Final answer:
Yara's income elasticity of demand for falafel sandwiches is -1.03, indicating an elastic demand. For new clothes, it is 0.69, indicating an inelastic demand. This is calculated by dividing the percentage change in quantity demanded by the percentage change in income.
Step-by-step explanation:
When Yara's income decreased from LBP 120,000 to LBP 85,000, her demand for falafel sandwiches increased by 30 percent, and her demand for new clothes decreased by 20 percent. To calculate the income elasticity of demand for falafel sandwiches and new clothes, you can use the following formula:
Income Elasticity of Demand (IED) = (% Change in Quantity Demanded) / (% Change in Income)
In this scenario, Yara's income decreased by 29.17 percent [(120,000 - 85,000) / 120,000]. The IED for falafel sandwiches is then (30 / -29.17) = -1.03, and for new clothes, it is (-20 / -29.17) = 0.69.
If the IED is greater than 1 or less than -1 (in absolute value), the good is considered elastic, meaning that the demand for the good is highly responsive to changes in income. In this case, falafel sandwiches have an elastic demand as the absolute value of the IED is greater than 1. Conversely, new clothes have an inelastic demand as the absolute value of the IED is less than 1.