 - 100) / ((200 + 100) / 2) / (($25 - $60) / (($25 + $60) / 2))
Cross elasticity ≈ ((100) / (300 / 2)) / (-$35 / ($85 / 2))
Cross elasticity ≈ ((100) / 150) / (-$35 / 42.5)
Cross elasticity ≈ 0.6667 / (-0.8235)
Cross elasticity ≈ -0.8109

Therefore, the cross elasticity of Lorena's demand at the price of $25 is approximately -0.81.

Finally, is the cross elasticity the same at all three prices?
No, the cross elasticity is not the same at all three prices. The cross elasticity at each price point is different.

To calculate the cross elasticity of demand using the midpoints approach, we need the following information:

- The percentage change in the quantity demanded of golf
- The percentage change in the price of golf

Let's first calculate the percentage change in quantity demanded (Qd) using the formula:

% change in Qd = [(New Qd - Old Qd) / ((New Qd + Old Qd) / 2 )] * 100

Then, we can calculate the percentage change in price (P) using the formula:

% change in P = [(New P - Old P) / ((New P + Old P) / 2)] * 100

Finally, we can use the formula for cross elasticity of demand:

Cross elasticity of demand = (% change in Qd) / (% change in P)

Now let's calculate the cross elasticity at each price:

At the price of $55:
Old Qd = 120
New Qd = 60
Old P = $55
New P = $40

% change in Qd = [(60 - 120) / ((60 + 120) / 2 )] * 100 = -50%
% change in P = [($40 - $55) / (($40 + $55) / 2)] * 100 = -27.78%

Cross elasticity at $55 = (-50% / -27.78%) ≈ 1.8

At the price of $40:
Old Qd = 120
New Qd = 90
Old P = $40
New P = $25

% change in Qd = [(90 - 120) / ((90 + 120) / 2 )] * 100 = -17.65%
% change in P = [($25 - $40) / (($25 + $40) / 2)] * 100 = -37.5%

Cross elasticity at $40 = (-17.65% / -37.5%) ≈ 0.47

At the price of $25:
Old Qd = 120
New Qd = 110
Old P = $25
New P = $10

% change in Qd = [(110 - 120) / ((110 + 120) / 2 )] * 100 = -4.76%
% change in P = [($10 - $25) / (($10 + $25) / 2)] * 100 = -58.82%

Cross elasticity at $25 = (-4.76% / -58.82%) ≈ 0.08

Now let's check if the cross elasticity is the same at all three prices:

The cross elasticity values are approximately 1.8, 0.47, and 0.08 at the prices of $55, $40, and $25 respectively. Therefore, the cross elasticity is not the same at all three prices.