16-3. The point elasticity of Y with respect to X is defined as = (dY/dX)(X/Y). For...

16-3. The point elasticity of Y with respect to X is defined as η =

(dY/dX)(X/Y). For the population regression equation estimated in Exercise 16-1, find an estimate of the point elasticity coefficient η at the point of means of the variables; that is, find ˆη = (d ˆY /dX)(X/Y). Interpret your result. (Hint: η serves as an index of the responsiveness of Y to a 1% change in X. So if, say, ˆη = 1.35, then a 1% increase in X leads to a 1.35% increase in Y (the elastic case, since ˆη > 1). And if ˆη = 0.80, a 1%
increase in X precipitates only a 0.80% increase in Y (the inelastic case, since ˆη < 1).