There is a paper plant facing the following marginal private cost of producing paper: MPC =...
There is a paper plant facing the following marginal private cost of producing paper:
MPC = $100 + 4Q where Q = amount of paper produced
This paper plant can freely dump waste into the river. This waste inflicts the following marginal externality cost to a downstream resort:
MEC = $20 + 2Q where Q = amount of paper produced
If the market demand for paper is:
Demand = $400 - Q
a. Without regulation, how much paper would be produced?
b. What is the socially optimal level of paper production?
What product tax should regulators impose on the production of paper in order to achieve the socially optimal level of production?
Homework Answers
(a) Unregulated equilibrium is found by equating Demand and MPC.
400 - Q = 100 + 4Q
5Q = 300
Q = 60
(b) Marginal social cost (MSC) = MPC + MEC = 100 + 4Q + 20 + 2Q = 120 + 6Q
Socially optimal output is obtained by equating Demand and MSC.
400 - Q = 120 + 6Q
7Q = 280
Q = 40
The unit tax is equal to value of MEC at efficient output.
Unit tax = MEC = 20 + (2 x 40) = 20 + 80 = $100
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