If these firms are in the private sector, as profit-maximisation is their goal, they are likely to charge very high price because in their knowledge, there will never be any competition. In the diagram, at the (profit-maximised) output, the price they sold (where AR cuts quantity output) is higher that average cost at that quantity output, generating Super Normal Profits. As a result, the market will fail to achieve allocative efficiency (equilibrium price is higher than marginal cost).
To tackle this issue, some economies conclude these natural monopolies, the best owner of it is the government. When the supplier in these industries are state-owned, their goal will no longer be profit-maximisation. Instead, they will attempt to achieve allocative efficiency. (There is no productive efficiency in natural monopolies because there is no minimum average cost.) Hence, as shown in the diagram, Price=AR=MC, achieving allocative efficiency. As a result, quantity output be higher and price consumers pay will be lower, compared to the situation which owners of natural monopolies are private firms.
For privatisation
In the history of British Rail, during the age of nationalisation (1948-1995), the number of passengers was falling until privatisation in 1995. Since then, the number of passenger has grown rapidly. This is because competition between railway operators has resulted in new routes for new journeys and better service for commuters.
Against privatisation
However, it also can be argued that the decrease of the number of passengers during the nationalisation period was not entirely due to nationalised but the fact that cars have become more affordable since 1960s, therefore more people preferred used road transport instead of rail transport, resulting in decreasing number of passengers of nationalised British Rail.
After selling British Rail to private shareholders, operating companies have legal duty to maximise their profits for shareholders, rather than put passengers first. It allows them to use a large amount of profits to pay out in dividends to shareholders instead of reinvesting. Furthermore, once big investment banks bought share from the public, benefits from train operating companies would no longer benefit the public.
For nationalisation
There are several advantages for public ownership of railway services. When train operators want to invest a new programme, it has lower borrowing cost for government-financial investment, which will save a lot.
Against nationalisation
Moreover, maintaining and upgrading the railway service will cost the government billons of pound per year. If costumers complain of high fares to the government, they must spend more to subsidise the railway, which means a reduction in public spending in other sectors.
In conclusion, when an economy attempt to deal with Natural Monopolies, it has to consider the consequence of either way.