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We consider a three‐phase optimal control model of economic growth and climate change mitigation through transiting to low‐carbon technologies. In the first phase, companies invest in adopting low‐carbon technologies and a part of the required investment is reimbursed through ‘climate’ bonds issued by the government. The second phase starts when the greenhouse gases’ concentration is reduced to a pre‐industrial level and firms have fully adopted low‐carbon technologies. In this phase, bonds are being repaid through taxation. In the last phase, the economy is accumulating capital and consume enjoying the stabilized climate. The standard consumption based utility function in the logarithmic form is applied over all three phases. We use GPOPS‐IIsoftware to find a locally optimalsolution in the model, including the optimal switching times between phases. We compare the obtained optimal solution with a business‐as‐usual version of this model, in which no mitigation action is undertaken. The social welfare function in the mitigation policy model turns out to be greater than the one in the business‐as‐usual model over almost the entire time horizon of consideration with the exception of a short period in the beginning of the first phase.