The Interpretation of the Slope Coefficient in the Model $\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }$

Multiple Choice

The interpretation of the slope coefficient in the model $\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }$
is as follows:

A) a 1 % change in X is associated with a $\beta _ { 1 } \%$ change in Y .
B) a change in X by one unit is associated with a $\beta _ { 1 }$ change in Y .
C) a change in X by one unit is associated with a 100 $\beta _ { 1 } \%$ change in Y .
D) a 1 % change in X is associated with a change in Y of 0.01 $\beta _ { 1 }$