State whether each of the following propositions is TRUE or FALSE. Explain your answer.

1. When a monopoly is maximizing profits, price is greater than marginal cost.

2. When a monopoly is maximizing its profits, marginal revenue equals marginal cost.

3. When consumers have many options and substitutes for a good, monopoly markup is lower.

4. A patent is a government-created monopoly.

5. A monopoly can never exist unless the government encourages it by issuing patents, copyrights and trademark protections to inventors.