For a profit-maximizing monopoly that charges the same price to all consumers, what is the relationship between price P, marginal revenue MR and marginal cost MC?

The relationship between price, marginal revenue, and marginal cost for the scenario in the question = P > MR and MR = MC

This is because the marginal revenue of Monopoly firms is lesser than the price at all times.

Thus, a fall in price would mean that some revenue is forgone

For profit maximization, the marginal revenue is always equal to the marginal cost. Hence the reason for the expression above.