12Monopoly and Monopoly behavior

Setting
price equal to marginal cost may be infeasible due to negative profits.
p, MC AC
Setting
price equal to pMC along with a subsidy SettingΒιβλιοθήκη price equal to pAC
p, MR
p' p*
.. . .
y' y* MR = a – 2by
MC = c + t
MC = c
Demand
y
y* = (a – c)/(2b) p* = (a + c)/2 p * = (a – c)2/(4b) y' = (a – c – t)/(2b) p' = (a + c + t)/2 2 p ' = (a – c – t) /(4b)
p, MR p*
MC(y*)
. .
y*
MC
Demand y
MR
p, MR p*
MC(y*)
. .
y*
MC
Deadweight loss Demand y
MR
What
if a monopolist acts like a competitive firm, that is, the firm sets its price p(y) = MC(y). Price declines, quantity increase and inefficiency disappears.

p, MR
p' A p*
CS* = A
B
. .
y' y*
PS* = B
MC = c
Demand
MR = a – 2by
y
p, MR
p' A' p*
CS ' = A '
PS ' = B '
B'
C
.. . .
D
y' y*
Tax = C Efficiency loss = D
MC = c + t
MC = c
p, MR
|e (y)| =1
|e (y)| >1
MC
.
|e (y)| <1 Demand y
MR
MR(y) = MC(y) MR(y) = p(y) [1 – 1 / |e (y)| ] Markup pricing p(y) = MC(y) / [1 – 1 / |e (y)| ] Markup 1 / [1 – 1 / |e (y)| ]
One Monopolist in computer market.
Monopoly power in CPU
Keyboard, Mice, Monitor Software, etc
What
causes monopolies? Administrative monopoly Patent Collusion (Cartel) Minimum efficient scale
MR(y)
= p(y) + [dp(y)/dy] y = p(y) [1+ 1 /e (y) ] = p(y) [1 – 1 / |e (y)| ] MR(y) >, =, < 0 if and only if |e (y)| >, =, < 1, respectively.
|e (y)| =1 p, MR
p, AC
p, AC
Demand AC
Demand
AC
MES
y
MES
y
Natural
monopoly Public utilities: large fixed costs and small marginal costs.
For
example, assume that c(y) = cy + F, where F is large and c is small.
Chapter 24
Monopoly: only
one firm in a
market. Price maker Market demand: y = 100 – p Note 1: Choosing the price and choosing the quantity are equivalent.
Demand
pAC pMC
.. .
yAC yMC
AC = c + F/y MC = c y
Note
6: Setting price equal to pAC is prevalent and it seems effective. Is it perfect? We need to investigate the true costs of monopolists. monopolists have no incentive to enhance efficiency. Should the government operate it?
Choosing the
quantity y Inverse demand curve: p = p(y) Revenue: r(y) = p(y) y AR = r(y)/y = p(y) Average revenue curve are coincident with inverse demand curve.
MR1
MR2
y1
y2
p, MR MC
p, MR MC
p, MR MC
p1
. .
y1
MR1 D1
p2
. .
MR2 D2 y2 y
.
y
MC
MR y
y
Monopolistic Competition
Product
differentiation Hotelling model
Homework Chap. 24: 2, 9, 10 Chap. 25: 2, 4
MR(y)
= dr(y)/dy = p(y) + [dp(y)/dy] y Direct effect vs. indirect effect Note 2: Marginal revenue is smaller than price when demand curve is decreasing.
|e (y)| >1
. .
|e (y)| <1 Demand y
MR
Profit-maximization
problem max y p (y) = r(y) – c(y) Optimization condition MR(y) = MC(y) Note 3: Maximum profits can only occur where |e (y)| ≥1.
p, MR p* pC
. . .
y* yC
MC
Demand y
MR
p, MR p* A pC
. . .
B C
MC
DPS = - A + C DCS = A + B DMS = B + C Demand y
y* yC MR
monopolists often
obtain extra profits through high monopoly price. So, should we impose a tax on monopolists?
Now,
it’s your turn. Do the exercise below. Suppose that a monopolist has constant marginal cost of 10. What is its optimal price in the following cases: (1) Inverse demand curve: p = 100 – q. (2) Demand curve has a constant elasticity of 2.
Do
you still remember that p(y) > MR(y) . Since the optimization condition is MR(y) = MC(y), we have p(y) > MC(y) Note 4: a monopoly is inefficient.
p1 (y1) = MC(y1+y2) / [1 – 1 / |e (y1)| ] p2 (y2) = MC(y1+y2) / [1 – 1 / |e (y2)| ] Note 7: the market with lower elasticity has higher price.
Division of output between two markets
Demand
MR = a – 2by
y
Note
5: Tax not only hurts the monopolist but also the consumers.
Regulation:
set price equal to marginal cost. Antitrust: forbid monopolistic mergers. Split a monopolist into several firms.
Chapter 25
Price
discriminations of first-degree (perfect) of second-degree (bulk discounts), of third-degree (market segmentation)
Two
separate market: p1 = p1(y1), p2 = p2(y2) max y1, y2 p = p1(y1) y1 + p2(y2) y2 – c(y1+y2) Optimization condition MR1 (y1) = MR2 (y2) = MC(y1+y2)
Suppose
that a monopolist has cost function c(y) = cy + F. The inverse demand function is p = a – by. What are the optimal quantity, price and profit? If a quantity tax t is imposed, what are the new optimal quantity, price and profit?