In this section, we ask you to write down a simple, formal, mathematical model. A small number of points will be awarded for an intuitive discussion of the problem, but most of the points are reserved for a formal solution. Be careful to state all assumptions, and remember above all to keep your answers simple and straight-forward!
In this question, we wish to analyze the consumer's choice of housing. In particular, we want to compare the impact on utility of a change in the price of housing for a renter and a homeowner. You may assume that all individuals consume two things - housing (H), and a second consumption good (C).
1. (10 points) Write down the renter's problem. Write down the homeowner's problem.
2. (10 points) What happens to the renter's utility when pH , the price of housing, changes? The homeowner's utility? What happens to the renter's optimal consump-tion of H and C? The homeowner's consumption?
1. Both the renter and homeowner try to increase their total utility of consumption. The homeowner's problem is that the higher is the price of housing, the lower is his utility of living in his house and higher is utility of renting the house or its part. The renter's problem is that the higher is the price of housing (pH), the lower is his utility of renting house.
2. The renter's utility changes indirectly when pH , the price of housing, changes. The homeowner's utility changes directly. The renter's optimal consumption of H and C changes too. If pH increases, the renter will consume more of C and less of H. The homeowner's consumption will change conversely.