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Monopoly

Here we see what a monopoly is and its revenue potential.

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OverviewMonopoly means one seller.

In perfect competition many sellers were price takers. Any one seller could not influence the price of the product in the market. The competitive firm could only choose what amount to sell.

A monopoly firm will have to determine both how much to sell and at what price. Let’s look at these ideas a little more on the following few slides.

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Review p

Market Q

In a market, consumers as a group are thought to want to buy a greater quantity the lower the price. We see this as a downward sloping demand curve.

D

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Review p $

Market Q Firm Q

P=MR=D

In a competitive market, the market demand from consumers interacts with market supply from many sellers and we get an equilibrium price, like p* in the graph. At this point, since any one firm is a small part of the market, when we look at a firm it is a price taker. Thus, when the firm thinks about selling another unit it can sell that unit at the same price as the previous unit and thus MR = P for a competitive firm.

D

S

p*

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Analogy: To think about the marginal revenue for a competitive firm I like to think about a pop machine. Say the price of a pop is $1.25.

Say the machine has been refilled and the pops are not chilled to perfection and you are the first one to make a purchase. What is the total revenue in the machine after you make your purchase? $1.25! Since the total revenue was zero before you bought, the change in total revenue from the sale of another unit (in this case the first one), was $1.25. This is exactly what we mean by marginal revenue. Marginal revenue is the change in total revenue from changing output by 1 unit.

Now say I buy a pop right after you. The total revenue in the machine is 1.25(2) = 2.50 and the marginal revenue is 1.25.

SO, MR = P for a competitive firm.

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MonopolyFor a monopoly firm the demand is the same as the market demand we see in competition. The demand is downward sloping to the right, what is called less than perfectly elastic.

Since the monopolist is the only seller, it is natural they face the market demand curve.

The situation of monopoly is often called imperfect competition.

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Sources of monopoly1) Exclusive control of an input – deBeers is an example

2) Economies of scale – the case of a natural monopoly. The idea here is that AC can be pushed really low by one firm and it then makes sense for only one firm to serve the market.

3) Patents – protecting inventions for a time may give monopoly power.

4) Network economies – Microsoft Windows is an example of the idea – once enough people use a product sometimes using another type of product becomes less functional.

5) Granted by government

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Maximize profitSince the monopolist is the only seller in the market, the monopolist must decide 1) what price to charge and2) how much to sell.

When the monopolist sells, she is worried about profit. The goal is to maximize profit. But, in order to maximize profit, the pattern of revenues and costs at various output levels must be understood. The pattern of cost was the topic of an earlier section. Now we look at the pattern of revenue.

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Monopoly p

Market Q

Here the monopoly is the only firm in the market. When the price is 6, in this example the consumers want 2 units. Total revenue would be 12. But, this firm, if it wants to sell 3 units has to lower the price on all units to 5. The competitive firm didn’t have to worry about another price like the monopoly firm.

D

6

5

2 3

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Monopoly – marginal revenue

So, because the way consumers are in this example on the previous screen, when P = 6, 2 units will be sold and when the P = 5, 3 units will be sold. Total revenue would move from 12 to 15 when the quantity moves from 2 to 3.

So, the additional revenue from the 3rd unit is $3. This is the marginal revenue of the 3rd unit.Note, the price to get the third unit sold is $5, but the marginal revenue is only $3.SO, P>MR at a quantity.

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InterpretationWhen the price is lowered from 6 to 5 the amount sold rises. In fact, the 3rd unit sold brings in 5 in revenue. But this isn’t all we need to look at to have MR. Since the monopolist must sell to all consumers at the same price, the first 2 units now get sold at 5 as well. That means revenue on those 2 units will not include $6 per unit when the price is lowered.

Continuing with the example,

MR(of the 3rd unit) = 5 - (6-5) 2 = 3

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interpretationP

Q

6

5

2 3

a

bc

Area a + b = 6 times 2= 12 = TR when P = 6Area b + c = 5 times 3 = 15 = TR when P = 5

MR = c - a = 5 - 2 = 3

area c is the gain in revenue from sellingmorearea a is the loss inrevenue from selling at a lower price.

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Let’s do another exampleP Q 5 04 13 22 31 40 5

Say this is the demand from consumers in the market. If the price is 5 consumers want nothing, for instance. Let’s put TR on the next slide.

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Let’s do another exampleP Q TR 5 0 04 1 43 2 62 3 61 4 40 5 0

Total revenue is just P times Q, so you should check what I have here.

Next let’s add MR to the table.

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Let’s do another exampleP Q TR MR 5 0 0 ----4 1 4 43 2 6 22 3 6 01 4 4 -20 5 0 -4

MR, marginal revenue, is the change in TR when we add a unit of output. Note at Q = 0 I have the line --- because we have not had a change yet.

The MR = 4 for a Q = 1 because TR went from 0 to 4 when Q went from 0 to 4. The MR = 2 for Q = 2 because TR went from 4 to 6 when Q went from 1 to 2.

Note: MR can become negative, in theory. Also note that P > MR at each Q (except Q = 1, but we usually ignore this.)

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MR from areas to heightP

Q

a

b c

P

Q

In the above diagram we think ofMR as area c - a and we get a number.

height = MR

In the bottom graph we can think of the numberas a height. Note still theMR is lower than the priceon the demand curve.

On the next screen we will see the whole MRcurve.

D

D

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Monopoly MR in a graph$

Q

D

3

5

3

I do not have a prooffor you, but you can see in this diagramthat MR is also a straight line that startsat the same place asdemand in the upperleft, but is always below demand becauseP>MR. Like at Q = 3, MR = 3 and P = 5.

Note that a good way to draw in MR is to first draw demand and then put MR through the Q axis halfway out to the demand curve. I put an X at that point.

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Monopoly Pricing and Output

We study the pricing and output decision of the

monopoly firm.

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Price and output decision for the monopolist in the short runThe amount of output the monopolist should sell in the short run is the amount where MR = MC(as long as P>AVC), just as in the case of the competitive firm.

The price charged would then be the price on the demand curve above the quantity where MR = MC. (recall P = MR for firms in comp, but P>MR for the monopolpy firm.)

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Logic of MR = MC rule$

Q

D

MR

MC

a b c

The Q = b is the Q whereMR = MC. But look at Q = a. Atthat point, Q could be increased and more would be added torevenue than to cost and thus profit would rise. We know this because the MR > MC for these Q (Compare the heights of the curves).

Now let’s look at a Q greater than where MR = MC, like at point c. More has been added to cost than to revenue and thus profit would fall. We know this because MC > MR at this Q.

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What price?$

Q

MC

D

MR

P*

Q*

At Q*, where MR = MC, P* is the price on the demand curveconsumers are willing to pay for Q* and thus this is the price charged by the monopolist.

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Qualification$

MC

D

MR

P*= .10

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ATC

AVC1

AVC2

AVC1=.11

AVC2= .08

Note that the ATCis above the demandcurve, so the firm will lose money. In the short run, the question is whetherthe firm should shutdown or continue to operate. Let’s go to the next screen and say moreabout this.

ATC = .12

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continueNote that the Q where MR = MC = 20. So, if the firm operates at all it should make 20.

Note at Q = 20, the price on the demand curve is .10 but the ATC = .12Now, remember ATC = TC/Q so ATC times Q = TC.

TR = P Q = .1(20) = 2TC = ATC Q = .12(20) = 2.4Profit = TR – TC = 2 – 2.4 = - .4OrProfit = (P – ATC)Q = (1 - .12)20 = -.4 The firm is losing money.

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continue 2If the AVC curve is AVC2 for the firm then at Q = 20 the AVC = .08. This means the TVC = AVC Q = .08(20) = 1.6.

Thus the TR = 2 can cover the 1.6 of TVC and what is left of TR, .4 can go to paying some of the total fixed costs. If the firm shuts down it would have nothing going to fixed cost. So the firm should operate.

Thus, operate if at the Q where MR = MC the P > AVC.

Note if the AVC is AVC 1 = .11 the P < AVC. The firm should shut down. TR of 2 falls short of TVC of 2.2 and covers none of fixed while if the firm shuts down it only has to cover the fixed cost.

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Quiz 1 – not a real quiz$

MC

D

MR

P*

Q*

ATC

Is this monopoly firmearning a profit? If so,draw in the graph therectangle that represents the profit.

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Quiz 2 not a real quizMC

D

MR

P*

Q*

AVC

$

ATC Is it possible for a monopoly to lose money?

Indicate in the graphhow much thismonopoly is losing byindicating the lossrectangle.

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Palm of hand

Thumb

Is a monopoly guaranteed a profit. I have a monopoly – I make a pizza fork (not really, but listen up). Look at the palm of your right hand, thumb up. When you wrap your hand around the fork your thumb is next to a button on the fork (sorry, only right handed version.). When you press the button

A razor blade edge comes out here and you move your hand so your thumb is now pointing left and you cut your pizza real easily.

The demand for my item is much lower than where my costs are.

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Can Monopolies charge whatever price they want? The answer is yes, but with a qualification.

Remember consumers have a demand for the product and have prices they are willing to pay. As long as the monopoly is charging a price the consumers are willing to pay then they can charge whatever they like. But if the monopoly charges too high a price consumers will not buy at all.

OUR ECONOMIC RULE – sell Q where MR = MC, charge the price on the demand curve above this Q (So charge whatever you want but to profit max charge this one) and both of these ideas are dependent on the P>AVC at this Q.

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The monopoly solution and elasticity

Without proof I tell you that with a given demand curve and MR curve for the monopoly, we have

MR = P (1 – F), where F = 1/absolute value of elasticity of demand.

Recall that elasticity of demand changes as we move down the demand curve (in absolute value the number gets smaller).

Monopoly mark-up

We see the monopoly has P > MC at its profit maximizing level of output. So the mark-up of P over MC as a percentage of the price is (P – MC)/P.

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Mark-up and elasticityThe mark-up again is (P – MC)/P.

The profit maximization condition was MR = MC.

The MR, elasticity connection was MR = P(1 – F) = P - PF.

SO, the mark-up can be changed to

(P – MC)/P = (P – MR)/P = (P –(P – PF))/P = (P – P + PF)/P

= PF/P = 1/absolute value of elasticity of demand.

The monopoly mark-up is a function of the elasticity of demand. Note that since we have absolute value of elasticity, the mark-up is a positive number, and since P>MC, 1/abs <1, or abs>1. This means the elasticity of demand will be in the elastic range for a monopoly.