Consider the market for gin, in perfect competition, where market demand is given by P=20-4Q and supply is given by P=Q. Suppose that alcoholism is a major problem in this community. Not only does it affect the health of the people who consume the gin, but it also affects community members who do not consume or sell alcohol. Thus, while the marginal private cost of gin is given by P=Q, the marginal social cost is given by P=5Q. What is the magnitude of the per unit tax that the local government should impose on suppliers of gin to bring the economy to the socially optimal allocation? [Round your answer to 2 decimal places when needed.]简答题
登录即可查看完整答案
我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

Question

Consider the market for gin, in perfect competition, where market demand is given by P=20-4Q and supply is given by P=Q. Suppose that alcoholism is a major problem in this community. Not only does it affect the health of the people who consume the gin, but it also affects community members who do not consume or sell alcohol. Thus, while the marginal private cost of gin is given by P=Q, the marginal social cost is given by P=5Q. What is the magnitude of the per unit tax that the local government should impose on suppliers of gin to bring the economy to the socially optimal allocation? [Round your answer to 2 decimal places when needed.]简答题

登录即可查看完整答案

我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

BlackTom AI · Accepted Answer

To begin, restate the setup: the market demand is P = 20 − 4Q, the private supply (without external effects) is P = Q, and the social marginal cost is MSC = 5Q due to externalities.
Next, determine the socially optimal quantity by equating the price consumers are willing to pay to the social marginal cost: P_d = MSC.
From the demand equation, P_d = 20 − 4Q. Setting 20 − 4Q = 5Q gives 20 = 9Q, so the socially optimal quantity is Q* = 20/9 ≈ 2.222.
Compute the corresponding price consumers would pay at this Q* using the demand curve: P* = 20 − 4Q* = 20 − 4*(20/9) = 20 − 80/9 = (180 − 80)/9 = 100/9 ≈ 11.111.
Now incorporate a per-unit tax t on suppliers. The private price received by suppliers (after tax) must satisfy the private supply relation P_private = Q, because the supply curve is P = Q without externalities. The price paid by consumers is P_consumer = P_private + t, or equivalently P_private = P_consumer − t. Using P_consumer = P_d and P_private = Q, we have Q = P_d − t.
Express P_d in terms of Q from the demand curve: P_d = 20 − 4Q. Substitute into Q = (20 − 4Q) − t to obtain 5Q = 20 − t, i.e., Q = (20 − t)/5.
Set this equal to the socially optimal quantity Q* to find the required tax: (20 − t)/5 = 20/9. Multiply both sides by 45 to clear denominators: 9*(20 − t) = 100, which yields 180 − 9t = 100. Solve for t: −9t = −80, so t = 80/9 ≈ 8.89.
Thus, the per-unit tax that brings the economy to the socially optimal allocation is approximately 8.89 (rounded to two decimals).

类似问题

Question54 Who wins from implementing an output tax on a good with negative environmental externality? Producers Government Consumers All of the other options ResetMaximum marks: 1 Flag question undefined

You have the following PMC, MD and SMB: PMC = 15 + 2Q MD = 1.2Q2 SMB = 70 - 3Q Find the Pigouvian tax t*

Now the government is considering imposing extra tax on polluting industry. From the first table, what is the optimal tax?

When production or consumption of a product results in negative externalities, a suitable method of government intervention may be

A pollution charge gives the trucking industry an incentive to reduce its emissions, as long as the of reducing the emissions is .

A pollution charge is a form of tax imposed on

更多留学生实用工具

智能学习助手

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