Using the midpoints approach to the cross elasticity of demand-calculate the cross eleasticity the demand for golf at all 3 prices.
Price Demand1 D2 D3
50 15 10 15
35 25 15 30
20 40 20 50
D1 -Income $50k per yr, movies $9
D2 -Income $50k -movies $11
D3 -Income $70k -movies $11
Using D2, D3, calculate income elasticity of demand for golf.
McConnell, Microecon 19e
Chap 4 -Problem #7
To calculate the cross elasticity of demand using the midpoints approach, you need to use the following formula:
Cross elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Where:
- Q1 and Q2 are the quantities demanded at two different price levels.
- P1 and P2 are the two different price levels.
Let's calculate the cross elasticity of demand for golf at all three prices:
For Price = $50:
- Q1 = 15, Q2 = 10 (Demand1)
- P1 = $35, P2 = $20 (Demand1)
Cross elasticity of demand = ((10 - 15) / ((10 + 15) / 2)) / (($20 - $35) / (($20 + $35) / 2))
For Price = $35:
- Q1 = 25, Q2 = 15 (D2)
- P1 = $50, P2 = $20 (D2)
Cross elasticity of demand = ((15 - 25) / ((15 + 25) / 2)) / (($20 - $50) / (($20 + $50) / 2))
For Price = $20:
- Q1 = 40, Q2 = 20 (D3)
- P1 = $35, P2 = $50 (D3)
Cross elasticity of demand = ((20 - 40) / ((20 + 40) / 2)) / (($50 - $35) / (($50 + $35) / 2))
To calculate the income elasticity of demand for golf, you need to use the formula:
Income elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((I2 - I1) / ((I2 + I1) / 2))
Where:
- Q1 and Q2 are the quantities demanded at two different income levels.
- I1 and I2 are the two different income levels.
Using D2 and D3:
For D2:
- Q1 = 10, Q2 = 15 (Price = $35)
- I1 = $50k, I2 = $50k (movies = $11)
Income elasticity of demand = ((15 - 10) / ((15 + 10) / 2)) / (($50k - $50k) / (($50k + $50k) / 2))
For D3:
- Q1 = 15, Q2 = 30 (Price = $35)
- I1 = $50k, I2 = $70k (movies = $11)
Income elasticity of demand = ((30 - 15) / ((30 + 15) / 2)) / (($70k - $50k) / (($70k + $50k) / 2))
Note: For both cross elasticity of demand and income elasticity of demand, the resulting values could be positive or negative. A positive value indicates a positive relationship, while a negative value indicates an inverse relationship.