  In a continuous time stochastic economy, this paper considers the problem of
consumption and investment in a financial market in which the representative
investor exhibits a change in the discount rate. The investment opportunities
are a stock and a riskless account. The market coefficients and discount factor
switches according to a finite state Markov chain. The change in the discount
rate leads to time inconsistencies of the investor's decisions. The randomness
in our model is driven by a Brownian motion and Markov chain. Following Ekeland
etc (2008) we introduce and characterize the equilibrium policies for power
utility functions. Moreover, they are computed in closed form for logarithmic
utility function. We show that a higher discount rate leads to a higher
equilibrium consumption rate. Numerical experiments show the effect of both
time preference and risk aversion on the equilibrium policies.
