What is the income elasticity of car as per capital income increases from, $10,000 to $11,000? The demand for car as a function of income per capital is given by the equation. Q= 50,000 +5(y).
To calculate the income elasticity of car demand, we need to determine the percentage change in the quantity demanded of cars resulting from a 1% change in income.
Step 1: Calculate the initial quantity demanded when income is $10,000:
Q1 = 50,000 + 5(10,000)
Q1 = 50,000 + 50,000
Q1 = 100,000
Step 2: Calculate the quantity demanded when income increases to $11,000:
Q2 = 50,000 + 5(11,000)
Q2 = 50,000 + 55,000
Q2 = 105,000
Step 3: Calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = ((Q2 - Q1) / Q1) * 100
Percentage change in quantity demanded = ((105,000 - 100,000) / 100,000) * 100
Percentage change in quantity demanded = (5,000 / 100,000) * 100
Percentage change in quantity demanded = 0.05 * 100
Percentage change in quantity demanded = 5%
Step 4: Calculate the percentage change in income:
Percentage change in income = ((11,000 - 10,000) / 10,000) * 100
Percentage change in income = (1,000 / 10,000) * 100
Percentage change in income = 0.1 * 100
Percentage change in income = 10%
Step 5: Finally, calculate the income elasticity of car demand:
Income elasticity of car demand = (Percentage change in quantity demanded) / (Percentage change in income)
Income elasticity of car demand = 5% / 10%
Income elasticity of car demand = 0.5
Therefore, the income elasticity of cars as per capita income increases from $10,000 to $11,000 is 0.5.