Recent climate modeling studies have concluded that cumulative carbon emissions determine temperature increase, regardless of emission pathways. Accordingly, the optimal emission pathway can be determined from a socioeconomic standpoint. To access the path dependence of socioeconomic impacts for cumulative carbon emissions, we used a computable general equilibrium model to analyze impacts on major socioeconomic indicators on a global scale for 30-50 pathways with different emission reduction starting years, different subsequent emission pathways, and three different cumulative 2100 emission scenarios (emissions that meet the 2 °C target, the 2 °C target emissions plus 10 %, and emissions producing radiative forcing of 4.5 W/m2). The results show that even with identical cumulative emission figures, the resulting socioeconomic impacts vary by the pathway realized. For the United Nations 2 °C target, for example, (a) the 95 % confidence interval of cumulative global gross domestic product (GDP) is 1355-1363 trillion US dollars (2010-2100, discount rate = 5 %), (b) the cumulative GDP of pathways with later emission reduction starting years grows weaker (5 % significance level), and (c) emissions in 2100 have a moderate negative correlation with cumulative GDP. These results suggest that GDP loss is minimized with pathways with earlier emission reduction followed by more moderate reduction rates to achieve lower emission levels. Consequently, we suggest an early emission peak to meet the stringent target. In our model setting, it is desirable for emissions to peak by 2020 to reduce mitigation cost and by 2030 at the latest to meet the 2 °C target.