Home renovation is generally asserted to be a highly effective means for households to lower expenditures on energy. In this sense, home renovation can also be thought as a means to reduce GHG emissions. In this paper we consider a homeowner who makes an irreversible energy-saving investment in an uncertain environment. In a general equilibrium framework, we solve the program of a representative consumer who uses his wealth to invest in the energy-saving technology, to save or to consume energy goods and non-energy goods. Resolution is analytical in a zero discounting case and numerical for the general case, based on collocation and Chebyshev polynomials. In particular, we show that the usual explanation of the energy paradox based on the existence of an option value in partial equilibrium is no longer valid when the analysis is extended to a general equilibrium framework.
Caporale and Cerrato (Comput Econ 35(3):235–244, 2010) propose a simple method based on Chebyshev approximation and Chebyshev nodes to approximate partial differential equations (PDEs). However, they suggest not to use Chebyshev nodes when dealing with optimal stopping problems. Here, we use the same optimal stopping example to show that Chebyshev polynomials and Chebyshev nodes can still be successfully used together if we solve the model in a matrix environment.
In this paper, we study the determinants of switching from non-renewable natural resource inputs to renewable resource inputs in energy production. We assume that the stocks of both natural resources are stochastic, and that the adoption of renewable resources is costly and irreversible. Our formulation gives raise to an optimal stopping/switching problem that cannot be solved analytically, then we turn to numerical simulations. Our results suggest that the optimal switching time depends not only on the uncertainty parameters, but also on energy demand, costs, and the relative productivity of the resources.