In this paper skill-biased technological change is linked with endogenous labor supply which allows for unemployment. This is a novel approach, as the literature on skill-biased technological change considers inelastic labor supply. Elastic labor supply allows us to explain how the observed increasing unemployment of unskilled workers is caused by skill-biased technological change. Our numerical analysis shows that if the skill-biased technological change is not followed by the growth of total factor productivity, then output, physical capital stock and consumption decline. Using empirical data on wages and education, we construct a time series for skill-biased technological change for Poland and the US. The empirical relevance of the model is tested by calibrating it to empirical data for Poland over the period 1996 and US over the period 1992. With only two necessary inputs, share of skilled workers in total population and the technology adopted by firms, this model allows to simulate the future behaviour of the labor market.