Value Price and Rental Price © Allen C. Goodman 2009

Demand and Supply of Housing Supply is fundamentally related to STOCK Demand is fundamentally related to FLOW STOCK  services Review –We recall that V = R/i, where R = rent i = interest rate

Value and Rent We recall that V = R/i Landlord charges R for the right to occupy a standard-sized dwelling for one year. This means: –If the owner is borrowing to pay for the house, he/she must pay iV. –Even if the owner is not paying a mortgage, he/she has an asset paying no interest. OPPORTUNITY cost is iV.

Cost of Capital If owner of capital is taxed at rate t (property tax), if rent is to cover landlord’s costs he/she must pass it along. Same occurs with Depreciation (d), and management costs e. If the landlord expects capital gains g, rental price can be lowered. R = iV + tV + dV – gV + eV, or: R = (i + t + d – g + e) V, or: V = R/ (i + t + d – g + e) Let (i + t + d – g + e) =  KEY: Taxes lower the value, but RAISE the rent.

Inflation and Taxes Suppose you would lend me $ at 5%. I would borrow at 5%. No inflation. If expected rate of inflation  to 3% what happens? This leads to: –i = r + c, where i is NOMINAL rate of interest, and c is expected rate of inflation. Look at cost of capital equation. R = (i + t + d – g + e) V, R = (r + c + t + d – (g r + c) + e) V, or: V = R/ (r + c + t + d – (g r + c) + e) g r = real rate of capital gains.

Inflation and Taxes V = R/ (r + c + t + d – (g r + c) + e) If inflation is anticipated, 10% mortgage with 8% inflation is no more costly than 2% mortgage with 0% inflation.

Federal Taxation In US and some other countries, people may deduct mortgage interest. If we pay iV interest, we can deduct from our incomes, so taxes are lowered by TiV. Ignoring other thing, this means that the rental cost of housing  R = iV – TiV = i (1 – T) V. Same for property taxes. Capital gains are essentially untaxed. SO: We tax nominal interest, but we don’t tax capital gains at all. R = [(r + c)(1-T) + Property Tax rate + d – (g r + c) + e) V], R = [(r + c)(1-T) + t(1-T) + d – (g r + c) + e) V], R = [(r + c)(1-T) – c + t(1-T) + d – (g r ) + e) V],

Federal Taxation R = [(r – (r+c)T + t(1-T) + d – (g r ) + e)] V, Clearly, as c or T ,  . Economics. –We allow a deduction or real interest PLUS inflation. –We are not taxing capital gains from inflation. Useful pedagogically, but there are problems estimating the expected capital gain. or now, expected Capital loss!

Imputed Rental Income Suppose you and I live next door to each other. Each house is worth $100,000, and would generate $10,000 per year in rent. We each earn $50,000 per year and pay taxes in the 28% bracket. We own houses free and clear. Net income is $36,000.

Implicit Rent Tax Break (impute.xls)impute.xls

Housing Market Supply is basically related to V. Demand is basically related to R. We relate them through  V R Q Q S D

Housing Market Supply is basically related to V. Demand is basically related to R. We relate them through  (here = 0.10). V R Q Q D = R/  S = V  S D

Suppose  changes? We relate them through  (here = 0.10).  rises to 0.15 Value  Rent  Stock and supply of services decrease. V R Q Q D = R/0.10 S = V*

Summary DEMAND is determined outside capital market model. SUPPLY is determined outside capital market model. Value and rental prices are linked w/in capital market eq’m. NEXT – Housing Demand.