Micheal and Mary are a couple currently planning to buy a property for residence. Their household income is $10,000, their current rent is $2,000, and their other living expenses are $2,000. Assume they can terminate their apartment lease at the end of any month without incurring any costs. We also assume their home purchase closing date is the same as their rental lease end date, and they can move into new home immediately. We assume that housing prices is decided by the following inverse demand function: HousePrice=100000 + 30⋅Qd - 5⋅Qs - 10000⋅Rate(%) + 1000⋅Size(sqft) The current market demand Qd is 10000, market supply Qs is 10000, and the market interest rate is 6%. (1) (4 points) Assuming the home price is the only cost of purchasing and that there is no down payment required, what is the maximum size (sqft) of house they can afford if they finance the purchase with a 30-year mortgage loan with a monthly payment schedule at a 6% interest rate? Please explain result economic meaning. (2) (6 points) Suppose they are interested in a house priced at 1 million dollars and decide to purchase it using a mortgage loan at the 6% interest rate. If the market interest rate changes from 6% to 12% in five years, should they refinance their mortgage loan and explain the reason? If they do refinance from the starting of the sixth year, how much more or less interest payment will they pay in total for the rest scheduled periods? Please explain economic meaning. (3) (4 points) Under the conditions where HousePrice=1 million dollar, Qd=10000, Qs=10000, and Rate=12%, what are the house price elasticities of these three variables respectively? Please explain result economic meaning. (4) (4 points) Given the situation in (3), if Qd, Qs, and Rate all exhibit a downward trend in the future, which factors will have a favorable impact on homebuyers, and which factors will have an unfavorable impact? Explain why and result economic meaning. Question 13 options: