# 7.3: Profit Maximization and Output

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Just as with a firm in a perfectly competitive industry, a monopolist’s profit is based on the output decision. There is one rate of output that will maximize Produce beyond this rate and profits will fall - produce less than this rate and profits will also fall.

Keep in mind that there is no guarantee that a monopolist will earn economic profit. There are a lot of entrepreneurs in the marketplace who have monopolies on worthless products.

What if happens to a money-losing monopolist produces the profit maximizing rate of output? Well, it is clear that the monopolist will not be maximizing profits. By producing one certain rate of output the firm will minimize losses.

## Seven Step Process

Some students struggle to make sense of all the curves (e.g., demand, marginal revenue, marginal cost, and average total cost). This is especially true when they must find the profit maximizing rate of output, price, and profit or loss.

To help clarify things we will walk through a seven-step process that will establish output, price, and profit or loss.

Step 1: Find the rate of output where the last unit produces has a marginal revenue equal to its marginal cost. You start by locating where the MR and MC curve cross (1)

Step 2: Move straight down to establish the profit maximizing rate of output: 50 units (2). You have found output.

output ◻price ◻profit

Step 3: You now need to find the price ($$\mathrm{P}$$) associated with the profit maximizing rate of output ($$\mathrm{Q}$$). Move up from output until you find the demand curve (3).

Step 4: Move to the left until you find the vertical axis to establish price (4).

☑ output price ◻profit

Step 5: With the price and quantity, we can calculate total revenue.

($$\mathrm{TR}=\mathrm{P} \times \mathrm{Q} \rightarrow$$ $5,000 =$100 x 50). This means we are halfway to calculating profit ($$\mathrm{TR}-\mathrm{TC}$$).

With $$\mathrm{TR}$$ established, we now need to calculate $$\mathrm{TC}$$. In order to do this, we need to determine the average total cost ($$\mathrm{TC}=\mathrm{ATC} \times \mathrm{Q}$$) by moving move back to the demand curve (5).

Step 6: We are now on the part of the demand curve that is directly above the profit maximizing rate of output. From this point we need to locate the ATC. Move down until you reach the $$\mathrm{ATC}$$ (6).

Step 7: From the $$\mathrm{ATC}$$ move to the left until you reach the vertical axis (7). We have now established the average cost ($75) for the output rate of 50 units. This yields a total cost of$3,750 ($$\mathrm{TC}=\mathrm{ATC} \times \mathrm{Q} \rightarrow$$ $3,750 =$75 x 50).

With both $$\mathrm{TR}$$ and $$\mathrm{TC}$$ established we now can calculate the profit or cost.

Profit = $$\mathrm{TR} – \mathrm{TC} \rightarrow$$ $1,250 =$5,000 - $3,750. See figure 7. ☑ output ☑price profit If this monopolist produces more than 50 units, profit will fall. If the monopolist produces less than 50 units, profits will fall. Figure 7 What if the manager of this monopoly went on a vacation and the assistant manager allowed production to increase to a rate of 60 units? What would happen to the picture depicted in figure 7? See figure 8. Figure 8 The most important difference between figures 7 and 8 is the level of profit. By producing beyond the profit maximization rate of 50 units, profits went from$1250 to \$900. This reduction in profits was because every single unit beyond 50 had a marginal cost greater than its marginal revenue.

Take the last unit produced as an example. The 60th unit had a marginal cost greater than its marginal revenue. This meant that the 60th unit caused profits to fall. Every single unit beyond a rate of 50 contributed to the fall in profits.

This page titled 7.3: Profit Maximization and Output is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Martin Medeiros.