Giffen Goods & Complementary Goods

Consider that good X and good Y are complements and good X is a Giffen good. If I increase the price of good X, what affect does this have on the price and quantity demanded of good Y?

My reasoning was as follows. An increase in the price of good X will increase the quantity demanded of good X (as it is a Giffen Good). Increasing the quantity demanded of good X decreases the price of good Y (as they are complements). A decrease in price of good Y will increase the quantity demanded of good Y (Law of Demand).

This is wrong. The correct answer according to my textbook is that both the price and quantity demanded of good Y will increase.

How can this be?

If $$X$$ and $$Y$$ are complements, an increase in the quantity demanded of $$X$$ also implies an increase in the demand for $$Y.$$ This is why both the price and the quantity of $$Y$$ will also have to increase.

• I agree with your first sentence. But if the quantity demanded of good Y increases, why doesn't the price of good Y decrease (Law of Demand)? – Bell Mar 8 '19 at 12:22
• @Bell: The demand for Y increases, meaning the demand curve for Y shifts to the right, resulting in higher equilibrium price and quantity in the market for Y. – Herr K. Mar 8 '19 at 18:15
• Does a similar argument work for substitute goods. For example, if good A and good B are substitutes, does an increase in the quantity demanded of good A decrease the quantity demanded of good B? – Bell Mar 9 '19 at 6:01