Discuss what elasticity conditions (labor demand/supply perfectly elastic, elastic, unitary elastic, inelastic, or perfectly inelastic) would be needed for the minimum wage to benefit low-income workers.

Although it might seem obvious that low-income workers would desire and would benefit most from an increase in minimum wage, that is not necessarily the case. Two conditions are most likely to benefit low-income worker. The first pertains to the minimum wage level, and the other concerns increases in the minimum wage rate. Therefore, one can observe the connection between the inelasticity of demand for low-wage labor and increases in minimum wage. This is the correlation identified by Leif Danziger in “The Elasticity of Labor Demand and the Minimum Wage.”
Minimum wage level corresponding to unitary elastic aggregate demand will generally most benefit low-wage workers. However, the same is not true for wage rate increases, as the best situation is associated with inelastic aggregate demand for labor. One main reason for this differential correlation is that raising workers’ wages tends to reduce the number of jobs because of lay-offs, so that the lower-paid workers end up with no employment and thus no wages. Instead, they will have a “reservation wage rate,” which primarily consists of account for benefits such as unemployment insurance. Workers may also benefit in non-financial ways from increased time available for other pursuits, including seeking employment.
Given the importance of reservation wage rates, analysis must account for the critical value of the elasticity of labor demand. This means in part that a higher minimum wage rate improves the low-wage workers’ situation when labor demand is less elastic than the critical value; in contrast, when labor demand is more elastic than the critical value, such workers will be worse off . Unemployment benefits are an important factor corresponding to decreasing elasticity of labor demand.
Danziger, L. J Popul Econ (2009) 22: 757. https://doi.org/10.1007/s00148-007-0179-y
https://link.springer.com/article/10.1007/s00148-007-0179-y