題組內容

II. Given a translog cost function $\ln TC = \beta0 + \beta1 \ln Q + \beta2 \ln w + \beta3 \ln r + \beta4 (\ln Q)^2 + \beta5 (\ln w)^2 + \beta6 (\ln r)^2 + \beta7 (\ln w)(\ln r) + \beta8 (\ln w)(\ln Q) + \beta9 (\ln r)(\ln Q)$, where $Q$ denotes output, and $w$ and $r$ denote the prices of input $L$ and $K$, respectively. Answer the following questions:

(b)(5%) What is the condition in \( \beta \)'s for the translog cost function to reduce to the constant elasticity cost function?