Lecture Notes
Monopoly
 Market environment where there is only one firm
in the market
Firm faces ALL of demand
So monopoly profit = p(y)y – c(y)
Where p(y) = inverse market demand let p(y)y = r(y)
revenue function
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Monopolistic problem:
Choose y to Max r(y) – c(y)
First order conditions are given by:
MR = MC
 The same condition we got with perfect competition
 But now MR does not equal P (i.e. firms not price
takers)
 Two effects of changing y (say increase y) on revenues
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1-sell more so revenue increases
2-price decreases so revenue decreases
 ∆ r (y) = p ∆y + y ∆p
 ∆ r(y)/ ∆ y = MR = p + y ∆p/ ∆y or:
 For price takers ∆p=0 => ∆r = p ∆y
 But now P decreases as y increases so the second term matters.
 Now both 1 and 2 measure Marginal Revenue (MR)
 MR= ∆r/ ∆y = p + y ∆p/ ∆y
 = p(1 + (y/p)(∆p/ ∆y)
 = p(y) (1 + 1/ε)
 Since ε = price elasticity of demand = (p/y)(∆y/∆p)
 => can re-write optimal condition, MR = MC as:
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p(y) (1 + 1/ ε(y)) = mc (y)
 Or p(y) (1- 1/| ε(y)|) = mc (y)
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Since ε < 0
Also recall that | ε | > 0 elastic
| ε | < 1 inelastic
So that if demand elastic regions | ε | > 1
MR > 0 but if demand inelastic MR < 0
 The above implies that the Monopolist only operates in elastic
portion of Demand since
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MR < 0 when demand inelastic and profit max. requires MR = MC
but MC < 0 is unlikely (impossible).
 Now with linear demand…
 P(y) = a –b y
 So R (y) = ay –by2
 => MR= a – 2by
 Notice 3 things:
 1. MR = D at y=0
 2. slope of MR = 2 times the slope of demand (i.e., twice as steep).
 3. MR = 0 where | ε | = 1 (this is always true not just for linear
Demand)
MC
AC
Pm
D
MR
Ym
y
 Look at tax example: suppose c(y) = cy
 => mc = c
 P(y) = a-by so MR = a -2by
 Now suppose a tax on the monopolist = t (quantity tax) so pc
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= ps + t
So mc w/ tax is c + t or c(y) = (c+ t)y
=> before profit max where c = a -2by
Or y* = a-c/2b
Now MC = c + t = a – 2by = MR
So y* = (a-c-t)/2b
=> Δy/ Δ t = -1/(2b) (why?)
What is the impact of the tax on price, p?
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Recall slope of demand function = Δp/ Δy = -b, so
The tax is imposed => y changes by -1/(2b) then
The price changes by – b, the overall impact is both of these together,
Or – b times -1/(2b) = -1/2
 Interpretation: if t increases by $1 => price increases by $.50
pt
P*
C+t
MC = C
MR
Yt
D
y*
 But note that p may actually increase more than by the
amount of tax. See book for example
 Now look at efficiency and compare to perfect
competition
 Again assume MC = C (constant returns) in the long run
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Produce at (pm, ym)
Deadweight loss to
society
Pm
MC=LRAC
Pc=c
MR
Ym
D
yc
But competitive firms would produce at MC = D
Or (pc, yc) which is the point that maximizes net surplus to
society.
 Or if upward sloping LRMC
Deadweight loss to
society
Pm
MC
Pc
MR
Ym
D
yc
 => appears that monopolist is inefficient (i.e. does not
max society’s net surplus)
 Public policy: may be to get rid of monopolies
 (1) contestable markets i.e. free entry => if profit > 0
more firms enter so profit = o even with one firm.
 (2) economies of scale and scope
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Consider natural monopoly (economies of scale)
Pm
Pt
LRMC
LRAC
MR
Ym
D
 Only one firm can cheaply produce given demand but
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(1) if p=mc=Pso(socially optimum price)
 Firms makes a loss and leaves
(2) if p=pm => deadweight loss
(3) if p=AC=pf (fair price) still a loss in profit but firm can
operate
But if break up of monopoly:
 Pc > Pm > Pf >Pso => competition is not more efficient due
to economies of scale.
Same may to be true due to economies of scope.
 Price Discrimination
 3 different types
 A. Perfect price discrimination—price the monopolists sells is
just equal to your willingness to pay =>
 With no price discrimination produce at (pm, ym) but this
assumes no ability to discriminate
Pm
Pe
MC
D
MR
Ym
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Ye
Now perfectly discriminate => D=MR and produce at Yc which
is efficient (assuming $1 to producer is the same as $1 to
consumer since CS=0)
 2nd degree Price Discrimination
 Pi= f(yi)
i.e. how much you pay depends on your
consumption
 Examples: utilities, bulk discounts for large purchases
 3rd degree price discrimination-different groups get
different prices but individuals within a group get the
same price
 Most common type: Examples
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1. movie theatre discounts (kids v. adults)
2. local ski discounts (locals v. non-locals)
More formally suppose 2 groups with different demand
=> max P1 (Y1) Y1 + P2 (Y2) Y2 – C(Y1 + Y2) by:
 MR1 – MC(Y1 + Y2) = 0
 MR2 – MC(Y1 + Y2) = 0
 Combine to get MR1 = MC(Y1 + Y2) = MR2 or
 P1 [1- 1/| ε1 |] = MC (Y1 +Y2) = P2 [1-1/| ε 2|]
 If P1 > P2 =>
[1-1/| ε 1|] < 1 – 1/| ε 2| or
 1/| ε 1| > 1/| ε 2| or | ε 2| > | ε 1|
 i.e. for P1 > P2 demand for group 1 must be more
inelastic
 Graphically, assume C= MC
Group 1
Group 2
P1
D1
C
P2
C
MR1
Y1
MR2
Y2
D2
 Innovation—monopolies have more incentive to
innovate (at least this is the argument)
 Define innovation
 Just a decrease in MC to MC2 assuming constant returns
P
MC1
MC2
Q
 What are the incentives to innovate for monopoly?
 I.e. increase profit due to innovation = shaded area.
Why?
P
MC1
MC2
MR
D
Y
 What are incentives to innovate for perfectly competitive
industry?
 None unless (1) innovative technology is secret or (2) a
patent system exists
 Under a patent system what is the incentive? What are
increased profits to patent holder?
 1st what does patent holders MR curve look like? As long
y < y* MR = C ; i.e. he’s a price taker.
P
MC1
C
MC2
C1
D
Y*
Q
P
C
C1
C*
MR
Y*
D
Y
 But if y > y* the firm becomes sole supplier
 R= p(y)y so MR is downward sloping and determined by
D when y > y*.
 Note: as long as C > C* ; y = y* in the market. This is a
small innovation.
 But if C < C* so y > y* then this is a large innovation.
 Now just look at a small innovation (i.e. y = y* before
and after innovation)
P
Incentive to innovate to
competitive industry
C
C2
MR
D
Y
 Notice that the incentive to innovate for a competitive
industry is greater than for a monopoly because output is
larger for the competitive firm.
 Q: What if economies of scale in innovation (i.e. small
firms in competitive industry don’t have resources to
innovate)
 A: Firms specialize in innovating, gain patents and
license to small competitive firms
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Example: agriculture where innovating is done by
 Universities
 Seed companies
 Etc.
 Monopolistic Competition
 Characteristics
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Large numbe r of potential sellers
All small relative to market
Differentiated product
Easy entry and exit
 The short-run looks like a monoply
Profit
MC
Pm
MR
Ym
ATC
D
 Profit can also be negative or zero in the short-run. If
negative => firms exit if p< avc.
 Long-run equilibrium is just like for competition:
 If profit > 0 => entry which drives profit down.
 If profit < 0 => exit which drives profit up.
 Therefore, long-run equilibrium is where profit equals
zero, where no exit or entry.
MC
ATC
Po
Pc
MR
Qo Qc
D
 Notice that at Equilibrium but P > MC
 Resource Allocation & Efficiency
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Since MSC does not equal MSB or MSB > MSC => inefficient
p.c. firm would produce the efficient amount.
Might be efficient if benefit from different products > Cost of
producing different products
=> in long run (1) each firm is on its demand curve
(2) each firm chooses y to max profit
(3) entry forces profit = 0
(4) P > MC => inefficient