The thesis consists of three chapters. The first chapter examines the behaviour of the New Keynesian (NK) model, which has been extended to include heterogeneous individuals who face idiosyncratic productivity risk. My main focus in this chapter is the heterogeneity innovation of the model, therefore, I consider the relatively simple NK setting where the idiosyncratic income risk follows a two-state Poisson process and in which households can save in productive capital. This model proved to be a good starting point for establishing the methodology and understanding the key properties of the HA class of models. The second chapter presents a HANK model with government debt which is both nominal and of long maturity. Other key features of the considered model include sticky prices, monetary policy, endogenous labour supply and distortionary taxation. This framework allows us to reconsider the distributional implications of interactions between monetary and fiscal policy. It has been found that heterogeneous agent economies generate significant differences in the monetary and fiscal policy transmission mechanisms which are likely to have a quantitative impact on the optimal design of the policy. The third chapter introduces Ramsey type of optimal policy to the HANK model with government bonds. To address the challenge of solving for optimal policy in HA models, I employ a variational approach inspired by Nuno and Thomas [2020], which incorporates the concept of Geautaux derivatives of infinite-dimensional spaces. As a result, I obtain an analytical characterization of optimal monetary policy, where the factors of aggregate wealth and income dispersion, as well as marginal consumption properties, define optimal inflation value. Specifically, the optimality condition for inflation reveals how the central bank trades off the disutility costs of inflation with its benefits. Notably, my findings align with those of Nuno and Thomas [2020]: the heterogeneous-agent model generates an inflationary bias with redistributive effects, distinct from the inflationary bias observed in classical New Keynesian literature. The extent of this unconventional inflationary bias depends on the stringency of the government budget constraint and income dispersion.