Problem
A model of the housing market. (Potherb, 1984.) Let H denote the stock of housing, I the rate of investment, pH the real price of housing, and R the rent. Assume that I is increasing in pH, so that I = I (pH), with I (•) > 0, and that H? = I -δH. Assume also that the rent is a decreasing function of H: R = R(H ), R (•) < 0. finally, assume that rental income plus capital gains must equal the exogenous required rate of return, r : (r +>H)/pH = r.
(a) Sketch the set of points in (H, pH) space such that H? = 0. Sketch the set of points such that p?H = 0.
(b) What are the dynamics of H and pH in each region of the resulting diagram? Sketch the saddle path.
(c) Suppose the market is initially in long-run equilibrium, and that there is an unexpected permanent increase in r. What happens to H and pH at the time of the change? How do H, pH, I, and R behave over time following the change?
(d) Suppose the market is initially in long-run equilibrium, and that it becomes known that there will be a permanent increase in r time T in the future. What happens to H and pH at the time of the news? How do H, pH, I, and R behave between the time of the news and the time of the increase? What happens to them when the increase occurs? How do they behave after the increase.
(e) Are adjustment costs internal or external in this model? Explain.
(f) Why is the H?= 0 locus not horizontal in this mode?