This the standard microeconomic theory of monopoly but the standard theory is deficient in that it does not emphasize that the theory only applies to the case of one seller (monopoly) in an industry when that seller does not have to consider potential entrants to the industry. The term protected is used to indicate that no competitors can enter the industry, usually because a government prohibits them from doing so.
In the case of a protected monopolist the industry demand curve for the product is the price-output tradeoff faced by the firm. The demand curve shows the quantities demanded at all different price levels given the other factors affecting demand are held constant. Looked at from the viewpoint of the firm the demand schedule tells it what the price has to be in order to sell all different levels of production. If it produces just a little it can get a relatively high price, but if it wants to sell a lot it has to charge a relatively low price. For a specific demand schedule the relationship between revenue (price times quantity sold) and quantity produced can be constructed.
Consider the demand schedule shown above. At a price of P the quantity demanded is Q. Therefore if the firm wants sell a quantity Q the price has to be P. The revenue, the price times the quantity, is the area of the rectangle shown in cyan.
At a price of p0 there is zero units sold so the revenue is zero. As the price decreases from p0 there is some positive revenue and the revenue increases as the price falls and quantitity sold increases. But ultimately the revenue has to decrease because in order to get consumer to take the quanitity q1 the price has to be zero; i.e., the firm has to give it away. At q=0 the revenue is zero and at q=q1 the revenue is zero. In between the revenue is positive. The shape of the relationship between revenue and output for the demand schedule shown above is a parabola such as the one shown below.
In order to determine what price the monopolist will charge we have to determine what is the level of output and sales that maximize profit. Since profit is the difference between revenue and cost we must show the relationship between total cost and output, as shown below.
The level of output that maximizes profit, the difference between revenue and cost, is that level where the slope of the cost curve is equal to the slope of the revenue curve. The slope of the cost curve is the marginal cost curve, the increase in cost for an additional unit of production. The slope of the revenue curve is called the marginal revenue curve and it represents the increase in revenue that results from an additional unit of production and sales. But in order to sell one more unit the price has to be lowered a little bit on the total production at each level.
The graph below shows the marginal cost and marginal revenue curves for a protected monopolist. The level of output at which marginal revenue and marginal cost are equal is qM. The price the monopolist sets is determined from the demand curve. When the quantity qM is put on the market the price established is pM.
One important implication of the theory of protected monopoly is the impact of an excise tax on the price paid by consumers. The theory for the impact of a new tax is the same as the theory of the impact of any increase in marginal cost; i.e., any upward shift in the marginal cost function. The graph below shows the impact of an upward shift in marginal cost on the output level and the price established by the monopolist.
What the graph indicates is that the price increase chosen by the monopolist is a fraction of the upward shift in marginal cost. The monopolist has the power to pass on to the consumer the full amount of the cost increase but chooses not to do so. If the full amount of the cost were passed on the monopolist would make less profit than if only part of it is passed on.
It follows from the analysis of the effect of the cost increase that the full amount of an excise tax would not be passed on to the consumer, even though the monopolist has the power to pass the entire pass on to the consumer through a price increasee.