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T. Brechet, Tz. Tsachev, V.M. Veliov:
"Markets for Emission Permits with Free Endowment: a Vintage Capital Analysis";
Optimal Control Applications and Methods, 33 (2012), 2; S. 214 - 231.

In this paper we develop a vintage capital model for a ¯rm involved in a market for tradable emission permits. We analyze both the firm's optimal investment plans and the market equilibrium. This allows us to scrutinize how firms use permits free endowment, and to highlight the implications of non-optimal uses both at the firm and at the market level. We provide a new rationale for the market of tradable permits not to be cost-e±cient. The novel technical points in this context are the use a distributed (vintage) optimal control model of the firm, the use of optimality conditions for non-smooth problems, and the involvement of a nonlinear Fredholm integral equation of the first kind for the description of the equilibrium price of permits, and its practical meaning for market regularization.

environmental economics, emission permits, optimal control, distributed systems

http://dx.doi.org/10.1002/oca.988

http://onlinelibrary.wiley.com/doi/10.1002/oca.988/abstract