Consider the Following Cobb-Douglas Production Function Y_i = AK $\begin{array} { c } \beta _ { 1 } \\i\end{array}$

question 8

Essay

Consider the following Cobb-Douglas production function Y_i = AK $\begin{array} { c } \beta _ { 1 } \\i\end{array}$ L $\begin{array} { c } \beta _ { 2 } \\i\end{array}$ $e ^ { u _ { i } }$ (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 = $\beta _ { 0 } ^ { * }$ + β₁k_i + β₂l_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.