Operational decision model with carbon cap allocation and carbon trading price

This paper considers a carbon emission cap and trade market, where the carbon emission cap for each entity (either government or firm) is allocated first and then the carbon trading price is decided interdependently in the carbon trading market among the non-cooperative entities which make their production decision. We assume that there are n entities emitting carbon during the production process. After allocating the carbon (emission) cap for each participating entity in the carbon cap and trade market, each participant makes a production decision using the Newsvendor model given carbon trading price determined in the carbon trading market and trades some amount of its carbon emission, if its carbon emission is below or above its own carbon cap. Here, the carbon trading price depends on how carbon caps over the entities are allocated, since the carbon trading price is determined through the carbon (emission) trading market, which considers total amount of carbon emission being equal to total carbon caps over entities and some fraction of total carbon emission should be from each entity participating in the carbon cap and trade market. Thus, we can see the interdependency among the production decision, carbon cap and carbon trading price. We model this as a non-cooperative Stackelberg game in which carbon cap for each entity is allocated in the first stage and each entity's production quantity is decided in the second stage considering the carbon trading price determined in the carbon trading market. First, we show the monotonic property of the carbon trading price and each entity's production over the carbon cap allocation. In addition, we show that there exists an optimality condition for the carbon cap allocation. Using this optimality condition, we provide various results for carbon cap and trade market.