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Although adjustment to the equilibrium may take a long time in a
stock-flow housing model, adjustment is fast under some circumstances,
which makes for an easy analysis. This problem considers such
a case and illustrates the effect of rent control. Suppose that the initial
demand curve for housing is given by p = 3 – H , where p is the rental
price per square foot of housing and H is the size of the stock in square
. Note that this equation gives the height up to the demand curve
at any H . The flow supply curve for housing is given by p = Δ H + 2,
where Δ H is the change in the stock. Again, this equation gives the
height up to the flow supply curve at any value of Δ H . Note that the
slopes of the two curves are – 1 and 1, respectively, a fact that allows
simple answers to be derived below.
(a) Compute the equilibrium price pe (the price at which Δ H = 0).
(b) Suppose that prior to the demand shock, the housing market is in
equilibrium, with a stock of size H = 1. Verify that the price in the
market equals pe when the stock is this size.
After the demand shock (e.g., arrival of the Cuban refugees), demand
increases to p = 8 – H .
(c) With the new higher demand, the price in the market shoots up to
a higher value, denoted by p’. Compute p’.
(d) Next, compute the change in the housing stock that occurs as
developers respond to this new price (compute Δ H ). Then, compute the
new size for the housing stock, which equals the original stock plus Δ H .
(e) Compute the price that prevails in the market after this increase in
the housing stock. Is further adjustment of the stock required to reach
equilibrium? How many periods does it take for the market to reach
the new equilibrium?
Instead of following the sequence you have just analyzed, now
suppose that rent control is imposed immediately after the demand
shock, with the controlled price set at pc = 3.
(f) Compute H’ , the stock size at which rent control ceases to have an
effect (in other words, the stock size where the equilibrium price is
equal to pc ). How many periods does it take for the stock to reach H‘
under rent control?
(g) How many periods does it take for the market to reach the new
equilibrium, where p = pe ?
(h) Illustrate your entire analysis in a diagram.
(i) On the basis of your analysis, does rent control seem like a good
response to a demand shock?
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