In this paper, we introduce two sources of unemployment in a two-factor general equilibrium model: search frictions and fairness considerations. We find that a binding fair-wage constraint increases the unskilled unemployment rate and can at the same time lead to a higher unemployment rate for skilled workers, as compared to an equilibrium where fairness considerations are absent or non-binding. Starting from a constrained equilibrium, an increase in the fairness parameter leads to increases in both skilled and unskilled unemployment. The wage of unskilled workers increases but the wage of skilled workers decreases. Next we allow for offshoring of unskilled jobs in our model, and we find that, as a result, it becomes more likely that the fair-wage constraint binds. Offshoring of unskilled jobs always leads to an increase in skilled wage, a decrease in skilled unemployment and an increase in unskilled unemployment. The presence of fairness considerations increases the adverse impact of offshoring on unskilled unemployment. The unskilled wage can increase or decrease as a result of offshoring.