I do not think you can say Apple has a monopoly over iOS as it is a product not a market. Would be equivalent to saying Tesla has a monopoly over Tesla infotainment software, ignoring that they are only a small part of the larger automobile market.
Looking at the overall phone market Apple has around 50% share in the US but only 20% globally. This is not high enough to constitute a monopoly especially when there are clearly competitors in the space.
It’s not global percentage of a certain market that defines a monopoly.
Apple has 100% market share in the iOS market. Due to that fact they’ve got exclusive control over a significant percentage of the population - consider that customers cannot install another OS on the hardware they’ve bought and they cannot move their iOS apps on another Android phone either.
To make an analogy consider that you’d complain about your local electricity provider having a monopoly and I’d tell you that you can always move to another city or country, there, problem solved, it was your fault for staying there.
A monopoly would require they control the entire market for a given product or service. Apple isn't a monopoly in any area - but they are a strong competitor in many areas. They're more like a western take on a chaebol [1] in my opinion.
A monopoly is usually a company which has price making power (on the whole industry) and has established barriers to entry that prevent competitors from entering the market.
The key reason Apple isn't considered a monopoly is that even though they are huge, they don't' have a monopolistic position in their products. For smartphones they have a market share of ~20% worldwide and in the PC market the hold ~5%. Even on the country level, the numbers never get to a level where people would usually scream monopoly.
You could argue that they probably have monopolistic market share on the tablet market but most wouldn't consider that an industry in itself (yet) and they haven't exhibited the characteristics of a monopoly: price setting for the industry and an inability for new players to enter the market. It's actually possible to not be considered a monopoly even with a huge market share if you can prove you don't control the industry.
Apple's normal business model allows them to thrive without being a high volume business; their per device profit margin greatly exceed any competitor, so they can still be hugely profitable with low market share.
Luckily for this discussion, the word 'monopoly' has an accepted definition, which is:
> The exclusive possession or control of the supply of or trade in a commodity or service
Since Apple has, at most, below 50% market share in developed countries (and a much lower market share in developing countries), they do not possess a monopoly on the smartphone market.
Except Apple doesn't have a monopoly in any of its markets. They don't have a monopoly in phones, laptops, desktops, tablets, music, TV, processors, none of their products dominate their market.
Of course you can try and distort the meaning of monopoly but that isn't going to get you very far.
Apple have ~65% Market Share in US and over 70% in Japan.
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