# Profit Maximization, Revenue Maximization and PED in Pure Monopoly

pure monopoly refers to: This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you Profit Maximization, Revenue Maximization and PED in Pure Monopoly. Following along are instructions in the video below:

” s lesson is going to look more closely at a purely monopolistic firm producing output output in a monopolistic market as we saw in a previous lesson in which we the monopolistic model. The demand as seen by a pure monopolist represents. The total market demand for the good being produced this makes sense. Because the firm is the only producer.

There is no need to draw two separate diagrams as we did in perfect competition. One for the market for the output and one for the individual firm. The individual firms demand is the market demand also in our previous lesson. We illustrated and explained.

Why marginal revenue for a monopolist. Always lies below the demand curve for the monopolist this means that at any given level of output. The firm s marginal revenue will be less than the price that it sells its output for in today s less we re going to explore three different concepts relating to pure monopolies first. We re going to revisit the profit maximization rule that we learned in our unit on perfect competition and determine whether the same rule for maximizing profits applies to a monopolist will compare the profit maximizing level of output produced by a monopolistic firm to the revenue maximizing level of output and will determine where monopolist should produce in order to maximize its total revenues instead of its profits finally.

We will be looking at the price elasticity of demand for monopolists output. And we ll see how we can determine over which range of output demand is relatively elastic and over which range of output demand is relatively inelastic for a monopolists product. Let s begin with the profit maximization rule. When studying perfect competition.

We learned that in order to maximize its profits. A firm should always produce at the level of output. Where the marginal revenue to the firm equals. The firm s marginal cost of production at this level of output.

There is no way a ferm can increase its total profits by either reducing its output or by increasing its output let s look at our graph and determine what the profit maximizing level of output for this monopolist is first we have our marginal revenue curve. We can see that marginal revenue slopes downwards and marginal cost slopes upwards. But there is clearly a point at which marginal revenue equals marginal cost. This point right here is our profit maximization point.

A monopolist hoping to maximizes total profits should determine the level of output at which marginal revenue equals marginal cost and that quantity right there we ll call that q pm. For the profit maximizing quantity so the question is how do we illustrate the area of economic profits earned by a monopolist at this quantity now a mistake that students commonly make and i m going to show you this mistake so that you don t make it yourself in the future is to draw a dotted line over from this point. And indicate that this is the price. The firm will charge at its profit maximizing level of output.

This is a mistake. However because in in fact that dotted line indicates. The firm s marginal cost and its marginal revenue at the quantity of qp m. To find the price.

We must go all the way up to the demand curve because as you recall demand represents the willingness and ability of consumers to pay for a good therefore demand represents. The price that consumers are willing to pay so in fact the price. The monopolist will charge when producing at its profit maximizing. Quantity is determined by the level of demand for that quantity.

If a monopolist charged a price lower than that down here equal to its marginal revenue. Let s say clearly there would be a disequilibrium in the market. Because the quantity demanded at a price of m r. Is much greater than the quantity that the monopolist is actually producing.

There would be a shortage in the market at a price of mr. Therefore. A monopolist will not charge that price instead it will charge the price. The consumers are willing to pay for this particular quantity.

Which on our graph is qp m..

Let s illustrate the area representing the firm s economic profits at a quantity of qp m in order to find and calculate economic profits. We must know the average total cost because total profits equal price minus average total cost times. The quantity being produced all we need now is our average total cost because we have the price and we have the quantity that the firm will produce in order to find average total cost. We d go up from the quantity to our atc curve draw a dotted line over and right there on our vertical axis is the firm s average total cost of producing qp m units.

The area of economic profit. Therefore is simply the price minus the average total cost times the quantity and on our graph. It is a rectangle. The blue rectangle on our graph represents the maximum level of economic profits that this monopolist can hope to achieve given the level of demand that it faces and given its costs of production.

Any level of output greater or less than qp m. Will result in a reduction in the size of its profit rectangle therefore by producing at qp m. The firm maximizes its total profits. We can see that a purely monopolistic seller has a better chance of earning economic profits in the long run due to the fact that these profits cannot attract new firms in pure competition profits attract new firms.

The entry of those firms reduces the price and eliminates the profits but due to barriers to entry a monopolist can help to maintain its economic profits in the long run entry into a monopolistic market is blocked economies of scale legal barriers ownership of essential resources. Any of these things might be reasons that new firms find it difficult to get into a monopolistic market therefore monopolist can earn economic profits in the long run as long as demand for its product remains strong and its costs remain relatively small let s move on to the second topic. Today next. We re going to talk about the level of output that a firm would wish to produce that in order to maximize its revenues now we don t typically think of firms as revenue maximizers.

We think of firms as profit maximizers. But what if a firm decided that its objective was not to earn the greatest level of profits possible. But to earn the highest revenues possible even if that meant its total profits would be less than it would be at the mc equals. Mr.

Point if a firm had the desire to maximize its revenues then it should produce at the quantity where marginal revenue equals zero. Now we re going to look at a graph and explain why this quantity is where total revenue is maximized first let s identify this quantity on our graph look at the marginal revenue curve. We can see that at low levels of output marginal revenue is relatively high. But as the firm increases its output.

The firm s marginal revenue decreases due to the fact that it is having to lower the prices of its output in order to sell additional units marginal revenue continues to decline until it equals zero. Which in our graph is right here when the firm s marginal revenue. Equals zero its total revenue is maximized. So i m going to put a quantity here that says q are m.

For revenue maximization. So what price should a monopolist charge at a quantity of q r m. Well just like we determine the price at qp m. We can draw our dotted line up to the demand curve and over to the price axis to show the price that the firm can charge at the quantity of qp m.

At qrm excuse. Me the revenue maximizing quantity. The firm can charge a price of p r m. As you can see the price.

The firm will charge when maximizing revenues is lower than the price it will charge when maximizing profits. But this is because the firm is producing at a greater quantity. Now the quantity qrm is greater than the quantity qp m. So why is this the revenue maximizing quantity.

And what impact is producing it the revenue maximizing quantity have on the firm s profits. Let s answer that first question first why is q r m. The revenue maximizing quantity well we need to remember what marginal revenue represents marginal revenue is the change in total revenue resulting from a particular change in output in other words as the firm firms output increases from zero units here at the origin to q. R m.

Its marginal revenue is positive if marginal revenue is greater than zero then total revenue is increasing because marginal revenue is the change in total revenue..

However if marginal revenue is less than zero. Then total revenue is decreasing in other words. If the firm continued to produce beyond q. Rm its marginal revenue would begin to diminish would become negative in fact beyond.

Q. Rm. Total revenue is falling a firm would in fact never wish to produce beyond the quantity of q r m. The firm s total revenues would be declining.

But in order to increase its output beyond q. Rm its total costs would be increasing this means. That of course. Economic profits are decreasing.

Even a revenue maximizing. Firm would not want to produce beyond. Q. Rm.

Of course. Total revenue is maximized at q r m. Therefore. Any level of output beyond that total revenue will decline.

So now let s examine the impact on the firm s economic profits by increase in its output from qp m. To q r m. In our particular firm. We can see that in fact at q r m.

The firm is still earning some economic profits simply because the price it can charge at that quantity is still slightly higher than the firm s average total cost. I went up to the atc curved u. My dotted line over and i can see that the firm s average total cost is still slightly lower than the price. But clearly the firm s economic profits at this quantity are less than they were at the quantity of qp m.

The firm sacrificed some profits. But it did earn greater revenues. The reason its profits are smaller. However is that the firm s total cost increased by more than its revenues increased between qp m.

And q. Rm. A firm wishing to maximize its profits should reduce its output back to the profit maximizing quantity of qp m. Now.

The final thing. We re going to discuss. Today is price elasticity of demand for monopolists output. Looking at a firm s demand.

Curve is there any way to determine over which range of output demand is relatively elastic and over which range of output demand is relatively in elastic. The answer is yes. Here s how we can determine whether demand is elastic. Or inelastic.

If the marginal revenue is greater than 1..

Then pe d. Is greater than 1 in other words. Demand is elastic. We ll explain why this is true in just a moment secondly.

If marginal revenue is less than. 1. Then pe d. Is less than 1 in other words.

Demand. Is inelastic. Why is this the case earlier in the course. We explained.

What is known as the total revenue test of elasticity. The total revenue test. We re going to move up here now essentially says that if a decrease in price. Leads to an increase in total revenue.

Then demand. Is elastic pe. D. Is greater than 1.

This. Means. That consumers are relatively responsive to the lower price. A particular percentage decrease in price must have led to a greater percentage increase in the quantity.

Demanded hence demand is elastic that s what s happening in a monopolistic market. As long as the marginal revenue is positive. If a firm lowers its price between 0. And q r m.

Demand. Is elastic. Because consumers are relatively response to the lower prices as the price falls consumers increase. The quantity they consume by a percentage greater than the decrease in price otherwise total revenues would not be rising for the firm.

The total revenue test. Also taught us that if a decrease in price leads to a decrease in total revenue. Then pe. D.

Is less than 1 in other words. A particular percentage decrease in price led to a smaller percentage increase in the quantity. Demanded. The firm s total revenue will fall.

If this condition holds true therefore price elasticity of demand is less than 1 consumers are no longer very responsive to decreases in the price so beyond the quantity at which m r equals. 0. Pe d is less than 1 demand is inelastic on our graph we can draw a dotted line up to the intersection. We can draw a dotted line up from the intersection of m r.

And the horizontal axis to our demand..

Curve and we can see that along the demand curve. There is a range over which pe. D. Is greater than 1.

And. Beyond. The q. R m.

Level of output. There is a range of the demand. Curve over which pe. D.

Is less than 1. This. Implies of course. That there is a quantity at which demand is unit elastic and that quantity is right where marginal revenue equals.

0. So right here above the qrm level of output pe d. Equals. 1.

A particular percentage decrease. In the price. Will lead to an identical percentage increase in the quantity. Demanded.

Therefore. There will be no change in the firm s total revenue as it changes its level of output. And its price right around the qrm level total revenue is maximized at q r m. So this lesson went through three different characteristics of a purely monopolistic market looked at the profit maximization rule.

Which says that a firm should produce where marginal revenue equals marginal costs in order to maximize his total profits. This rule is true for any market structure. Whether it s perfect competition or pure monopoly or something in between we then talked about the revenue maximization rule. If a firm wishes to maximize his total revenues.

It should produce where marginal revenue equals zero. Because if the firm s marginal revenue is greater than zero then decreasing its price and increase in its output will add to total revenues when marginal revenue becomes negative. Then a decrease in price and an increase in output will decrease. The firm s total revenues therefore total revenues are maximized when marginal revenue equals zero.

Finally. We explained how the total revenue test teaches us if marginal revenue is greater than zero. Then demand is elastic since a particular decrease in price will lead to a greater percentage increase in the quantity demanded causing the firm s revenues to rise if however marginal revenue is less than zero. Then the price elasticity of demand is less than one since a particular percentage decrease in price would lead to a smaller percentage increase in quantity demanded causing the firm s total revenues to decrease in our next lesson.

We re going to look at purely monopolistic markets and firms and determine the extent to which. Such firms are productively and allocated li efficient compared to similar perfectly. ” ..

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