The equation of translog cost function is
A).
$$\begin{aligned}
\log T C = & b _ { 0 } + b _ { 1 } \log Q + b _ { 2 } \log w + b _ { 3 } \log r + b _ { 4 } ( \log Q ) ^ { 2 } \
& + b _ { 5 } ( \log w ) ^ { 2 } + b _ { 6 } ( \log r ) ^ { 2 } + b _ { 7 } ( \log w ) ( \log r ) \
& + b _ { 8 } ( \log w ) ( \log Q ) + b _ { 9 } ( \log r ) ( \log Q )
\end{aligned}$$
B)
$$\begin{array} { l }
M P _ { L } = \left[ L ^ { \frac { 1 } { 2 } } + K ^ { \frac { 1 } { 2 } } \right] L ^ { - \frac { 1 } { 2 } } \
M P _ { K } = \left[ L ^ { \frac { 1 } { 2 } } + K ^ { \frac { 1 } { 2 } } \right] K ^ { - \frac { 1 } { 2 } }
\end{array}$$
C)
$$T C \left( Q _ { 1 } , Q _ { 2 } \right) = \left\{ \begin{array} { l }
0 , \text { if } Q _ { 1 } = 0 \text { and } Q _ { 2 } \
1000 + 2 Q _ { 1 } + 3 Q _ { 2 } ,
\end{array} \right.$$
D) $T = \mathrm { t } + c Q + \mathrm { a } w + \mathrm { b } r$

Question

The equation of translog cost function is 
A).
$$\begin{aligned}
\log T C = & b _ { 0 } + b _ { 1 } \log Q + b _ { 2 } \log w + b _ { 3 } \log r + b _ { 4 } ( \log Q ) ^ { 2 } \
& + b _ { 5 } ( \log w ) ^ { 2 } + b _ { 6 } ( \log r ) ^ { 2 } + b _ { 7 } ( \log w ) ( \log r ) \
& + b _ { 8 } ( \log w ) ( \log Q ) + b _ { 9 } ( \log r ) ( \log Q )
\end{aligned}$$
B)
$$\begin{array} { l } 
M P _ { L } = \left[ L ^ { \frac { 1 } { 2 } } + K ^ { \frac { 1 } { 2 } } \right] L ^ { - \frac { 1 } { 2 } } \
M P _ { K } = \left[ L ^ { \frac { 1 } { 2 } } + K ^ { \frac { 1 } { 2 } } \right] K ^ { - \frac { 1 } { 2 } }
\end{array}$$
C)
$$T C \left( Q _ { 1 } , Q _ { 2 } \right) = \left\{ \begin{array} { l } 
0 , \text { if } Q _ { 1 } = 0 \text { and } Q _ { 2 } \
1000 + 2 Q _ { 1 } + 3 Q _ { 2 } ,
\end{array} \right.$$
D) $T = \mathrm { t } + c Q + \mathrm { a } w + \mathrm { b } r$

Quizplus · Accepted Answer

The translog cost function is a well-known function used in economics for estimating short- and long-run cost behaviors. It is a flexible function, allowing for a wide range of cost behaviors, including economies of scale, scope, and substitution possibilities. The given equation of the translog cost function is correct. Therefore, the best choice is (A). Choices (B), (C), and (D) are not relevant to the translog cost function. The translog cost function is commonly used in economic analysis to estimate the relationship between input prices, input quantities, and output quantities. It allows for flexible and nonlinear relationships between variables, which is useful in many real-world situations. Options B, C, and D are not translog cost functions. Option B provides the marginal product of labor and capital, but it does not include prices or output quantities. Option C is a specific cost function that only applies to a certain range of input quantities, and is not a general translog cost function. Option D is a generic equation that includes input prices and output quantities, but does not have the necessary nonlinear terms to be a translog cost function.

The Equation of Translog Cost Function Is A) B)

The Equation of Translog Cost Function Is
A) B)