This depends upon what you mean by "big demand". Overall there is moderate demand for veterinarians in private practice; in rural areas there are unmet needs for large animal and production veterinarians, although there is not enough work to support a full-time veterinarian in these areas. In food safety and public health there is a major need for veterinarians, although most employers don't recognize that they could use veterinarians to fill their vacancies.
As with most jobs, this will depend upon where you are at. In the United States, the demand is moderate - veterinary medicine is currently undergoing a small contraction (this is as of July 2013), so the profession isn't adding as many jobs as it used to be.
Yes in two senses - veterinarians are in high demand and the work can be physically demanding.
In the United States, yes, there are many more small animal veterinarians than large animal veterinarians. However, this proportion changes depending upon the geographic region you are talking about, and in many developing countries there are many more large animal veterinarians than small animal veterinarians.
A recent survey published by the American Veterinary Medical Association shows veterinarians are currently not working to their full capacity, to the tune of about 12.5% excess capacity for services. As a profession, therefore, there is probably going to be a contraction in terms of clinic numbers, job openings and other metrics of growth over the next decade or so. However, for an individual veterinarian, there is a lot of growth potential. There are opportunities to become board certified, to work in areas outside of typical private practice and various openings to work in public health, regulatory medicine and non-profit outreach groups.
No, there is not a big demand for online employment. There is not even a big demand of in-person employment. So, if looking for a job, don't get your hopes up too much.
In the United States, there are approximately 100,000 veterinarians currently working in the profession.
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This will depend upon what worker in the veterinary field you are talking about, the specific career path and the geographical location. In general, vet techs are in demand, as are large animal veterinarians and non-practicing veterinarians.
No, veterinarians is a plural noun.
Inelastic
Yes, veterinarians can advertise their services.
Becoming a world-renown veterinarian is a life-long project - most internationally known veterinarians have been in their specialty for at least twenty years, and many times closer to thirty. However, there really isn't much need to push yourself to become one of the top veterinarians - there is only so much room at the top, and a generally competent veterinarian is always in demand.
There are veterinarians in every country in the world.
Yes, because in the future new things will be invented right?...Doctors need to have at LEAST 50 patients in 4 days. AND THAT IS A DEMAND. A BIG ONE!