4. In the market for rental housing in a small town, demand is given by and supply is up to a limit of 400 units, at which point the supply becomes perfectly inelastic.

A) Calculate the market-clearing price and quantity

B) Calculate the consumers' and producers' surplus.

C) Suppose one of the landlords was able to invest its scarcity rents into acquiring all of its competitors, leaving it as a monopolist in the market. Assuming the monopolist has marginal costs reflected by up to a limit of 400 units (same as before) and it must charge the same price to all renters, what is the price and quantity the monopolist landlord will choose?

D) Re-calculate the landlord's producer surplus under the monopoly scenario.

E) Suppose the town has approved new housing and zoning policies to allow for new housing construction. The landlord estimates that the presence of new competitors would reduce its producer surplus, leaving it with $100,000 in surplus. The landlord decides to hire a lobbying firm for $20,000 to see if it can sway the city council against the new policy. With the lobbyist, they have a 50% chance of success, which would allow the landlord to keep their current surplus (from part d). What is the landlord's expected value of the outcome with the city council?

F) It turns out the lobbying firm is also a monopolist and realizes it could charge the landlord more than $20,000. Assuming the landlord is risk-neutral, what is the most the lobbying firm could charge the landlord?