Substitute goods are those whose cross-price elasticity is positive:
is the demand function for some good
stands for the price of another good
, which has some relation to good
. Price and demand are both non-negative quantities by definition, so the sign of the expression is determined by the term
On the contrary, for complementary goods the sign of the expression above is negative.
Set the price of some good (in the left plot) with the
slider. Notice that a change in price does not influence the demand curve on the left market itself. (From the right-market point of view, one observes price change on the left market, perhaps without knowing the reason).
Depending on the mode chosen by the "goods" setter bar ("substitute" or "complementary"), the results are reflected in the right plot. Relevant shifts may be seen in the demand curve.
The other slider changes the slope of demand on the left market, so it does not affect the price
(i.e. supply occasionally adjusts). If the price
stays unchanged, we may not expect any change in demand on the right market due to the effect in question. In this rather artificial case, cross-price elasticity is undefined (because of the term
), and we observe no relationship between the markets. Nonetheless, in general, shift in demand should affect current prices.