Refer to Scenario 12.3. Suppose that the marginal cost falls such that: MC = Q - 10
What is the profit maximizing price?
A) 205.72
B) 240
C) 210
D) all of the above
E) none of the above

Question

Quizplus · Accepted Answer

To determine the profit maximizing price, we need to find the point where marginal revenue (MR) is equal to marginal cost (MC). From the scenario, we know that the demand function is P = 300 - Q. We can calculate the total revenue function by multiplying price and quantity: TR = PQ = (300 - Q)*Q = 300Q - Q^2. The marginal revenue function is the derivative of the total revenue function with respect to Q: MR = 300 - 2Q.

Setting MR equal to MC: 
300 - 2Q = Q - 10 
Solving for Q: 
3Q = 310 
Q = 103.33 
Plugging Q into the demand function to find P: 
P = 300 - 103.33 = 196.67

Therefore, the profit maximizing price is $210 (option C).