The market for baked beans is perfectly competitive. The market demand for baked beans is given byQ= 90-P/2. The market supply curve for baked beans followsP = 2Q.

i) Find the competitive equilibrium price and quantity in the market for baked beans.[3 marks]

ii) It turns out baked beans impose a negative externality on people who don't even eat them. The marginal external cost is given byMEC = 2Q. What is the marginal social cost? Note: the Marginal Private Cost is of courseMPC = 2Q. Find the socially optimal production of baked beans.[3 marks]

iii) What is the size of the deadweight loss in a competitive equilibrium?[3 marks]

iv) Find the Pigouvian per-unit tax that results in the socially production of baked beans.[2 marks]

v) Show the results of i), ii), iii) and iv) in a well-labelled diagram.[3 marks]