Housing and the Arbitrage Equation An agent is considering buying a house and is trying to assess the fair market value they should pay, denoted by P house. They have enough savings for a down-payment of size D. Given local market conditions, the agent expects being able to receive rent x. Local property taxes are proportion τ of the house value, given by τ × P house. The prevailing market interest rate is R, which applies both to bank savings and to mortgages.
(A) Write down the no-arbitrage condition linking the returns to buying a house to the market interest rate R. Interpret what the equation says.
(B) Solve for the equilibrium price of the house. How do home prices respond to lower interest rates R? Provide an economic explanation.
(C) Recently, Democrats have restored the State and Local Tax (SALT) deductions that allow households to deduct their property taxes from their federal taxes. What effect does SALT have on house prices? Evaluate if this policy is consistent with the politi- cians’ stated aim to help middle class and working class families. Explain your answer.
(D) In response to sharp year-after-year increases in home prices around the world, many politicians have advocated for rent control policies that cap how fast or high rents can be set. What effect does rent control have on home prices? Can rent-control policies effect the home prices even when they are set above existing rents? Explain.
(E) Suppose instead of buying a house, the agent considers purchasing a small business in the city’s downtown. If the economy is in equilibrium, how does the return on investing in a house compare to investing in the small business? How do the returns compare after the rent control policy? Explain your answer.