A monopoly price is set by a monopoly. A monopoly occurs when a firm is the only firm in an industry producing the product, such that the monopoly faces no competition. A monopoly has absolute market power, and thereby can set a monopoly price that will be above the firm's marginal (economic) cost, which is the change in total (economic) cost due to one additional unit produced.
The monopoly will ensure a monopoly price will exist when it establishes the quantity of the product it will sell. As the sole supplier of the product within the market, its sales establish the entire industry's supply within the market, and therefore the monopoly's production and sales decisions can establish a single monopoly price for the industry without any influence from competing firms. The monopoly will always consider the demand for its product as it considers what price is appropriate; such that it will choose a production supply and price combination that will ensure a maximum economic profit. It does this by ensuring the marginal cost (determined by the firm's technical limitations that form its cost structure) is the same as the marginal revenue (as determined by the impact a change in the price of the product will impact the quantity demanded) at the quantity it decides to sell. The marginal revenue is solely determined by the demand for the product within the industry, and is the change in revenue that will occur by lowering the price just enough to ensure a single additional unit will be sold. The marginal revenue is positive, but it is lower than the price associated with it because lowering the price will:
"Marginal Cost" solely relates to the firm's technical "Cost Structure" within production, and indicates the rise in Total (Economic) Cost that must occur for an additional unit to be supplied to the market by the firm. "Marginal Cost" is higher than "Average Cost" because of the existence of "Diminishing Marginal Product" in the "Short Run".