Determine income elasticity (E1) at Birr 16,000 level of income.

Steps to Solve

1. Identify the Given Data From the provided table, we need the quantities at income levels around Birr 16,000.

• At Birr 12,000, ( Q = 10 )
• At Birr 20,000, ( Q = 15 )

2. Calculate the Change in Quantity and Income To find the income elasticity, we first calculate the change in quantity and the change in income:

• Change in Quantity (( \Delta Q )): $$ \Delta Q = Q_{20,000} - Q_{12,000} = 15 - 10 = 5 $$

• Change in Income (( \Delta I )): $$ \Delta I = 20,000 - 12,000 = 8,000 $$

3. Use the Income Elasticity Formula The formula for income elasticity of demand ( E^d ) is given by: $$ E^d = \frac{\Delta Q / Q}{\Delta I / I} $$ We can substitute ( I = 16,000 ) and calculate based on the average quantity around that income level, which is ( Q = 12.5 ) (average of 15 and 10).

4. Substitute the Values into the Formula Plugging our values into the formula:

• Average ( Q ) can be estimated as: $$ Q = \frac{Q_{12,000} + Q_{20,000}}{2} = \frac{10 + 15}{2} = 12.5 $$

Now substitute: $$ E^d = \frac{5 / 12.5}{8000 / 16000} $$

5. Calculate the Income Elasticity Perform the necessary calculations:

• $$ \frac{5}{12.5} = 0.4 $$
• $$ \frac{8000}{16000} = 0.5 $$

Thus, $$ E^d = \frac{0.4}{0.5} = 0.8 $$