A new mathematical theory of the diffusion of price inflation over time, in an imperfect market similar to the residential housing market, is developed. The underlying economic force is the imperfect arbitrage operating with time delays upon ‘close’ substitutes for related products arranged according to an idealized index of desirability (for example, distance from a city center). The analysis is based on a second-order partial differential equation with appropriate initial and boundary conditions. The model is illustrated with three-dimensional plots for the price of housing at the city center and at various distances from the city center at specified time lags.
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