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Given below are the annual demand for movie tickets for young adults with differing annual income
Given below are the annual demand for movie tickets for young adults with differing annual income.
| Price ($) | Quantity Demanded ($20,000 income) | Quantity Demanded ($24,000) |
|---|---|---|
| 8 | 40 | 50 |
| 10 | 32 | 45 |
| 12 | 24 | 30 |
| 14 | 16 | 20 |
| 16 | 8 | 12 |
A. Calculate the price elasticity of demand for both income when price increases from $8 to $10.
B. Calculate the income elasticity of demand if the person earning $20,000 annually has an increase in income to $24,000 for a price of $12 and a price of $16.
Expert Solution
A. Price Elasticity of Demand:
Price Elasticity = Percentage Change in Quantity demanded/ Percentage Change in Price
- When the income of the Consumer is $20000
Initial Price (P0) = $8
New Price (P1) = $10
Initial Quantity (Q0) = 40
New Quantity (Q1) = 32
Percentage Change in Price = (P1-P0)/ P0 * 100
Percentage Change in Price = (10 - 8) / 8 * 100 = 25%
Percentage Change in Quantity = (Q1- Q0)/ Q0 * 100
Percentage Change in Quantity = (32-40)/ 40 * 100 = -20%
Price Elasticity = -20%/25% = -0.8
Hence for the consumers earning an income of $20000, the price elasticity will be equal to -0.8
- When the income of the Consumer is $24000
Initial Price (P0) = $8
New Price (P1) = $10
Initial Quantity (Q0) = 50
New Quantity (Q1) = 45
Percentage Change in Price = (P1-P0)/ P0 * 100
Percentage Change in Price = (10 - 8) / 8 * 100 = 25%
Percentage Change in Quantity = (Q1- Q0)/ Q0 * 100
Percentage Change in Quantity = (45 - 50)/ 50 * 100 = -10%
Price Elasticity = -10%/25% = -0.4
Hence for the consumers earning an income of $24000, the price elasticity will be equal to -0.4.
B. Income Elasticity:
Income Elasticity = Percentage Change in Quantity demanded/ Percentage Change in Income
- When the Price of the good is $12:
Initial Income (I0) = $20000
New Income (I1) = $24000
Initial Quantity (Q0) = 24
New Quantity (Q1) = 30
Percentage Change in Income = (I1-I0)/ I0 * 100
Percentage Change in Income= (24000 - 20000) / 20000 * 100 = 20%
Percentage Change in Quantity = (Q1- Q0)/ Q0 * 100
Percentage Change in Quantity = (30 - 24)/ 24 * 100 = 25%
Income Elasticity = 25%/20% = 1.25
Hence for the income elasticity of consumer when the price of the good is $12 is 1.25.
- When the Price of the good is $16:
Initial Income (I0) = $20000
New Income (I1) = $24000
Initial Quantity (Q0) = 8
New Quantity (Q1) = 12
Percentage Change in Income = (I1-I0)/ I0 * 100
Percentage Change in Income = (24000 - 20000) / 20000 * 100 = 20%
Percentage Change in Quantity = (Q1- Q0)/ Q0 * 100
Percentage Change in Quantity = (12 - 8)/ 8 * 100 = 50%
Income Elasticity = 50%/20% = 2.5
Hence for the income elasticity of consumer when the price of the good is $16 is 2.5.
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