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?

查看解析

登录即可查看完整答案

类似问题

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?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单