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### Course: AP®︎/College Microeconomics>Unit 4

Lesson 2: Monopoly

# Monopolist optimizing price: Total revenue

In this video we explore how a monopolist decides on the best quantity to produce and the price to charge for that quantity.  Created by Sal Khan.

## Want to join the conversation?

• If you integrate P = -Q + 6, you get -.5Q^2 + 6Q, but Sal got -Q^2 +6Q when he multiplied P x Q. Which is correct?
• Sal is. Integrating the price curve will get you the total area underneath the triangle: but realize that on sal's graph when he is determing revenue, he is multiplying price by quantity to get the area of rectangles (or squares in the case of 3 x 3). Total revenue is not the area of triangles under the graph, but rectangles instead. Try drawing it out to help yourself visualize it. I hope this helps.
• At around , when the producer is producing 6000 oranges and selling them for \$0 (free), wouldn't that result in a negative profit, which would be plotted on the negative price axis of the graph?
• It would be plotted on a graph showing Profit vs Q of oranges sold. But Sal never draws that graph in the video.

In the two graphs he plots Revenue vs Q and Price vs Q. But remember revenue is different to profit because Profit = Total Revenue - Total Cost.

Revenue is how much cash is coming in from sales regardless of expenditures. if you sold say 5999 oranges at \$0.01 then profit would be negative but the revenue would be positive. In fact the farm would be generating \$59.99 of revenue.

Only at the point where you make the price so high that not one orange sells or you give oranges away for free will revenue equal 0.
• As a company, how would you find out about the demand curve?
• There are two ways to get an idea of what the demand curve looks like.

The first one is trial and error. Let's say that on day one you sell your oranges for \$2.80 per lb. you sell 3,200 lb oranges that day. At day 2 you sell them for \$2.90 per lb and you sell 3,100 lb. On day three you sell them for \$3 per lb and you sell 3,000 lb. By connecting these three points you can figure out the demand curve.

The second one is through market research. Try to survey all of your customers for one day by asking them questions like: 'How many pounds of oranges would you buy if I would sell them for \$2.50 per lb?' After looking at the results it's possible to draw the demand curve.

Note that both explanations are simplified. If you'd want to execute them in real life you'd have to take other things into account. For example, if you'd sell your oranges for \$3 per lb it would be unlikely you'd sell exactly 3,000 lb every day. It would change a little bit from day to day.
• How did Sal come to the conclusion that P= 6-Q?
• It is derived from the equation of a straight line y = mx +c (or y = mx + b if you're from America), where c is the y-intercept, m is the gradient, y is the y-axis and x is the x-axis. In this case the y-intercept is 6, the gradient is -1, the y-axis is P, and the x axis is Q. Substitute these back into the formula and you get P = -1Q + 6, which can also be written as P = 6 - Q.
• what would be the intutive explaination for the revenue curve to be an inverse parabola,i.e., why does the revnue increase with slight increase in units sold and decrease as the number of units sold keeps on increasing
• A literal example could be explained as such: Lets say you're buying oranges from farmers and creating orange juice with them, it follows that the higher quantity you produce the higher your revenue you would make. But only to a certain extent. Perhaps your delivery trucks have to drive further and further every day to get more oranges since you bought up all the local ones. Or perhaps you were buying the least expensive oranges and now, since those have already been consumed by your Orange Juice Factory, you have to buy the slightly more expensive oranges. Perhaps you have to hire even more employees, or rent a larger Factory building. At this point, your revenue would turn from continuing to go up with volume, and start going back down while volume continues to increase.
• which video helps with price of dollares to revenue?
• At the beginning of the video, why does the demand curve intersect with the y-axis? Why bother plotting a point when 0 quantity is present?
(1 vote)
• In the video, it is showing a supply and demand chart. One of the reasons why zero is present, is because if the price was 6 dollars per pound, no body would buy oranges. They would most likely buy a substitute, like apples or grapes. Thus, the quantity sold would be 0. Hope that helps!
• If we were break up monopoles into smaller firms we would be guaranteed to get more output at a lower price
(1 vote)
• Depending on the industry, it would either become more or less efficient. In most cases, breaking up the monopoly would create competition, which drives down prices, ultimately reaching equilibrium. This is a socially optimal result. However, in the case of a natural monopoly, it is most efficient for the industry to be a monopoly. An example of this is power generation. If there were many small power generation companies, there would be much redundancy and waste of resources. Most of the time, breaking up monopolies will result in more output at a lower price.
• I still don't understand what the term "revenue" exactly means. What is the difference between total revenue and profit?
• Total revenue is the total amount of money customers pay for your products.
Profit is the total revenue minus the costs.

For example, I sell 3000 pounds of oranges for \$3 per pound. That means my total revenue is 3000 * \$3 = \$9000.
But oranges don't magically appear. It's required to water the orange trees, pay somebody to harvest the oranges, transport them to the customer, etc. All of those things cost money. Let's say it costs \$6000 to cultivate and sell those 3000 pounds of oranges.
Then the profit is the total revenue of \$9000 minus the total cost of \$6000, which is \$3000.

I hope this cleared things up.