The definition of the word "Monopoly" is already widely denoted as supply side control:
- Wikipedia: The exclusive possession or control of the supply of or trade in a commodity or service. (https://en.wikipedia.org/wiki/Monopoly)
- Investopedia: A monopoly exists when a single entity is the sole provider of a particular asset or service. (https://www.investopedia.com/ask/answers/032415/whats-differ...)
- Oxford Dictionary: The exclusive possession or control of the supply of or trade in a commodity or service. (https://en.oxforddictionaries.com/definition/monopoly)
That's obviously too narrow. Someone controlling the demand side could be just as obnoxious. A company in a company town is in control of the demand side of the labor market, for example.
Control of the demand side of a market is called a Monopsony, not Monopoly. It's mentioned in the thread above, more info here: https://www.investopedia.com/terms/m/monopsony.asp
I can’t think of any scenarios where people referred to the military as having a monopoly on the missile market. It doesn’t make sense because it doesn’t even make missiles.
But Farmers being ravaged by middlemen would use that term about the middlemen buying their crops.
"An unlawful monopoly exists when one firm controls the market for a product or service, and it has obtained that market power, not because its product or service is superior to others, but by suppressing competition with anticompetitive conduct." [1]
That's somewhat different from your definition in that it is deliberately open to interpretation (the Sherman Act, for instance, doesn't actually define monopoly) and revolves around anti-competitive conduct rather than exclusive control of supply (which isn't required - ex. Microsoft never had 100% of the OS market, nor did Standard Oil have 100% of the oil market).
[1] https://www.justice.gov/atr/antitrust-laws-and-you