Never Reason from a Price Change

In introductory microeconomics, professors introduce the concepts of substitute and complement goods. In my Econ 101 class at the University of Michigan, the professor stated the concept as:

If two goods are substitute goods, an increase in the price of one increases the demand of the other.

If two goods are complementary goods, an increase in the price of one decreases the demand of the other.

This might make sense in most situations, but my Sumnerian senses are tingling -- why are we reasoning from a price change? What is causing the price of one good to increase, and how does this change whether the demand of the other good to increase or decrease?

Let us first consider the case of substitute goods. If two goods are substitutes for each other, it seems logical to consider that if supply in the second good contracted, pushing prices up, then people would substitute out of that second good and increase demand for the first good. If cars become harder to produce and become more expensive, it's logical that the demand for bicycles will increase. However, does this hold up if the price change was because of a demand shock? If cars became more expensive because demand increased, it seems peculiar to think that the demand for bicycles also increases. Just because it's a price change doesn't mean it's the price change you were looking for.

A similar scenario plays out in the case of complement goods. If two goods are complements, it seems logical to consider that if the supply for one good increases, then the price decrease would increase the demand for the second good. If tortilla chips become easier to make, we can expect the demand for salsa to increase. But does the same hold true if it was a demand shock that caused the price change? If people start demanding more potato chips, pushing up the price, what do we expect will happen to the demand for chip dip?  We would expect it to increase -- directly contrary to what the definition suggests.

Reasoning from a price change fails because it neglects whether the price change in one good is from a change in production technologies or from a change in preferences. If it's a change in technology, the standard analysis applies. However, if it's a change in preferences, we need a more nuanced view that encompasses both modes of analysis.

If two goods are substitute goods, an increase in the equilibrium quantity of one decreases the demand of the other.

If two goods are complementary goods, an increase in the equilibrium quantity of one increases the demand of the other.

So in the market for cars and bicycles, if the equilibrium quantity of cars increases, whether from a supply expansion or a demand contraction, then the demand for bicycles will decrease. This is true regardless of what happens to the price of cars. Similarly, if the equilibrium quantity of potato chips increases, then the demand for chip dip increases -- regardless of where the price for potato chips go. This makes sense because it encompasses the lay person view of substitutes and complements. If I ride my bike more, I drive less. If I eat more chips, I buy more salsa.

The fact that this isn't taught on the first pass around is understandable -- you don't want to confuse the auditorium of 300+ students with a model of both supply and demand when you're introducing the demand curve. But it does pose a problem when there are exam questions such as "Does an increase in price of a complement good raise the demand of the original good?" To which I have to say, "it might". A possible solution is to ask "Holding the demand of a complement good constant, does raising its price raise the demand of the original good?" This would be more comprehensive, and those who understand can better answer the question, while those who don't understand can forget about the first clause and just answer the second question.