2 That is taking derivatives of bot

2 That is taking derivatives of both sides of regression (1) with respect to we obtain
.Solving for yields
which is the elasticity of Y with respect to C (for the subset of cars with petrol engine). For, because is a discrete variable, fix , then
we can write, which is approximately the proportional difference between
and the exact proportional difference being
, but the two quantities are
similar for small