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 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?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.