In this paper we study an optimization problem of an investor in which there is a better investment opportunity when he is rich than when he is poor. We model the betterment of the investment opportunity by considering an exogenously speciffied wealth threshold such that the investor`s investment opportunity is better when his wealth is above the threshold than when it is below the threshold. We derive a closed form solution for the optimal consumption and investment strategies by using a dynamic programming method, and investigate the effiects of the potential investment opportunity changes on the optimal strategies. We show that the investor consumes less for all wealth levels and takes more(resp. less) risk at wealth below(resp. above) the threshold level than he would in the absence of potential investment opportunity changes. Furthermore, we show that such effiects of the potential investment opportunity changes on the optimal strategies become stronger as the investor`s wealth gets closer to the threshold level, while the effiects are negligible when his wealth is sufficiently far from the threshold level. We also show that the marginal propensity to consume out of wealth and the revealed coefficient of relative risk aversion are strictly decreasing for all wealth levels except at the threshold level, where they exhibit upward jumps.