An elasticity coefficient is the ratio of the percentage cha

An elasticity coefficient is the ratio of the percentage change in the forecast variable (yy) to the percentage change in the predictor variable (xx). Mathematically, the elasticity is defined as (dy/dx)×(x/y)(dy/dx)×(x/y). Consider the log-log model,

log y = B0 + B1 log x + e

Express yy as a function of xx and show that the coefficient 11 is the elasticity coefficient.

Solution

log y = 0 + 1 log x + e

y can be written as :

y = e^( 0 + 1 log x + e)

differentiate w.r.t x:

dy/dx = (1/x)e^( 0 + 1 log x + e)

dy/dx = 1*y/x

1= (dy/dx) *(x/y) = ratio of the percentage change in the forecast variable (y) to the percentage change in the predictor variable (x)

1= (dy/dx) *(x/y)