What would be the monopolist price and quantity calculate, Business Economics

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What would be the monopolist price and quantity calculate

Assume that a monopolist faces the following demand curve: P=250-2Q

Also assume that the total cost function is given as: TC=1/2 Q2

a) What would be the monopolist price and quantity? Calculate the profit for the monopolist and the DWL .

b) Calculate the learner index for this monopolist.

c) Now assume that the government imposes a specific tax of $1 per unit. What will happen to price and quantity? What will happen to the profit of the monopolist?

d) The government decides to impose a price ceiling on the monopolist to increase total welfare. What should be the optimal price ceiling?

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