(100 - Q) is the price according to our market demand curve. This 100 - Q represents the marginal revenue brought in by selling the next unit. However, in order to sell the next unit, we had to lower the price by 1 for all units sold (the demand curve has a slope of -1, so the tradeoff between Q and P is 1 for 1). Therefore, on the margin, we lost 1 unit of revenue for all Q units sold. The marginal revenue is then (100 - Q) - Q = 100 - 2*Q.
To solve for the monopolistic equilibrium, we find the quantity at which MR = MC. Solving:
100 - 2 * Q = 10 => Q = 45
At this quantity, the market price would be 100 - 45 = 55. Assuming no fixed costs, the profits for this firm would be 45*(55 - 10) = 2025. Naturally, this is a vast improvement for the firm over the competitive outcome of zero profits.
So what's wrong with making profits? Certainly, profits are good for the monopolistic firms. The consumers are willing to pay for the goods at the monopoly price. Nobody is being forced to do anything, so we have a system of mutually beneficial exchange with no coercion. I think it would be overstepping our bounds for SparkNotes to say there is something wrong with monopoly power, but the foundations for government intervention in monopolistic markets can be found in welfare analysis.
Let's identify the deadweight loss in the example from the previous section. Let Qm be the output quantity chosen by the monopolist, 45 in this market. Let Q* be the output quantity at which the marginal cost curve intersects the market demand curve. Q* = 90 in this market.
Q* is the socially optimal output quantity. Imagine the firm is trading at a quantity less than Q*. At this point, the marginal cost curve is below the demand curve. In other words, the marginal cost to society is less than the marginal benefit (the demand curve). The society stands to gain by trading at a higher quantity. The opposite is true at quantities greater than Q* (convince yourself of this).
Remember that Qm is no greater than, and most often less than, Q*. If Qm is less than Q*, it is suboptimal. The deadweight loss is the area between the demand curve and the marginal cost curve over the quantities between Qm and Q*. The marginal cost is the marginal cost to society, and the marginal benefit is the demand curve. Over these quantities, the marginal benefit is greater than the marginal cost, so the area between the curves represents social surplus unrealized at the monopolistic equilibrium.
The impact of monopolistic behavior on social welfare varies with the shape of the demand curve. For example, with a perfectly inelastic demand curve, the market cannot help but trade at the socially optimal quantity. However, the monopolist has the power to set prices as high as it pleases (for this reason, many of these industries are regulated, such as suppliers of insulin or water). Therefore, there exists no deadweight loss, but all social surplus is absorbed by the monopolistic firm.
A monopolist's power is determined by its ability to set prices, which relies completely on the demand curve a firm faces. In perfect competition, a firm sees a flat demand curve and therefore does not have a practical choice as to what price to offer. The monopolist's power comes from facing a downward sloping demand curve.