A consumer’s income is $100. There are two goods, food (F) and housing (H). Food costs $2 per unit and housing costs $5 per unit. At these prices, the consumer chooses 8 units of housing and 30 units of food.

a) Show the consumer’s utility maximization choice on an appropriate diagram. Put housing units (H) on the horizontal axis and food (F) on the vertical axis (4%).

Assume the government decides to allocate housing directly and reduces the price of allocated housing to $3 per unit. The consumer would like to choose 12 units of housing and 32 units of food at these prices. The government, however, decides to allocate 15 units of housing to the household at a price (or cost) of $45. Show the effect on the consumer’s utility of:

b) The government’s allocation policy (2%).

c) The subsidized price without government allocation constraints (3%).

d) A government subsidy to income with original prices but raising the consumer’s income from $100 to $130 (3%).

e) Does this analysis suggest that governments should always allow the market to set rents and simply subsidize the incomes of poorer consumers? Explain your reasoning. (3%).