Greenhouse gas (GHG) emission targets are becoming more stringent for both automakers and electricity generators. With the introduction of plug-in hybrid and electric vehicles, transportation and electricity generation sectors become connected. This provides an opportunity for both sectors to work together to achieve the cost efficient reduction of CO2 emission. In addition, the abundant natural gas (NG) in USA is drawing increased attention from both policy makers and various industries due to its low cost and low carbon content. NG has the potential to ease the pressure from CO2 emission constraints for both the light duty vehicle (LDV) and the electricity generation sectors while simultaneously reducing their fuel costs. To quantify the benefit of this collaboration, an analytical model is developed to evaluate the total societal cost and CO2 emission for both sectors. A large-scale linear programming (LP) problem is formulated to conduct tradeoff studies between the two sectors in various scenarios, and some high level insights of cost efficient capacity planning strategies for automakers and electricity generators are then identified by solving the optimization problems. The results will show the cost differences between the two sectors working together and independently to meet the CO2 emission constraints. Moreover, the results will reveal the differences in capacity planning in the scenarios when NG is available or unavailable as an alternative automobile fuel source. This will help to understand the potential natural gas impact on cost efficient capacity planning for both automakers and electricity generators in a carbon constrained world.