Suppose that a 12 percent rise in the price of pancakes decreases the quantity of pancakes demanded by 22 percent and increases the quantity of waffles demanded by 14 percent.
a) price elasticity of demand for pancakes
b) cross elasticity of demand for waffles with respect to the price of pancakes
In order to find these two answers, all you have to do is some basic division. The way to find price elasticity of demand (with the kind of information we have here) is to divide the percentage change in the quantity demanded by the percentage change in the price.
According to your question, the quantity demanded of pancakes dropped by 22% when the price of the pancakes rose by 12%. Therefore, to find the price elasticity of demand, we have to do the following:
22/12 = 1.83
The price elasticity of demand for pancakes is 1.83.
Pancakes and waffles are, presumably, substitutes or competing goods. This means that when the price of pancakes goes up, some people should abandon pancakes and switch to waffles. This change is captured in the cross elasticity of demand. It measures how much the demand for waffles changes when the price of pancakes changes. To find cross elasticity, we divide the percent change in quantity demanded of the second product (waffles) by the percent change in the price of the first product (pancakes). In this case:
.14/.12 = 1.17
The cross elasticity of demand for these two products is 1.17.