This paper deals with Markov decision processes with finite state space, compact action sets and a nonnegative reward. For an exponential utility function with risk-sensitive coefficient, the performance of a decision policy is measured by the corresponding risk-sensitive expected total reward criterion. Under some mild conditions of continuity, the authors derive the risk-sensitive optimality equation when the value function is finite. Moreover, if the number of ergodic classes depends continuously on the policy, when a stationary policy is used to drive the system, then there exists an optimal stationary policy.