This paper investigates the effects of total factor productivity and energy price shocks in a real business cycle (RBC) model with heterogeneous agents. It extends standard RBC models by including the distinction between durable goods and non-durable goods but also including energy in production of non-durable goods. Furthermore, we combine two sources of heterogeneity using idiosyncratic shocks in labor supply and limited asset market participation by a fixed proportion of agents. We study to what degree the empirically observed inequality in income and wealth can be explained by the provided framework. The model can predict the evolution of inequality in income and wealth, unlike traditional homogeneous macroeconomic models with a representative agent. We show that the distinction between nondurable and durable goods leads to a significant improvement in predicting most of the moments close to the one in observational data from Germany. Furthermore, we find that energy price shocks lead to decreasing inequalities, with respect to both income and wealth. In a brief policy analysis, we give an outlook about the effects of redistribution of income between classes of agents.