If $S T C = 200 + 2 q + 4 q ^ { 2 } , S M C = 2 + 8 q$, where $q$ is output and all fixed costs are sunk, the firm's short-run supply curve is:
A) $s ( P ) = 2 + 8 q$ for $P \geq 2$ and zero otherwise.
B) $s ( P ) = \left\{ \begin{array} { l } 0 P

Question

If $S T C = 200 + 2 q + 4 q ^ { 2 } , S M C = 2 + 8 q$, where $q$ is output and all fixed costs are sunk, the firm's short-run supply curve is:
A) $s ( P ) = 2 + 8 q$ for $P \geq 2$ and zero otherwise.
B) $s ( P ) = \left\{ \begin{array} { l } 0 P < 2 \ 0.125 P - 0.25 P \geq 2 \end{array} \right.$
C) $s ( P ) = 2 + 8 q$ for $P \geq 0$ and zero otherwise.
D) $s ( P ) = \left\{ \begin{array} { l } 0 P < 0 \ 0.125 P - 0.25 P \geq 0 \end{array} \right.$

Quizplus · Accepted Answer

The firm's short-run supply curve is derived from the marginal cost (MC), which is the derivative of the total cost (TC) with respect to quantity (q). Given $SMC = 2 + 8q$, the firm will supply where price (P) equals or exceeds marginal cost. The correct supply function is $s(P) = 0.125P - 0.25$ for $P \geq 2$, indicating the firm will supply a positive quantity when the price is at least 2, and zero otherwise. This matches option B, which correctly translates the condition for supply based on the price.

If STC=200+2q+4q2,SMC=2+8qS T C = 200 + 2 q + 4 q ^ { 2 } , S M C = 2 + 8 qSTC=200+2q+4q2,SMC=2+8q

If $S T C = 200 + 2 q + 4 q ^ { 2 } , S M C = 2 + 8 q$