A firm\'s total cost is C = 10q^3 - 40q^2 + 100q + 30, where q is measured in hu

Question

A firm's total cost is C = 10q^3 - 40q^2 + 100q + 30, where q is measured in hundreds of units. It has 3 workers that cannot be fired in the short run and wage is w = 10. The firm doesn't have any other fixed costs. Derive the average variable cost. Find the price level at which the firm prefers to shut down in the short run. Imagine the firm is producing a quantity q = 1. Is there any price at which the firm could be choosing q = 1 in order to maximize profits? (You can use MC = 30q^2 - 80g + 100.) What about q = 2?

Explanation / Answer

C = 10q3 - 40q2 + 100q + 30

(a) TVC is that portion of total cost that varies with q. So,

TVC = 10q3 - 40q2 + 100q

AVC = TVC / q = 10q2 - 40q + 100

Firm will shut down in short run if Price < Minimum AVC.

AVC is minimum when dAVC / dq = 0

20q - 40 = 0

q = 2

When q = 2, AVC = 10q2 - 40q + 100 = 10 x 4 - (40 x 2) + 100 = 40 - 80 + 100

= 60

So, if Price = 60, firm shuts down in short run.

(b) MC = dC / dq = 30q2 - 80q + 100

When q = 1, MC = 30 - 80 + 100 = 50

For a perfectly competitive firm, Price = MC

So, the required price level = 50

When q = 2, MC = 30 x 4 - 80 x 2 + 100 = 120 - 160 + 100 = 60

Price = 60

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.