The aluminum industry faces a private marginal cost curve PMC = 2Q and a market

Question

The aluminum industry faces a private marginal cost curve PMC = 2Q and a market inverse-demand curve of PD = 60 – QD. However, production creates an externality with marginal damages of MD = Q.

Graph the private marginal cost, the social marginal cost, the marginal damages, and the demand curve.

Find the market equilibrium without any government control and the associated deadweight loss.

Find the corrective tax which eliminates the deadweight loss, and find the efficient quantity produced.

What is the resulting price that consumers face with the corrective tax?

Explanation / Answer

PMC = 2Q

D = 60-Q

MC = Q

SMC = PMC +MD

SMC = 2Q+Q=3Q

When social cost is not included, equilibrium will be wher Pd=PMC

2Q=60-Q

3Q =60

Q=30

P = 60-30

P=30

When social damage cost is included

3Q=60-Q

4Q=60

Q=15

P=60-15=45

Dead weight loss due to damage:

0.5 x (30-15) x (45-30)

= 112.5

The upplier shoudl be taxed by amount of marginal damage. $1 per unit since Md = Q

With this nex tax, consumers would pay

$45 wheras producer woudl receive $30. $15 is tax paid to governmnet.

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