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You have been hired by the town of Bedford, Ohio, to conduct an analysis of ongoing operations by a local Coca Cola bottler
You have been hired by the town of Bedford, Ohio, to conduct an analysis of ongoing operations by a local Coca Cola bottler. A study by the Ohio Environmental Protection Agency found that this firm's water pollution is negatively affecting the environment. The study has been read by several politicians and they have requested the state government to impose a tax. Politicians expect to observe a decrease in the environmental damage (specifically, eliminate the deadweight loss). Your task is to find the optimal tax that the government should impose to this Coca Cola bottler.
To help you in your task, you are given the following information:
- Inverse Demand: P=10- Q
- Inverse Supply (Marginal Private Cost): MCp = 5+Q
- Externality Cost (Marginal Cost of Externality): MCE = 0.5Q
a. Find the equilibrium market price and quantity (Pm,Qm)
b. Find the socially optimal equilibrium price and quantity ( P*,Q *)
c. Determine the optimal tax (the Green Tax) the state government should charge the local Coca Cola bottler to deal with the negative externality. Hint: To find this, measure the difference between the socially optimal equilibrium price (P*) and the price the firm receives at the socially optimal equilibrium quantity (Q*), that is, MCp (Q=Q*)
Expert Solution
a.
To find the equilibrium market price and quantity, we just equate the Inverse Demand and Inverse Supply.
That is,
10 - Q = 5 + Q
Qm = 2.5
Pm = 10 - 2.5 = 7.5
So, the equilibrium market price and quantity is Qm = 2.5 and Pm = 7.5
b.
To determine the socially optimal equilibrium price and quantity, we need to equate Inverse Demand and Marginal Social Cost, i.e., (Marginal Private Cost + Marginal Cost of Externality).
MSC = MCp + MCE
MSC = 5 + Q + 0.5Q = 5 + 1.5Q
Now, equate, Inverse Demand and MSC, we get, socially optimal equilibrium price and quantity,
10 - Q = 5 + 1.5Q
Q* = 2
P* = 10 - 2 = 8
So, the socially optimal equilibrium price and quantity is Q* = 2 and P* = 8.
c.
The price the firm receives at the socially optimal equilibrium quantity is
MCp = 5 + 2 = 7.
the optimal tax (the Green Tax) = the socially optimal equilibrium price - MCP
the optimal tax (the Green Tax) = 8 -7 = 1
So, the optimal tax (the Green Tax) = 1.
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