As a part of training and development for Consumer Anthropology at Northstar, I have been putting together a “handbook” / training guide to help researchers (both green and seasoned) understand the role 0f this practice area and how it is applied.
In the spirit of beginning with the end in mind, It was important for me to make sure to include a foundation in philosophy and theory as well as in the definition of those social agents that impact and are impacted by consumers: The company, the brand and products.
So, I started by taking to the academic publications and then turned loose on LinkedIn, posing the questions to practicing academic and private sector anthropologists.
Here is where I netted out, but of course welcome a continued conversation in the spirit of constant evolution:
A Company is a functional collection of humans within our culture
Company is what Malinowski calls “an institution” in the broader anthropological and sociological sense. It is the basic unit in a socio/cultural system. Its product(s) is its function(s) in and contribution to in a larger system. Since a company is a human institution it could be sole proprietor of an ice cream stand with three ice cream flavors as the, or Goldman-Sachs, with the financial system of United States of America as its product.
Products are the outputs of human ingenuity and are definitive part of human culture
“As for the term “product,” it is the output of a company. It requires the transformation of raw materials (physical, human, or intellectual) into something that has value in the marketplace”. – Barry Bainton
“A third part of our definition of culture is “products.” Human thought and behavior often lead to the production of material artifacts or tools. In this people are not alone; other forms of life also make and use simple tools. Birds make nests; some ants use sticks as prods; caged monkeys use sticks to get bananas. But in transmitting knowledge to successive generations so that it becomes cumulative, humans are distinctive. And as human knowledge and technology grow, human tools become increasingly complex, and growing bodies of information stimulate an even more rapid rate of expansion”. – http://home.snu.edu/~hculbert/points.htm
A Brand is an IDEA, completely dependent on collective culture’s interaction with and perceptions of products and companies
“A brand is a process of attaching an idea to a product. Decades ago that idea might have been strictly utilitarian: trustworthy, effective, a bargain. Over time, the ideas attached to products have become more elaborate, ambitious and even emotional. This is why, for example, current branding campaigns for beer or fast food often seem to be making some sort of statement about the nature of contemporary manhood. If a product is successfully tied to an idea, branding persuades people — consciously or not — to consume the idea by consuming the product. Even companies like Apple and Nike, while celebrated for the tangible attributes of their products, work hard to associate themselves with abstract notions of nonconformity or achievement. A potent brand becomes a form of identity in shorthand. – Walker, Rob. 2006. The Brand Underground. New York Times, July 30, 2006
A ‘brand’ is much like an ‘imagined community,’ a symbolic cluster that’s partially created by the company & its partners (advertisers, PR) and partially created by the consumer community (both those who invest in the brand and those who avoid it)”. – Greg Downey, Macquarie University
At the end of our work day, the study of consumer culture involves the study of companies, brands and products alongside thw culture of consumption. Ultimately, however, the benefactors of that work are also the same objects of study. It is because all three of these are intensely human in nature and driven by culture. We explore the context of that culture to bring meaning and meaningful change to the way we do business and the way we “consume” our world.
The Brand Sherpa's Blog 
I have taken a different approach to defining brand – http://strengtheningbrandamerica.com/blog/2012/04/selling-marketing-and-branding-defined/
I agree with your defining a company as an institution in the Malinowskian sense. However, the implication is too strongly pointing toward a legal entity such as the corporate form. Your definition leaves out the sole proprietor and ex-legal forms that make up the start-up universe and entrepreneurial components of this economic institution. It is here were the traditional approach of ethnology really applies. These are more like preliterate institution/societies based on an oral history, family and/or band based exploiting a unique ecological niche.
The product is, in an anthropological sense, a technological adaptation to the ecology of the commercial environment (market). It is how the “company” derives energy from that environment and points to the resources that it depends upon to survive and succeed in that environment (market).
For me, the brand is to totem that “company” uses to differentiate itself from other companies in the same economic environment. It creates a proprietary claim on a share of the market. which is recognized formerly by the legal system and informally by the consuming public.
For an very interesting and insightful look at this end of the Consumer spectrum I would strongly recommend The Other Path by Hernando de Soto
Too many people see a brand and a company as the same thing, your definition of both clearly explains the difference.