Suppose the demand for new housing is Qo=980 – P – 10PR + 0.51 = where Q, is the quantity demanded (in thousands), P is the price of new housing (in thousands), Pris the rental price of housing (in thousands), and average income (in thousands). Os = 115 + 2P – 3PL = where Qs is the quantity supplied (in thousands), P is the price of new housing (in thousands), PL is the price of a square foot of lumber (NOT in thousands). a. Suppose the rental rate is a $1,000, the average income is $60,000, and the price of a square foot of lumber is $5. What are the equilibrium price and quantity? b. Calculate the following elasticities: 

i. Price elasticity of demand for new housing

ii. Rental price elasticity of demand for new housing

iii. Income elasticity of demand of new housing iv. Price elasticity of supply of new housing

What are the new equilibrium price and quantities if the following changes occur? 

i. Average income is $90,000

ii. The price of a square foot of lumber is $8 (and income is still $60,000)

Assume the initial equilibrium from part a. The government is concerned about high housing prices and imposes a $260,000 price ceiling. Is there a shortage or surplus? How much? How many units are sold in the market? 

Assume the initial equilibrium from part a. The government decides to remove the price ceiling and instead provide a subsidy to the market. If the government offers a $60,000 per house subsidy what are the new market quantity, price paid by consumers, and price received by producers?