You are given the following: C = 1.0Q2 + 40Q + 75 and p = 180 -1Q where Q is out

Question

You are given the following: C = 1.0Q2 + 40Q + 75 and p = 180 -1Q where Q is output, p is price, and C is the total cost of production. Determine the profit-maximizing price and output for a monopoly. The profit-maximizing output level is units. (Enter a numeric response using an integer.) The profit-maximizing price is $ .(Enter a numeric response rounded to two decimal places ) The profit per units is $ .(Enter a numeric response rounded to two decimal places) The tool profit is $ .(Enter a numeric response rounded to two decimal places)

Explanation / Answer

If P= 180-1Q
Then total revenue equals PQ= 180Q-Q^2
and marginal revenue is 180-2q (derivative of total revenue function).
If C= 1.0Q^2 +40Q +75
Then marginal cost equals 2Q+40 (derivative of total cost function).
profit maximizing output is where marginal cost equals marginal revenue so
180-2Q= 2Q+40
4Q= 140
Q= 35 and P= 180-35= $145.
Total profit equals total revenue minus total cost or 35*145- 35^2 -40*35-75= 2,375
Profit per unit is 2,375/35= 67.86

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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