Suppose $Q = \sqrt { \bar { K } } L$ in the short-run. The firm's short-run total cost curve is:
A) $S T C = \frac { Q ^ { 2 } } { \bar { K } }$
B) $S T C = \frac { w \bar { K } } { Q } + r \bar { K }$
C) $S T C = Q ^ { 2 } + \bar { K }$
D) $S T C = \frac { w Q ^ { 2 } } { \bar { K } } + r \bar { K }$

Question

Quizplus · Accepted Answer

In the given production function $Q = \sqrt { \bar { K } } L$, the short-run total cost (STC) involves both variable and fixed costs. The variable cost is associated with labor (L), and the fixed cost is associated with capital ($\bar{K}$). To find the STC, we first express labor (L) in terms of Q, which gives $L = \frac{Q^2}{\bar{K}}$. The cost of labor is $wL$, where w is the wage rate, and the cost of capital is $r\bar{K}$, where r is the rental rate of capital. Thus, the total cost is the sum of labor and capital costs, leading to $STC = w\frac{Q^2}{\bar{K}} + r\bar{K}$, which matches option D.

Suppose Q=KˉLQ = \sqrt { \bar { K } } LQ=Kˉ​L

Suppose $Q = \sqrt { \bar { K } } L$