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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...

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?