We show that, contrary to widespread belief, low-pay workers do not generally prefer that the minimum wage rate be increased until the labor demand is unitary elastic. Rather, there exists a critical value of elasticity of labor demand so that increases in the minimum wage rate make low-pay workers better off for higher elasticities, but worse off for lower elasticities. This critical value decreases with unemployment benefits and increases with workers’ risk aversion. We also show that in some countries the benefits for long-term unemployed are so low that workers would probably prefer that the minimum wage rate be decreased.