Suppose a perfectly competitive market has the following supply and demand functions:

Supply function: P = 2Q + 10
Demand function: P = 90 - 0.5Q

Where P is the price of the product, Q is the quantity sold, and the supply and demand functions are expressed in terms of P and Q.

a) Calculate the equilibrium price and quantity in the market.
b) Calculate the consumer surplus, producer surplus, and total welfare at the equilibrium price and quantity.
c) Suppose a tax of $5 is imposed on each unit sold. Calculate the new equilibrium price and quantity in the market and the tax revenue generated by the government.
d) Calculate the deadweight loss caused by the tax.
Show all calculations.