What are the shortcomings of the Neo-classical description of the labour market exchange, which is based on the notion of the price mechanism?

One of the shortcomings of the Neo-classical description is the lack of a social aspect. The labour market should be intertwined with society. Your position in society has a large influence on the level and type of job you are expected to achieve and which jobs you believe that you can do. Levels of education, especially secondary education, and the opportunities available after secondary schooling will open more or less doors for you into the …

…many areas not covered by the description. These areas are too important to be overlooked. The Neo-classical description is based almost entirely on financial gain and would be better suited to a 19th Century market place than to a 21st century market place. To describe the labour market as a simple Supply and Demand system is wrong, labour is not a commodity to be traded, it is people and not just as factor of production.