Exercise 7.1 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 feet. 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 = ?H + 2, where ?H is the change in the stock. Again, this equation gives the height up to the flow supply curve at any value of ?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 ?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 ?H). Then, compute the new size for the housing stock, which equals the original stock plus ?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 period 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 period 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?