This paper analyzes the possible circumstances of indeterminacy and determinacy for a two-sector small open economy with social constant return to scale technologies. In comparison with the other papers which show that the indeterminacy will happen if there exist sector-specific externalities or asymmetric factor taxation respectively, this paper shows that the indeterminacy will not happen if these two external forces exist simultaneously and alter the private optimal decision to the same direction. Under this circumstance, the economy will produce the traded or non-traded goods in a capital-intensive way and there exists a unique saddle path for the equilibrium dynamics. In addition, this paper investigates the source factors of indeterminacy among capital mobility, endogenous labor supply, sector-specific externalities and asymmetric factor taxation. The conclusion is that sector-specific externalities and asymmetric factor taxation are the key contributors of indeterminacy, while capital mobility makes indeterminacy easier to emerge. The endogenous labor supply will not cause the indeterminacy, but it will enlarge the effect of asymmetric factor taxation on the steady state value of the price and capital stock.