Julia has usual preferences over X and Y, and, at current prices and income, she spends 1/2 of her income on X. Her demands for both goods respond to changes in her income, but at current prices and income the income elasticity of her demand for Y is equal to exactly 1/3 times the value of her income elasticity of demand for X. And do you know what? If the price of Y were to go up by 1 percent, the quantity of X she demands would remain unchanged.

a. If the price of X were to fall, would her demand for X increase, decrease or remain unchanged? More precisely, what is the own-price elasticity of her demand for X?

b. If her income were to rise, would her demand for X rise, fall or remain unchanged? More precisely, what is the income elasticity of her demand for X?