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I am searching for a model of the market for capital goods applied on purchase prices, rents, and supply of new housing.

The model, operating in continuous time, considers prices as a function of future discounted rents, derives the demand for houses as a function of said rents.

Importantly, the model was interesting by simultaneously analyzing two situations: 1) The steady relations between stable level of capital (i.e., houses) and demand for houses, denoting steady state. 2) The relation between prices of houses and current capital, depicted in a phase diagram, utilizing saddle path between stable stock (denoted by supply of capital) and stable prices (depending on the demand for capital).

Do you know how is this model called?

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