Question

In: Economics

Assume that the demand for a good is given by p=12-2q.the supply is given by p=q....

Assume that the demand for a good is given by p=12-2q.the supply is given by p=q. there is also an externality equal to 3 for each quantity produced. Derive and show in figures

The optimal level of production for the firm and the society separately

How large is the welfare loss due to the externality?

Which tax rate and how much would remedy the problem with externality

How much revenue would it raise?

Expert Solution

Demand for a good is given by p=12-2q.the supply is given by p=q. there is also an externality equal to 3 for each quantity produced.

The optimal level of production for the firm and the society separately

For the firm it is given by Marginal benefit = marginal private cost

12 - 2q = q

q* = 4 and price is p* = $4

Social optimal quantity is when Marginal social cost = marginal benefit

12 - 2q = q + 3

q = 9/3 = 3 units, P = 12 - 6 = $6 per unit

How large is the welfare loss due to the externality?

Welfare loss = DWL = 0.5*(6 - 3)*(4 - 3) = $1.5

Which tax rate and how much would remedy the problem with externality

Tax should be equal to marginal external cost so tax is $3 per unit. This would shift the MPC curve upwards and determining the social equilibrium at F

How much revenue would it raise?

Tax revenue = tax * quantity bought = 3*3 = $9

Rahul Sunny answered 2 years ago

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