GM faces an inverse demand curve P=200-Q and a marginal cost MC=10. What is the monopolist profit-maximizing level of output?

Question

BlackTom AI · Accepted Answer

To determine the monopolist's profit-maximizing output, start by deriving marginal revenue from the given inverse demand.
Demand: P = 200 − Q. Revenue R(Q) = P · Q = (200 − Q)Q = 200Q − Q^2. MR is the derivative of R with respect to Q: MR = 200 − 2Q.
Now set MR equal to marginal cost: MR = MC = 10.
Thus, 200 − 2Q = 10 ⇒ 2Q = 190 ⇒ Q = 95.
Let’s evaluate the given options one by one:
- Option 190: If Q = 190, MR = 200 − 2(190) = 200 − 380 = −180, which is far below MC. This cannot maximize profit since producing less would raise profit. So 190 is incorrect.
- Option 100: If Q = 100, MR = 200 − 2(100) = 0, which is below MC (0 < 10). Since MR < MC, increasing output would reduce profit, so 100 is not optimal.
- Option 95: If Q = 95, MR = 200 − 2(95) = 200 − 190 = 10, which exactly equals MC. This satisfies the profit-maximizing condition MR = MC, so 95 is the optimal quantity.
- Option 85: If Q = 85, MR = 200 − 2(85) = 200 − 170 = 30, which is greater than MC. Since MR > MC, increasing output would raise profit, so 85 cannot be optimal.
In summary, the only quantity that equates marginal revenue to marginal cost here is Q = 95, which aligns with the condition MR = MC and confirms the monopolist’s profit-maximizing output.

ECON3200001.1251 Quiz 12: Market Power

GM faces an inverse demand curve P=200-Q and a marginal cost MC=10. What is the monopolist profit-maximizing level of output?

View Explanation

Log in for full answers

Similar Questions

Use the model above to answer the following question. The profit maximizing quantity for the monopoly is?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

A monopolist faces the following demand curve: P=50-0.5Q where Q is the quantity demanded and P is the price. The monopolist's total cost function is given by: TC=50+4Q where TC is the total cost and Q is the quantity produced. What is the profit maximizing quantity?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler