Production | Monopoly 1
Proflt Maximisation
The monopolist is the only flrm in the industry,Therefore,they face the entire demand curve.
Proflts are given by total revenue minus total costs,… = p(y)y?c(y),p(y) is the inverse demand curve.
The monopolist is assumed to maximise proflts,That is,they choose output to solve:
maxy … =maxy p(y)y?c(y) =) MR = MC
The maximisation condition is MR = MC,If MR > MC then an increase in output generates more revenue than
cost,and if MR < MC a decrease in output would generate more revenue than cost.
As there are barriers to entry,no flrm can enter if positive proflts are being made and the short run is the same as
the long run,A monopolist can earn positive proflts in the long run | unlike competitive flrms.
Production | Monopoly 2
The Monopolist
These facts can be illustrated in the following essential diagram.
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0
p
y
ACMC
p?
y?
AR = p(y)
MR
…
Note that revenue is p(y)y,So average revenue is AR = p(y)y=y = p(y),which is the inverse demand curve.
MR falls at twice the rate of AR for linear demand,MC = MR generates the optimal quantity y?.
To flnd the optimal price (p?) use the demand curve value at y?,Finally,proflts are given by … (the box with a
dashed outline),the area between average revenue and average cost.
Production | Monopoly 3
Mark-up Pricing
Marginal revenue can be written in terms of elasticity,·,The equilibrium condition becomes:
MR = p(y)
‰
1? 1j·j
= MC
If j·j=1 the demand curve is at and MC = p | the perfectly competitive case.
If j·j < 1 then 1=j·j > 1 and MR < 0,The monopolist would produce nothing when demand is inelastic.
The condition MR = MC can be rewritten to give the price mark-up.
p(y)= MC(y)1?1=j·j =) Mark-up= 11?1=j·j
The mark-up is the factor by which market price exceeds marginal cost.
Production | Monopoly 4
Ine–ciency,Monopoly vs Competition
A monopoly prices higher than a perfectly competitive market,They produce less,Is this e–cient?
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0
p
y
pm
ym
pc
yc
p(y)
Recall the demand curve is the \willingness to pay" of the consumers,Suppose a small amount beyond the
monopolist’s output (ym) was produced,The consumers would pay p(ym +￠y) for this,This exceeds MC.
Hence there is a positive gain from this extra sale,It would be better for both consumer and monopolist.
The monopolist refuses to do this however,as a lower price will reduce total proflts.
A perfectly competitive flrm prices at pc = MC | no gains from further output can be made | it is e–cient.
Production | Monopoly 5
Deadweight Loss
The deadweight loss of a monopoly is a measure of this ine–ciency.
It is the sum of lost consumer and producer surplus due to the restriction of output and rise in price.
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p
y
p?
y?
pc
p(y)
a b
c
a+b is the loss in consumer surplus,But a is regained in proflt by the flrm,It is redistributed,but not lost.
c is the loss in producer surplus,Hence total deadweight loss is the area b+c.
Production | Monopoly 6
Natural Monopolies
The government may wish to force a monopolist to price at marginal cost.
However,if there are very large flxed costs p = MC may result in negative proflts | the flrm will close down.
This is the case with natural monopolies,The utilities are good examples.
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0
p
y
ACMC
pc
yc
p(y)
pa
Loss
In order to allow the flrm to cover their costs the government might regulate to set pa = AC,The flrm will not wish
to close down,but will produce less than an e–cient amount at too high a price.
Production | Monopoly 7
The Minimum E–cient Scale
The minimum e–cient scale (MES) is the point at which average costs are minimised.
If this is small relative to demand,there is \room" for many flrms charging p?.
If it is large relative to demand,there is \room" for only one flrm charging p?.
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...0
p
y 0
p
y
AC
AC
p(y) p(y)
p? p?
MES MES
The MES helps to determine which sort of industry | monopolistic or competitive | is likely to arise.
This makes sense,High flxed costs relative to demand lead to a high MES and make monopoly more likely.
Other factors in uencing market structure are | the law,historical accident and cartels.
Production | Monopoly 8
1st Degree Price Discrimination
Suppose the monopolist can sell difierent units of output at difierent prices and can sell at difierent prices to
difierent people,This is 1st degree price discrimination.
Each unit will be sold to the person who values it most highly at the maximum price they are willing to pay.
The demand curve represents consumers’ willingness to pay,The flrst unit is sold at the highest price and so on.
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...0
p
y
MC
y1c
p(y)
0
p
y
MC
y2c
p(y)a
b
Suppose there are two consumers,The monopolist charges a total of a to the flrst and the b to the second for
consumption of y1c and y2c respectively,All the consumer surplus is appropriated by the flrm.
An e–cient amount is produced | output is set where p(y)= MC.
Production | Monopoly 9
2nd Degree Price Discrimination
Suppose a monopolist can sell difierent units of output for difierent prices,This is 2nd degree price discrimination
| often called non-linear pricing,Bulk buying is an example.
Suppose MC =0 and two consumers for simplicity,The monopolist would like to 1st degree price discriminate.
However,it can’t,The consumers would lie about their type | the high-willingness-to-pay consumer would pretend
to be a low-willingness-to-pay person and pay the lower price,How should the monopolist behave in such scenarios?
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p
y
yL yH
pH(y)
pL(y)
0
p
y
yL yH
a
b
c
a
b
c
d
First graph,Monopolist sells yL at price a and yH at price a+b+c,High type lies about their type,buys yL and
gets b surplus,rather than 0,Could charge a for yL and a+c for yH | now high type self selects yH,gets surplus b
| exactly what they would get at yL,Monopolist can do better by decreasing yL,Loses some a,gains some c.
Second graph,Monopolist lowers yL until marginal gains are exhausted,Sells yL at price a and yH at price
a+c+d,High type buys yH,gets b,low type buys yL and gets zero surplus.
Production | Monopoly 10
3rd Degree Price Discrimination
Suppose the flrm can sell to difierent consumers at difierent prices,This is 3rd degree price discrimination.
One consumer (a student) has demand elasticity ·S and the other (a lecturer) has elasticity ·L.
The flrm maximises proflt,maxyS;yL 'p(yS)yS +p(yL)yL?c(yS +yL)“,At the optimum:
MRS(yS)= MC(yS +yL)= MRL(yL)
Recall marginal revenue can be written as a function of elasticities | at the optimum:
p(yS)
‰
1? 1j·Sj
= p(yL)
‰
1? 1j·Lj
Students have more elastic demand so flfl·Sflfl > flfl·Lflfl,This implies that,at the optimum,p(yS) < p(yL).
The higher elasticity market faces a lower price,Student cards will obtain a lower price in many shops.
Production | Monopoly 11
Monopoly and Factor Demands
The monopolist’s demand for the factors of production will difier from the perfectly competitive case.
Suppose there is only one factor of production,and the monopolist demands x of it when producing output y.
The marginal product of the factor is MPx =￠y=￠x,the increase in output due to an increase in the input,The
marginal revenue product measures the increase in revenue due to an increase in the input | it is the increase in
revenue due to output changes times the increase in output due to increased factor use,MRPx = MR￡￠y=￠x.
MRPx = p(y)
‰
1? 1j·j
MPx? p(y)MPx
The marginal cost of hiring a factor is the price of the input w,A monopolist will demand the factor until the
marginal beneflt from doing so (MRPx) equates to the marginal cost.
Recall that perfectly competitive flrms in equilibrium hired until pMPx = w,The monopolist does not | they only
hire until MRPx = w,They employ less of the factor.
Production | Monopoly 12
Monopsony
A monopoly is a single seller in a market,A monopsony is a single buyer in a factor market.
Suppose the monopsonist sells to a competitive market (this can be easily generalised).
The flrm will maximise proflt,maxx fpf(x)?w(x)xg,(f(x) is the production function).
The flrm will operate where pMPx = MCx,But the marginal cost is no longer a constant,w,The flrm faces the
entire supply curve (much like a monopolist faces the entire demand curve).
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w
x
SupplyMCx
MR = pMPx
MR = MC
w?
x?
Marginal costs can be written as MCx = w(x)(1+1=·S) where ·S > 0 is the price elasticity of supply,Hence
marginal costs lie to the left of the supply curve,The flrm will hire x? at price w?.
They demand less,and pay a lower price for it than a competitive flrm | ine–cient,Minimum wage?
Proflt Maximisation
The monopolist is the only flrm in the industry,Therefore,they face the entire demand curve.
Proflts are given by total revenue minus total costs,… = p(y)y?c(y),p(y) is the inverse demand curve.
The monopolist is assumed to maximise proflts,That is,they choose output to solve:
maxy … =maxy p(y)y?c(y) =) MR = MC
The maximisation condition is MR = MC,If MR > MC then an increase in output generates more revenue than
cost,and if MR < MC a decrease in output would generate more revenue than cost.
As there are barriers to entry,no flrm can enter if positive proflts are being made and the short run is the same as
the long run,A monopolist can earn positive proflts in the long run | unlike competitive flrms.
Production | Monopoly 2
The Monopolist
These facts can be illustrated in the following essential diagram.
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0
p
y
ACMC
p?
y?
AR = p(y)
MR
…
Note that revenue is p(y)y,So average revenue is AR = p(y)y=y = p(y),which is the inverse demand curve.
MR falls at twice the rate of AR for linear demand,MC = MR generates the optimal quantity y?.
To flnd the optimal price (p?) use the demand curve value at y?,Finally,proflts are given by … (the box with a
dashed outline),the area between average revenue and average cost.
Production | Monopoly 3
Mark-up Pricing
Marginal revenue can be written in terms of elasticity,·,The equilibrium condition becomes:
MR = p(y)
‰
1? 1j·j
= MC
If j·j=1 the demand curve is at and MC = p | the perfectly competitive case.
If j·j < 1 then 1=j·j > 1 and MR < 0,The monopolist would produce nothing when demand is inelastic.
The condition MR = MC can be rewritten to give the price mark-up.
p(y)= MC(y)1?1=j·j =) Mark-up= 11?1=j·j
The mark-up is the factor by which market price exceeds marginal cost.
Production | Monopoly 4
Ine–ciency,Monopoly vs Competition
A monopoly prices higher than a perfectly competitive market,They produce less,Is this e–cient?
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....,......,.....,......,......
......
......
.
......
.
......
.
0
p
y
pm
ym
pc
yc
p(y)
Recall the demand curve is the \willingness to pay" of the consumers,Suppose a small amount beyond the
monopolist’s output (ym) was produced,The consumers would pay p(ym +￠y) for this,This exceeds MC.
Hence there is a positive gain from this extra sale,It would be better for both consumer and monopolist.
The monopolist refuses to do this however,as a lower price will reduce total proflts.
A perfectly competitive flrm prices at pc = MC | no gains from further output can be made | it is e–cient.
Production | Monopoly 5
Deadweight Loss
The deadweight loss of a monopoly is a measure of this ine–ciency.
It is the sum of lost consumer and producer surplus due to the restriction of output and rise in price.
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..0
p
y
p?
y?
pc
p(y)
a b
c
a+b is the loss in consumer surplus,But a is regained in proflt by the flrm,It is redistributed,but not lost.
c is the loss in producer surplus,Hence total deadweight loss is the area b+c.
Production | Monopoly 6
Natural Monopolies
The government may wish to force a monopolist to price at marginal cost.
However,if there are very large flxed costs p = MC may result in negative proflts | the flrm will close down.
This is the case with natural monopolies,The utilities are good examples.
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.......................
.........................
.,,,,
0
p
y
ACMC
pc
yc
p(y)
pa
Loss
In order to allow the flrm to cover their costs the government might regulate to set pa = AC,The flrm will not wish
to close down,but will produce less than an e–cient amount at too high a price.
Production | Monopoly 7
The Minimum E–cient Scale
The minimum e–cient scale (MES) is the point at which average costs are minimised.
If this is small relative to demand,there is \room" for many flrms charging p?.
If it is large relative to demand,there is \room" for only one flrm charging p?.
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p
y 0
p
y
AC
AC
p(y) p(y)
p? p?
MES MES
The MES helps to determine which sort of industry | monopolistic or competitive | is likely to arise.
This makes sense,High flxed costs relative to demand lead to a high MES and make monopoly more likely.
Other factors in uencing market structure are | the law,historical accident and cartels.
Production | Monopoly 8
1st Degree Price Discrimination
Suppose the monopolist can sell difierent units of output at difierent prices and can sell at difierent prices to
difierent people,This is 1st degree price discrimination.
Each unit will be sold to the person who values it most highly at the maximum price they are willing to pay.
The demand curve represents consumers’ willingness to pay,The flrst unit is sold at the highest price and so on.
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y
MC
y1c
p(y)
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p
y
MC
y2c
p(y)a
b
Suppose there are two consumers,The monopolist charges a total of a to the flrst and the b to the second for
consumption of y1c and y2c respectively,All the consumer surplus is appropriated by the flrm.
An e–cient amount is produced | output is set where p(y)= MC.
Production | Monopoly 9
2nd Degree Price Discrimination
Suppose a monopolist can sell difierent units of output for difierent prices,This is 2nd degree price discrimination
| often called non-linear pricing,Bulk buying is an example.
Suppose MC =0 and two consumers for simplicity,The monopolist would like to 1st degree price discriminate.
However,it can’t,The consumers would lie about their type | the high-willingness-to-pay consumer would pretend
to be a low-willingness-to-pay person and pay the lower price,How should the monopolist behave in such scenarios?
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y
yL yH
pH(y)
pL(y)
0
p
y
yL yH
a
b
c
a
b
c
d
First graph,Monopolist sells yL at price a and yH at price a+b+c,High type lies about their type,buys yL and
gets b surplus,rather than 0,Could charge a for yL and a+c for yH | now high type self selects yH,gets surplus b
| exactly what they would get at yL,Monopolist can do better by decreasing yL,Loses some a,gains some c.
Second graph,Monopolist lowers yL until marginal gains are exhausted,Sells yL at price a and yH at price
a+c+d,High type buys yH,gets b,low type buys yL and gets zero surplus.
Production | Monopoly 10
3rd Degree Price Discrimination
Suppose the flrm can sell to difierent consumers at difierent prices,This is 3rd degree price discrimination.
One consumer (a student) has demand elasticity ·S and the other (a lecturer) has elasticity ·L.
The flrm maximises proflt,maxyS;yL 'p(yS)yS +p(yL)yL?c(yS +yL)“,At the optimum:
MRS(yS)= MC(yS +yL)= MRL(yL)
Recall marginal revenue can be written as a function of elasticities | at the optimum:
p(yS)
‰
1? 1j·Sj
= p(yL)
‰
1? 1j·Lj
Students have more elastic demand so flfl·Sflfl > flfl·Lflfl,This implies that,at the optimum,p(yS) < p(yL).
The higher elasticity market faces a lower price,Student cards will obtain a lower price in many shops.
Production | Monopoly 11
Monopoly and Factor Demands
The monopolist’s demand for the factors of production will difier from the perfectly competitive case.
Suppose there is only one factor of production,and the monopolist demands x of it when producing output y.
The marginal product of the factor is MPx =￠y=￠x,the increase in output due to an increase in the input,The
marginal revenue product measures the increase in revenue due to an increase in the input | it is the increase in
revenue due to output changes times the increase in output due to increased factor use,MRPx = MR￡￠y=￠x.
MRPx = p(y)
‰
1? 1j·j
MPx? p(y)MPx
The marginal cost of hiring a factor is the price of the input w,A monopolist will demand the factor until the
marginal beneflt from doing so (MRPx) equates to the marginal cost.
Recall that perfectly competitive flrms in equilibrium hired until pMPx = w,The monopolist does not | they only
hire until MRPx = w,They employ less of the factor.
Production | Monopoly 12
Monopsony
A monopoly is a single seller in a market,A monopsony is a single buyer in a factor market.
Suppose the monopsonist sells to a competitive market (this can be easily generalised).
The flrm will maximise proflt,maxx fpf(x)?w(x)xg,(f(x) is the production function).
The flrm will operate where pMPx = MCx,But the marginal cost is no longer a constant,w,The flrm faces the
entire supply curve (much like a monopolist faces the entire demand curve).
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w
x
SupplyMCx
MR = pMPx
MR = MC
w?
x?
Marginal costs can be written as MCx = w(x)(1+1=·S) where ·S > 0 is the price elasticity of supply,Hence
marginal costs lie to the left of the supply curve,The flrm will hire x? at price w?.
They demand less,and pay a lower price for it than a competitive flrm | ine–cient,Minimum wage?
