Solved: In a perfectly competitive market for coal consumers, Dissertation

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In a perfectly competitive market for coal consumers

I'm in an energy economics course and need help with a homework question.

The question reads:

In a perfectly competitive market for coal, consumers' benefit function from consuming tons of coal Q, is given by:

B(Q)=-0.25(Q^2)+ 240Q

In addition, the coal producer has a function given by:

C(Q)=0.1(Q^2)+2Q.

Suppose the government imposes an ad valorem tax on coal producers of 7% of the sale price.

a. What is the competititive equilibrium in the absence of the tax?

b. What is the competitive equilibrium with the ad valorem tax?

c. What is the change in consumer surplus as a result of the tax?

d. What is the change in producer surplus as a result of tax?

e. How much revenue is generated by the tax?

f. What is the deadweight loss from the tax?

g. What is the change in total welfare due to the tax?

If someone could help me get started on this problem, that would be great.

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