Why are real estate prices not becoming infinite?

We will illustrate our remarks with the cases of the United States and the euro zone. Real estate prices are normally equal to the discounted sum of future rents. If the long-term interest rate is lower than the rate of growth in rents, then in the absence of a risk premium, the equilibrium real estate price is infinite. However, a very high real estate price is impossible, because there would no longer be any buyers due to liquidity constraints, even though the theoretical fundamental price is infinite. This points to a dynamics for real estate prices when the long-term interest rate is lower than the rate of growth in rents: the price rises until the point where demand for housing falls; real estate prices then fall, even in the absence of a rise in interest rates, which leads to a high risk premium that justifies the fall in real estate prices even though the interest rate is lower than the rate of growth in rents and the fundamental price without a risk premium is very high (or even infinite). Real estate crises are therefore still possible when interest rates are very low - even if they do not rise.