To compute the optimal monopoly price with a linear demand curve, the monopolist:

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The monopolist should set MC = MR to determine the optimal quantity, but then should insert that optimal quantity into the demand curve to find the corresponding price. This is because the demand curve shows the maximum price consumers are willing to pay for each quantity, and the monopolist should charge that maximum price to maximize profits. Setting price equal to MC and MR would not necessarily maximize profits, as it depends on the specific shape of the demand curve and cost structure. Doubling the marginal cost would not produce an optimal price either. Total revenue is not necessarily maximized at the output level where it is the greatest, as it may be more profitable to produce a smaller quantity at a higher price. The monopolist should set MC (marginal cost) equal to MR (marginal revenue) to determine the optimal quantity. Then, to find the optimal price, the monopolist should insert the optimal quantity into the demand curve to see what price consumers are willing to pay for that quantity. This results in the profit-maximizing combination of price and quantity.

To Compute the Optimal Monopoly Price with a Linear Demand