Endowment Effects and Housing Markets: In end-of-chapter exercises 6.9 and 7.6, we derived the curious prediction that homeowners are made better off by housing price fluctuations — regardless of whether housing prices go up or down. This was due to the fact that, assuming some degree of substitutability between housing and other goods (and no transactions costs), homeowners will sell their homes when ever housing prices change—buying smaller homes and consuming more when price increases and buying larger homes and consuming less when housing prices fall.
A: Revisit the logic behind this conclusion before proceeding.
(a) One reason that homeowners do not constantly switch homes when housing prices fluctuate arises from the fact that there are moving costs that make switching homes not worthwhile for small price fluctuations. Now consider another explanation rooted in endowment effects uncovered by behavioral economists. Within the context of the model you used in exercises 6.9 and 7.6, how might you be able to model such endowment effects in terms of the shapes of indifference curves for homeowners?
(b) Next, consider the problem faced by a homeowner who needs to move during a “down” market. Suppose the homeowner originally purchased his home at price p0 — and suppose that this price has become a “reference point” — with the homeowner interpreting a sales price above p0 as a “gain” and a sales price below p0 as a “loss”. Explain how behavioral economists might predict that the level of p0 will affect the asking price that the homeowner sets.
(c) Housing economists have uncovered the following empirical fact: During times when housing demand is falling (putting downward pressure on home prices), houses that are for sale typically take longer to sell—resulting in an increase in the number of houses on the market. Can you explain these using reference-based preferences with “loss aversion”?
B: Consider the optimization problem faced by a homeowner who is moving and is determining an asking price for his home. Such a homeowner faces the following trade-off: A higher asking price p means a lower probability of selling the home, but it also means greater utility for the homeowner if the home sells. Suppose that the probability of a sale is given by δ (p) = 1−0.00001p. Suppose further that p0 = $100,000 was the price at which the homeowner had originally bought the home, and his utility from not selling the home is u¯ = (10,000−αp0). His utility of selling the home depends on the price p and is given by u (p, p0) = (p −αp0) when p ≥ p0 and v (p, p0) = β (p −αp0) when p < p0.
(a) What values do α and β take in a model without reference-based preferences?
(b) Set up the optimization problem for the homeowner under the assumptions in (a) and solve for the optimal asking price.
(c) Next, suppose (from here on out) that α = 1 and β = 2.25. Repeat the optimization exercise assuming that the homeowner uses the function u (and not v). What would be the optimal asking price?
(d) If the homeowner has reference-based preferences as specified by u and v, is the price you calculated in (c) the true optimal asking price?
(e) Next, set up the optimization problem again — but this time use v instead of u. What is the optimal asking price you now get? Is this the true optimal asking price for this homeowner? Explain.
(f) What is the probability that the home will sell for the price you calculated in (b) and (c) — and how does it compare to the probability that the home will sell at the price you calculated in (e)? Can you reconcile this with the empirical fact stated in A (c)?