We study optimal monetary policy in an analytically tractable heterogeneous agent New Keynesian model with rich cross-sectional heterogeneity. Optimal differs from a representative benchmark because can affect consumption inequality, by stabilizing risk arising both idiosyncratic shocks and unequal exposures to aggregate shocks. The trade-off between productive efficiency, price stability is su...

The optimal control p roblem of Markov jump linear quadratic model with controlled jump probabilities of modes is investigated. Two kinds of mode control policies , open2loop control policy and close2loop control policy , are considered. By using policy iteration and performance potential concept , a sufficient condition for the optimal close2 loop control policy being better than the optimal o...