Suppose perfect competition prevails in the market for hotel rooms

Suppose perfect competition prevails in the market for hotel rooms. The current market equilibrium price of a standard hotel room is $100 per night. Show that the current market equilibrium is efficient, assuming that both the marginal cost incurred by sellers and the marginal benefit perceived by buyers reflect all costs and benefits associated with production and use of hotel rooms. Suppose a $10 per night tax is levied on hotel occupancy. Show how this tax will prevent the market from achieving efficient output. Show the loss in net benefits from hotel use resulting from the tax.