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a) A monopoly has the inverse demand function P=200-Qand the cost function C=40Q. Set up the profit maximization problem and solve for the profit-maximizing price and quantity. How much will the monopoly raise the price if it faces a quantity tax, t=40? Show the (additional) welfare loss of the tax in a graph.
b) Instead of using a quantity tax of t=40 , the government contemplates a proportional tax on profits, τ=-3/8 . Compare tax revenue and welfare effects under this two different tax schemes and make a policy recommendation to the government based on your findings.
The result you derived in a)leads to the conclusion that a monopolist always passes on a fraction of the tax as an increase in consumer price. Find out if this statement is true for all demand functions by analyzing the effects of a tax of t=40 when the monopoly faces the constant elasticity, inverse demand function P=Q- ½ and cost function C=40Q
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