# Finding “own” price elasticity of demand

Only two groups buy the Dripfix, abbreviated as good $D$. Group 1's demand function for the Dripfix is $f_1 (p_D)=300-p_D$, where $p_D$ is the price of Dripfix. Group 2's demand function is $f_2(p_D)=120-p_D$.

1. What is each group's "own" price elasticity of demand?
2. What is the equation for the market demand?
3. At what price $p_D$ is the market elasticity $-1$?

Here is my work so far:

1. Group 1's price elasticity is $\epsilon_1=-\frac{p_D}{300-p_D}$. Group 2's is $\epsilon_2=-\frac{p_D}{120-p_D}$.
2. The market demand is $420-2p_D$ for $p_D \leq 120$ and $300-p_D$ for $p_D > 120$.

Are these two parts correct so far? If so, how do go about determining the market elasticity when the market demand is made up of two components?

For 3, look at each segment individually. There are two points which have an elasticity of $-1$, one on each segment.