The market for sweet potatoes consists of 1,000 identical firms. Each firm has a short-run total cost curve of STC = 100 + 100q + 100q², and a short-run marginal cost curve of $S M C = 100 + 200 q$ where q is output. What is the equation of an individual firm's short-run supply curve in this market?

Question

Quizplus · Accepted Answer

To find the individual firm's short-run supply curve, we need to determine at what price the firm is willing to produce a certain quantity of output. This means we need to equate the price with the firm's marginal cost, and then solve for the quantity.
Setting P = SMC = 100 + 200q, we get:
P - 100 = 200q
q = (P - 100)/200
This equation represents the quantity the firm is willing to produce at any given price.
However, in the short-run, the firm may not be willing to produce any quantity if the price does not cover its variable costs. This means that the firm's short-run supply curve is:
q = (P - 100)/200 if P ≥ 100, and q = 0 otherwise.
This is option D.

The Market for Sweet Potatoes Consists of 1,000 Identical Firms SMC=100+200qS M C = 100 + 200 qSMC=100+200q

The Market for Sweet Potatoes Consists of 1,000 Identical Firms $S M C = 100 + 200 q$