This paper investigates the quantitative implications of real wage rigidities and heterogeneity for two long-lasting puzzles in the business cycle literature: the low correlation between total hours worked and labor productivity and the large volatility of the labor wedge, defined as a gap between the marginal rate of substitution of aggregate leisure for aggregate consumption and the marginal product of aggregate labor. I shed light on these issues by extending a heterogeneous-agent model with an indivisible labor supply choice to real wage rigidities. I find that a small amount of real wage stickiness would be sufficient to resolve both anomalies when long-term wage contracts and heterogeneity are taken into account.