Defining quality and making sure it is very central to all processes, especially those that are core competencies, are critical if a business is going to grow and sustain itself over the long-term. Student #2:

"Why should a firm never outsource its core capabilities? What happens if a supplier who is willing to supply goods and services based on these core capabilities at a significantly lower price approaches the firm? What should the firm do?"

Price is a terrible way to make a decision about what your company is going to produce. In fact price can drive a company to ruin if a price ware is initiated with a much stronger rival. Quality and value needs to be at the center of any company's outsourcing and long-term cost strategy. Instead of just driving down costs of everything, including what makes a business unique, companies have got to focus on what makes them unique instead. The ideas behind purpose-driven outsourcing are completely focused on this idea of only outsourcing what a business can afford to from a quality standpoint (Esperne, 2009a).

The need for outsourcing has never been greater as companies struggle to keep their expenses under control while dealing with...

Instead of focusing on trimming way back on costs to the core competency level, companies need to decide to compete on value first. Only by putting value first will any business be able to survive. In response to the questions then, no, it would be a terrible idea to outsource much of the core competency of any business to make it more competitive. Companies who engage in this approach to cost cutting and hurting, not helping, themselves in the short- and long-run.
Sources:

Byrne, J.A. (1996, Apr 01). Has outsourcing gone too far? Business Week, (3469), 26-26. Link: http://www.businessweek.com/archives/1996/b3469048.arc.htm

The debate on outsourcing. (2004, Apr 02). Computer Dealer News, 20(5), 12-12. Link: http://www.itbusiness.ca/it/client/en/home/News.asp?id=5590

Esperne, E. (2009, Outsourcing: The real questions is not "why" but "how?." Contract Management, 49(6), 46-56,58,60-61. Source: http://www.ncmahq.org/files/Articles/CM0609%20-%2046-63.pdf

Esperne, E. (2009a), Purpose-driven outsourcing. Supply & Demand Chain Executive, 10(2), 16-18. Link: http://www.sdcexec.com/article/10269454/purpose-driven-outsourcing