Consider the Following Cobb-Douglas Production Function $Y _ { i } = A K _ { i } ^ { \beta _ { 1 } } L _ { i } ^ { \beta _ { 2 } } e ^ { u _ { i } }$

Essay

Consider the following Cobb-Douglas production function $Y _ { i } = A K _ { i } ^ { \beta _ { 1 } } L _ { i } ^ { \beta _ { 2 } } e ^ { u _ { i } }$
(where Y is output, A is the level of technology, K is the capital stock, and L is the labor force), which has been linearized here (by using logarithms) to look as follows:
$y _ { i } = \beta _ { 0 } ^ { * } + \beta _ { 1 } k _ { i } + \beta _ { 2 } l _ { i } + u _ { i }$
Assuming that the errors are heteroskedastic, you want to test for constant returns to scale. Using a t -statistic and "Approach #2," how would you proceed.