This paper proposes a framework of endogenous energy production with convex costs to investigate the general equilibrium effects of energy price shocks on the business cycle. This framework explicitly models the consumption of durables and nondurables and implements a high complementarity between energy and the usage of durables and capital. The model predicts energy price elasticities of various consumption variables that fall within reasonable agreement with empirical estimates. Convex costs in energy production produce energy price and energy supply dynamics that tallies well with empirical behavior. Our analysis confirms in a theoretical setting recent observations that not all energy price shocks are the same. They can be distinct in terms of energy price dynamics and impact on the business cycle, as well as energy price elasticities of various macro variables that can be useful indicators for their underlying causes.