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.