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.]
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.]
Solution
To find the per unit tax that the local government should impose on suppliers of gin to bring the economy to the socially optimal allocation, we need to equate the marginal social cost (MSC) to the demand.
The marginal social cost is given by P=5Q and the demand is given by P=20-4Q.
Setting these two equal to each other gives:
5Q = 20 - 4Q
Solving for Q gives:
9Q = 20
Q = 20/9 ≈ 2.22
Substituting Q = 2.22 into the supply equation P=Q gives P = 2.22.
Substituting Q = 2.22 into the MSC equation P=5Q gives P = 5*2.22 = 11.11.
The per unit tax that the local government should impose on suppliers of gin to bring the economy to the socially optimal allocation is the difference between the marginal social cost and the supply price, which is 11.11 - 2.22 = 8.89.
So, the per unit tax should be approximately $8.89.
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