Suppose that the demand and supply schedules for rental apartments in city of Go

Question

Suppose that the demand and supply schedules for rental apartments in city of Gotham are as given in the table below Monthly Rent Apartment Demanded Apartment Supplied $2,500 10,000 15,000 2000 12,500 12,500 1500 15,000 10,000 1000 17,500 7,500 500 20,000 5,000 a) What is the market equilibrium rental price per month and the market equilibrium number of apartments demanded and supplied? b) If the local government can enforce a rent-controlled law that sets the maximum monthly rent at $1500, will there be a surplus or a shortage? Of how many units? And how many units will actually be rented each month? c) Suppose that a new government is elected that wants to keep out the poor. It declares that the minimum rent that can be charged is $2500 per month. If the government can enforce that price floor, will there be a surplus or a shortage? Of how many units? And how many units will actually be rented each month? d) Suppose that the government wishes to decrease the market equilibrium monthly rent by increasing the supply of housing. Assuming that demand remains unchanged, by how many units of housing would the government have to increase the supply of housing /in order to get the market equilibrium rental price to fall to $1500 per month? To $1000 per month? To $500 per month?

Explanation / Answer

Note the original price was 2000 and the quantity in the market was 12,500. Now we have a market price of 2500 and a quantity traded 10,000. Since 10,000 units are traded and the tax is 1000 per unit the government tax revenue is 1000(10,000) = $10 million! The loss in consumer surplus is the change in price times the new quantity plus ½ of the change in price times the change in quantity traded = (2500 – 2000)10,000 + .5(2500 – 2000)(12,500 – 10,000) = 500(10,000) + .5(500)(2,500) = $5,000,000 + $625,000 = $5,625,000. The loss in producer surplus is the change in what the seller gets to keep times the new quantity + ½ of the change in what the seller gets to keep times the change in the quantity traded = (2000 – 1500)10,000 + .5(2000 – 1500)(12,500 – 10,000) = $5,000,000 + $625,000 = $5,625,000.

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