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 short-run, the total cost includes both variable cost and fixed cost. Since the given cost function includes only fixed cost, we need to add the variable cost component. The variable cost formula is typically given as VC = wL + rK, where w represents the wage rate, L represents labor, r represents the rental rate, and K represents the capital. In this case, we can substitute Q = sqrt(KL) in the variable cost equation to get VC = w(Q^2/K) + rK. Adding this to the fixed cost (rK) gives us the total cost function as STC = VC + FC = w(Q^2/K) + 2rK. Simplifying this equation, we get STC = (wQ^2/K) + rK. This matches the form of option D.

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

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