We build a dynamic multi-region model of climate and economy with emission permit trading among 12 aggregated regions in the world. We solve for the dynamic Nash equilibrium under noncooperation, wherein each region adheres to the emission cap constraints following commitments that were first outlined in the 2015 Paris Agreement and later strengthened under the Glasgow Pact. Our model shows that the emission permit price reaches $845 per ton of carbon by 2050, and global average temperature is expected to reach 1.7{\deg}C above the pre-industrial level by the end of this century. We demonstrate, both theoretically and numerically, that a regional carbon tax is complementary to the global cap-and-trade system, and the optimal regional carbon tax is equal to the difference between the regional marginal abatement cost and the permit price. We show that optimal regional carbon tax has significant heterogeneity between regions, and the tax needs to be implemented in both the developed and the developing regions.