# If demand for complement good 1 goes up, BOTH its P and Q go up, so why does the demand for the complement good 2 fall?

If the demand curve for Coffee shifts to the right, both Price of Coffee and Quantity of Coffee that gets sold go up.

What happens to the Price of Sugar?

Coffee and Sugar are complements, so one would think that as price of coffee goes up, people consume less of both complement goods, so demand for sugar should fall (demand curve for sugar shifts to the left).

However, since the reason for the price going up is the demand for coffee increasing, Quantity of Coffee is higher, meaning that people purchase MORE Coffee AND More Sugar. Is the demand curve for sugar shifting to the right, after all?!

Is it the case that the demand curve for sugar shifts to the left only if the price increase is due to supply of coffee falling?

Thank you for the clarification!

It is not easy to give a definitive answer to these demand shift questions when the reason for the demand shift is not given. If we assume that the underlying relationship between sugar and coffee is unchanged, they are still perfect complements and at the same ratio, then sugar's demand will have to shift like coffee's demand did: $$s(p_c,p_s,I) = r_{\text{complement_ratio}} \cdot c(p_c,p_s,I)$$ If, however, coffee's demand shift is, for example, because in addition to drinking sugary coffee people also started to chew coffee beans without sugar, then sugar's demand curve could be unaffected.