Daily exercise on managing a negative externality

Suppose a good creates a negative externality and has the market WTP, market WTA and externality marginal cost curves given below:

• `WTP=400-4Q_M^D`
• `WTA=80`

• `MC_e = Q_M^S`

Please determine the following:

1. The market P and Q before any policy is adopted to deal with the externality.
2. The efficient Q and the optimal tax rate `T` needed to achieve it.
3. The overall change in external costs, `\Delta Ext`, caused by the tax.

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