Incorporating consumption–savings choices under a general concave utility function and hence an endogenous capital supply into a model of capital tax competition, we re‐investigate Nash equilibrium and compare it with the optimum under cooperative tax policy. In contrast to the case of fixed capital supply, it is shown that if savings sufficiently increase with the interest rate, a Nash equilibrium may be more efficient than a cooperative tax policy. Therefore, the distortionary effects of capital supply are important to issues of tax policy coordination.