Exercise 1. Monopoly with Linear Costs facing a Linear Demand A monopoly has the cost function...

Exercise 1. Monopoly with Linear Costs facing a Linear Demand

A monopoly has the cost function c(y)=10y+100, and is facing a market demand D(p)=100-2p.

a) What is the inverse demand function, p(y)? Having profits be π = p(y)∙y – c(y), what is the profit maximizing output level? What is the corresponding market price?

b) Calculate the monopolist’s profit and producer surplus. What is the consumer surplus? What is the deadweight loss?

c) The government imposes a production tax, tP=10, so that the new cost function is c(y)=(10+tP)y+100. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

d) The government imposes instead a lump sum tax, T=300, so that the new cost function is c(y)=10y+100+T. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss?

e) The government imposes instead a sales tax, tS=25%, so that the new demand function is D(p)=100-2p(1+tS). What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

f) The government imposes instead a profit tax, τ=40%, so that the new profit function is π=(1- τ)[p(y)∙y–c(y)]. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

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Rahul Sunny answered 1 week ago

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