The market for sweet potatoes consists of 1,000 identical firms. Each firm has a short-run total cost curve of $S T C = 100 + 100 q + 100 q ^ { 2 }$, and a short-run marginal cost curve of $S M C = 100 + 200 q$, where $q$ is output. Suppose that sunk costs are 75 and nonsunk costs are 25 . What is the equation of an individual firm's average nonsunk cost curve?

Question

Quizplus · Accepted Answer

The equation for average nonsunk cost curve (ANSC) can be derived from the formula: 
ANSC = (STC - sunk cost)/q 
ANSC = (100 + 100q + 100q² - 75)/q 
ANSC = (25 + 100q + 100q²)/q 
ANSC = 25/q + 100 + 100q 
Therefore, the correct equation for an individual firm's average nonsunk cost curve is ANSC = 100 + 100q + 25/q. The equation for average cost (AC) is $\frac{S T C}{q}=\frac{100+100q+100q^{2}+75}{q}$. 
Solving for nonsunk costs only, we get: 
$\frac{25}{q}+100+100q$. 
This is the equation for the average nonsunk cost curve for each individual firm. Option B is the only one that matches this equation.

The Market for Sweet Potatoes Consists of 1,000 Identical Firms STC=100+100q+100q2S T C = 100 + 100 q + 100 q ^ { 2 }STC=100+100q+100q2

The Market for Sweet Potatoes Consists of 1,000 Identical Firms $S T C = 100 + 100 q + 100 q ^ { 2 }$