How are start-up costs related to natural monopolies?

See below.

Explanation:

Monopolies create barriers to entry. These barriers restrict the competition from entering and thus allow the monopolies to earn economic profits over and above accounting profits. Some times these barriers are natural.

For example, a company may require massive start-up costs that are simply so large that it creates a barrier. Even when potential competitors see economic profits they just do not have the capital to enter the market and grab a share.  This way high start-up costs create natural monopolies.

An example may include power stations.

Hope that helps.

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