In this question write down a simple, formal, mathematical model. 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 p_H , 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?

3.  (10 points) Some economists believe that, during the last economic crisis, the government should take action to boost housing prices. Analyze the effects of such a policy in light of your model.