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(Solution) - A portion of the housing market in New York City

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A portion of the housing market in New York City (and many other cities in the world) is regulated through a policy known as rent control. In essence, this policy puts a price ceiling (below the equilibrium price) on the amount of rent that landlords can charge in the apartment buildings affected by the policy.
A. Assume for simplicity that tastes are quasilinear in housing.
(a) Draw a supply and demand graph with apartments on the horizontal axis and rents (i.e. the monthly price of apartments) on the vertical. Illustrate the ?disequilibrium shortage? that would emerge when renters believe they can actually rent an apartment at the rent-controlled price.
(b) Suppose that the NYC government can easily identify those who get the most surplus from getting an apartment. In the event of excess demand for apartments, the city then awards the right to live (at the rent-controlled price) in these apartments to those who get the most consumer surplus. Illustrate the resulting consumer and producer surplus as well as the deadweight loss from the policy.
(c) Next, suppose NYC cannot easily identify how much consumer surplus any individual gets? and therefore cannot match people to apartments as in (b). So instead, the mayor develops a ?pay-to-play? system under which only those who pay monthly bribes to the city will get to ?play? in a rent-controlled apartment. Assuming the mayor sets the required bribe at just the right level to get all apartments rented out, illustrate the size of the monthly bribe.
(d)Will the identity of those who live in rent-controlled apartments be different in (c) than in (b)? Will consumer or producer surplus be different? What about deadweight loss?
(e) Next, suppose that the way rent-controlled apartments are allocated is through a lottery. Whoever wants to rent a rent-controlled apartment can enter his/her name in the lottery, and the mayor picks randomly as many names as there are apartments. Suppose the winners can sell their right to live in a rent-controlled apartment to anyone who agrees to buy that right at whatever price they can agree on. Who do you think will end up living in the rent-controlled apartments (compared to who lived there under the previous policies)?
(f) The winners in the lottery in part (e) in essence become the suppliers of ?rights? to rent controlled apartments while those that did not win in the lottery become the demanders.
Imagine that selling your right to an apartment means agreeing to give up your right to occupy the apartment in exchange for a monthly check q. Can you draw a supply and demand graph in this market for ?apartment rights? and relate the equilibrium point to your previous graph of the apartment market?
(g) What will be the equilibrium monthly price q? of a ?right? to live in one of these apartments compared to the bribe charged in (c)? What will be the deadweight loss in your original graph of the apartment market? How does your answer change if lottery winners are not allowed to sell their rights?
(h) Finally, suppose that instead the apartments are allocated by having people wait in line. Who will get the apartments and what will deadweight loss be now? (Assume that everyone has the same value of time.)
B. Suppose that the aggregate monthly demand curve is p = 10000?0.01x while the supply curve is p = 1000+0.002x. Suppose further that there are no income effects.
(a) Calculate the equilibrium number of apartments x? and the equilibrium monthly rent p? in the absence of any price distortions.
(b) Suppose the government imposes a price ceiling of $1,500. What?s the new equilibrium number of apartments?
(c) If only those who are willing to pay the most for these apartments are allowed to occupy them, what is the monthly willingness to pay for an apartment by the person who is willing to pay the least but still is assigned an apartment?
(d) How high is the monthly bribe per apartment as described in A(c)?
(e) Suppose the lottery described in A(e) allocates the apartments under rent control, and suppose that the ?residual? aggregate demand function by those who did not win in the lottery is given by x = 750,000?75p. What is the demand function for y ?the ?rights to apartments? (described in A(f ))? What is the supply function in this market? (Hint: You will have to determine the marginal willingness to pay (or inverse demand) curves for those who did not win to get the demand for y and for those who did win to get the supply for y. And remember to take into account the fact that occupying an apartment is more valuable than having the right to occupy an apartment at the rent controlled price.)
(f) What is the equilibrium monthly price of a right y to occupy a rent-controlled apartment? Compare it to your answer to (c).
(g) Calculate the deadweight loss from the rent control for each of the scenarios you analyzed above.
(h) How much would the deadweight loss increase if the rationing mechanism for rent-controlled apartments were governed exclusively by having people wait in line? (Assume that everyone has the same value of time.)


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