Monopoly Profit

Monopoly Profit Demand Curve

The key to monopoly profit maximization is that the monopolist faces a downward-sloping demand curve. This is the case because the monopolist is the only firm serving the market. Average revenue is equal to demand in the case of a monopoly.

\(\hbox{Demand (D)}=\hbox{Average Revenue (AR)}\)

Further, when the quantity is increased by 1 unit, the price has to decrease for every unit the firm sells. Therefore, the marginal revenue of the monopoly firm is less than the price. That's why a monopolist's marginal revenue curve is below the demand curve. Figure 1 below shows the demand curve and marginal revenue curve that the monopolist faces.

Fig. 1 - A monopolist's marginal revenue curve is below the demand curve

Monopoly Profit Maximization

Let's now dive deep into how a monopolist does profit maximization.

Monopoly Profit: When Marginal Cost < Marginal Revenue

In Figure 2, the firm is producing at point Q1, which is a lower level of output. Marginal cost is less than marginal revenue. In this situation, even if the firm increases its production by 1 unit, the cost incurred while producing the additional unit will be less than the revenue earned by that unit. Therefore, when the marginal cost is less than the marginal revenue, the firm can increase its profits by increasing the production quantity.

Fig. 2 - Marginal cost is less than marginal revenue

Monopoly Profit: When Marginal Revenue < Marginal Cost

Likewise, in Figure 3, the firm is producing at point Q2, which is a higher level of output. Marginal revenue is less than marginal cost. This scenario is the opposite of the scenario above. In this situation, it is favorable for the firm to decrease its production quantity. As the firm is producing a higher level of output than optimal, if the firm reduces the production quantity by 1 unit, the production cost saved by the firm is more than the revenue earned by that unit. The firm can increase its profits by decreasing its production quantity.

Fig. 3 - Marginal revenue is less than marginal cost

Monopoly Profit Maximization Point

In the two scenarios above, the firm has to adjust its production quantity to increase its profit. Now, you must be wondering, which is the point where there is maximum profit for the firm? The point where the marginal revenue and marginal cost curves intersect is the profit-maximizing quantity of output. This is Point A in Figure 4 below.

After the firm recognizes its profit-maximizing quantity point, i.e., MR = MC, it traces to the demand curve to find the price that it should charge for its product at this specific level of production. The firm should produce the quantity of Q_M and charge the price of P_M to maximize its profit.

Fig. 4 - Monopoly profit maximization point

Monopoly Profit Formula

So, what is the formula for monopoly profit? Let's have a look at it.

We know that,

\(\hbox{Profit}=\hbox{Total Revenue (TR)} -\hbox{Total Cost (TC)}\)

We can further write it as:

\(\hbox{Profit}=(\frac{\hbox{Total Revenue (TR)}}{\hbox{Quantity (Q)}} - \frac{\hbox{Total Cost (TC)}}{\hbox{Quantity (Q)}}) \times\hbox{Quantity (Q)}\)

We know that, total revenue (TR) divided by quantity (Q) is equal to price (P) and that total cost (TC) divided by quantity (Q) is equal to the average total cost (ATC) of the firm. So,

\(\hbox{Profit}=(\hbox{Price (P)} -\hbox{Average Total Cost (ATC)})\times\hbox{Quantity(Q)}\)

By using the above formula, we can figure out the monopoly profit in our graph.

Monopoly Profit Graph

In Figure 5 below, we can integrate monopoly profit formula. The point A to B in the figure is the difference between the price and the average total cost (ATC) which is the profit per unit sold. The shaded area ABCD in the above figure is the total profit of the monopoly firm.

Fig. 5 - Monopoly profit