In this study, we develop a novel modelling framework that may be useful in forecasting evolution of efficiency distributions and price-efficiency correlations seen in efficient appliance markets. The framework is founded on three basic assumptions: (1) technological learning is the primary driver of price changes for products at fixed efficiency, (2) the dynamics of product market distributions can be accurately characterized by simple dynamic cumulative distribution functions, and (3) price distributions at any particular time can be characterized by a ‘willingness-to-pay” price distribution that is correlated with efficiency and which can be interpolated between a top-of-market value, and a bottom of market value. We combined these three fundamental assumptions with the mathematics of partial differential equations to derive a set of equations that describe the evolution of price and efficiency as a function of time and as a function of a transformed market share variable. The transformed market share variable quantifies the market position of each efficiency performance level relative to other efficiency performance levels. The key driver for the change in price at different efficiency levels is the increase of a “cumulative experience” variable that reflects the technological learning that occurs at and above each efficiency performance level. We demonstrate that the model captures the basic empirical observations regarding the evolution of efficiency distributions and price-efficiency functions seen in efficient refrigeration appliance markets in Europe between 1995 and 2009.
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