When the production function is given by Q = L, which of the following statements is true?
A) $\mathrm { TC } = w \mathrm { Q } ^ { 2 } , \mathrm {~L} = \mathrm { Q } ^ { 2 }$ and $\mathrm { AC } = \mathrm { w }$
B) $\mathrm { TC } = \mathrm { w } - \mathrm { Q } , \mathrm { L } = \mathrm { Q }$ and $\mathrm { AC } = \mathrm { w }$
C) $\mathrm { TC } = w Q , \mathrm {~L} = \mathrm { Q }$ and $\mathrm { AC } = \mathrm { w }$
D) $T C = w Q , L = Q$ and $A C = L$

Question

When the production function is given by Q = L, which of the following statements is true? 
A) $\mathrm { TC } = w \mathrm { Q } ^ { 2 } , \mathrm {~L} = \mathrm { Q } ^ { 2 }$ and $\mathrm { AC } = \mathrm { w }$
B) $\mathrm { TC } = \mathrm { w } - \mathrm { Q } , \mathrm { L } = \mathrm { Q }$ and $\mathrm { AC } = \mathrm { w }$
C) $\mathrm { TC } = w Q , \mathrm {~L} = \mathrm { Q }$ and $\mathrm { AC } = \mathrm { w }$
D) $T C = w Q , L = Q$ and $A C = L$

Quizplus · Accepted Answer

Since the production function is given as Q = L, we know that total cost (TC) is directly proportional to Q and to the wage rate (w), so TC = wQ. Also, since Q = L, we have L = Q. Finally, we can calculate average cost (AC) as TC/Q = wQ/Q = w, so AC = w. This matches exactly with option C. With Q = L, the production function is a linear function with a slope of 1. Therefore, the total cost function is TC = wQ, where w is the wage rate. Also, the average cost function is AC = TC/Q = w. Finally, L = Q because the production function is given by Q = L. Therefore, the correct choice is C, which includes all of these statements.

When the Production Function Is Given by Q = L TC=wQ2, L=Q2\mathrm { TC } = w \mathrm { Q } ^ { 2 } , \mathrm {~L} = \mathrm { Q } ^ { 2 }TC=wQ2, L=Q2

When the Production Function Is Given by Q = L $\mathrm { TC } = w \mathrm { Q } ^ { 2 } , \mathrm {~L} = \mathrm { Q } ^ { 2 }$