Supply and demand equations

Suppose that a market is described by the following supply and demand equations:
QS =2P,
QD =300−P.

(a) Solve for the equilibrium price and the equilibrium quantity.
(b) Suppose that a tax of T is placed on buyers, so the new demand equation is QD = 300 − (P + T). Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? Explain.
(c) Tax revenue is T · Q. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 300. Explain.
(d) Solve for deadweight loss as a function of T. Graph this relationship for T between 0 and 300. Explain.
(e) Use your results in (c) and (d) to plot the dead weight loss as a function of tax revenue.
(f) If the government doubles the tax on gasoline, can you be sure that revenue from the gasoline tax will rise? Can you be sure that the deadweight loss from the gasoline tax will rise? Explain.

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