Nadia consumes two goods, food and clothing. The price of food is $2, the price of clothing is $5, and her income is $1,000 . Nadia always spends 40 percent of her income on food regardless of the price of food, the price of clothing, or her income

a. What is her price elasticity of demand for food?
b. What is her cross-price elasticity of demand for food with respect to the price of clothing?
c. What is her income elasticity of demand for food?

a. Nadia's expenditure on food does not change when the price of food changes. This means that her demand for food must be unit elastic.
b. Her expenditure on food does not change when the price of clothing changes. Since the price of food is unchanged, this must mean that her demand for food must not change when the price of clothing changes. Therefore her cross price elasticity of demand for food with respect to the price of clothing must be zero.
c. Initially, Nadia's expenditure on food is 40% x $1,000 = $400 . Since the price of food is $2, this means that she initially consumes 200 units of food. Now suppose her income rises by 100 percent (i.e., her income doubles). If she continues to spend 40 percent of her income on food this must mean her expenditure rises to $800 and her consumption of food rises to 400 units (since the price of food remains constant at $2). So Nadia's demand for food has doubled when her income doubled, and therefore her income elasticity of demand for food must equal 1 .