For a production process that involves two inputs, capital and labor, the constant elasticity long-run total cost function defined in linear relationship using logarithms is:
A) $\log T C = \log a + b \log Q + c \log w + d \log r$
B) $\log T = \log \mathrm { t } + c \log Q + \mathrm { a } \log w + \mathrm { b } \log r$
C) $T = \log \mathrm { t } + c \log Q + \operatorname { alog } w + \mathrm { b } \log r$
D) $T = \mathrm { t } + c Q + \mathrm { a } w + \mathrm { b } r$

Question

For a production process that involves two inputs, capital and labor, the constant elasticity long-run total cost function defined in linear relationship using logarithms is: 
A) $\log T C = \log a + b \log Q + c \log w + d \log r$
B) $\log T = \log \mathrm { t } + c \log Q + \mathrm { a } \log w + \mathrm { b } \log r$
C) $T = \log \mathrm { t } + c \log Q + \operatorname { alog } w + \mathrm { b } \log r$
D) $T = \mathrm { t } + c Q + \mathrm { a } w + \mathrm { b } r$

Quizplus · Accepted Answer

The constant elasticity long-run total cost function is often defined using a Cobb-Douglas production function with two inputs, capital (r) and labor (w), and is represented in logarithms as $\log T C = \log a + b \log Q + c \log w + d \log r$. Here, the logarithmic transformation is necessary to obtain a linear relationship between the variables. Thus, choice A is the correct option. The constant elasticity long-run total cost function for a production process that involves two inputs, capital, and labor is typically defined as: 
$\ln T C=\ln a+b \ln Q+c \ln w+d \ln r$
where T is the total cost, Q is the quantity of output, w is the wage rate, and r is the rental rate of capital. This function represents a linear relationship between the logarithm of total cost and the logarithms of the input prices and the quantity of output. Choice A is the only option that closely matches this formula.

For a Production Process That Involves Two Inputs, Capital and Labor