The recent crisis in the U.S. housing market was in part precipitated by the fact that many consumers bought houses using "sub-prime mortgage contracts". These contracts specified an initially below-market interest rate that would adjust upward in the future depending on how market interest rates moved. Then market interest rates went up - which substantially increased the cost of housing for consumers who were holding sub-prime mortgage contracts - in some cases making it unaffordable for consumers to remain in the house they purchased earlier. For purposes of this problem, use the attached graph for such a consumer to answer the question. (Caution: Don't think of housing as an endowment in this problem - but rather treat the cost of housing as if the consumer were simply renting square feet of housing, with the "rent" having increased as a result of higher interest rates.) The two solid budget lines represent the budget before and after the increase in interest rates that led to an increased cost of housing for this consumer. Before the current crisis, this consumer optimized at bundle C. Assume throughout this problem that all consumer tastes are homothetic.
a. In principle, could this consumer continue to stay in his current house?
b. In the absence of any policy intervention, will this consumer consume more or less in non-housing consumption given the current crisis?
c. It turns out that some consumers have increased current consumption and others have decreased it as a result of the housing crisis. Assuming that all consumers have homothetic tastes, what is the crucial difference between the tastes of these consumers?
d. Suppose the government intervenes and subsidizes housing in such a way that (per square feet) housing costs remain unchanged despite the housing crisis. How much will this policy cost for the consumer graphed in the attached graph?
e. Suppose that, instead of lowering the cost of housing to the pre-crisis level, the government gave a tax credit to this consumer (which is equivalent to giving the consumer cash). How much of a tax credit would it need to give to make the consumer indifferent between this and the previous policy?
f. How much of a deadweight loss does society incur from the policy that reduces the cost of housing to the pre-crisis level?
g. On the lower graph (on the attached page), indicate where this consumer's demand curve lies. Then indicate where the marginal willingness to pay curve you would use to derive deadweight loss lies.
h. Suppose the government only has estimates of (regular) demand curves. As a result, it uses the demand curve (and not the marginal willingness to pay curve) to estimate the deadweight loss from the policy that lowers housing costs to pre-crisis levels. Will this be an over or under-estimate of the true deadweight loss?