The type of unemployment that will exist even if the wage is at the competitive equilibrium is:
d. frictional unemployment
Frictional unemployment occurs when individuals are temporarily unemployed while transitioning from one job to another. This type of unemployment stems from the natural turnover in the labor market and is not caused by wage rigidities or other market distortions. It exists regardless of whether the wage is at the competitive equilibrium.
In contrast, unemployment due to unions, minimum-wage laws, or efficiency wages can create distortions in the labor market that can prevent the wage from clearing the market, leading to higher levels of unemployment than what would be found at competitive equilibrium.