The unit step function I is dened by
I (x) =
x 0,
x > 0.
0,
1,
Let f be continuous on [a, b] and suppose cn 0 for
n = 1, 2, 3, . . . and n cn is convergent. Let
= N=1 cn I (x sn ) where sn is a sequence of distinct points
n
in (a, b). Then
N
b
f d =
a
()
Lecture: Optimal Policies for Natural Monopolies,
Ronald R. Braeutigam
1. Introduction, Topics to be covered.
Natural monopoly: What is it? Telephone-20th cent., they exist today.
Regulations: natural response to natural monopoly; why? how?
Competition in
Managerial Economics
Module III
Session 15
Sequential moves First movers advantage
BM - Term I AY 2015-16
Sumit Sarkar, XLRI Jamshedpur
If there isnt any Dominant Strategy?
Often there is no dominant strategy
Some games may have multiple equilibria
Equi
Managerial Economics
Module II
Sessions 12-13
Competition to monopolization;
Equilibrium of a monopolist;
Price discrimination by monopolist
BM - Term I AY 2015-16
Sumit Sarkar, XLRI
Entry of a firm with decreasing AC
MC, MR
P
AC
S0
P0
P1
MC, MR
S1
MC
a
A
Managerial Economics
Module III
Session 14
Introduction to Game Theory
Simultaneous move games and Nash equilibrium
BM - Term I AY 2015-16
Sumit Sarkar, XLRI Jamshedpur
Alternate offer bargaining
Suppose I give you ten Rs. 10 notes, which are to be divide
Managerial Economics
Module II
Session 11
Perfectly competitive markets
Short-term equilibrium and market
dynamics
Long term equilibrium
BM - Term I AY 2015-16
Sumit Sarkar, XLRI
Short term equilibrium in Perfect Competition
P
MC
MR
S0
MC AC
A
P0
a
MR0
D
Managerial Economics
Module II
Session 10
Cost and Revenue functions
Introduction to perfectly competitive
markets; Understanding profit maximization
of price taker firms;
Short-term equilibrium in perfectly
competitive markets
Supply curve of a perfectly
Managerial Economics
Module II
Session 9
Production planning Choice of
technology
Returns to scale
BM - Term I AY 2015-16
Sumit Sarkar, XLRI
Producers equilibrium Choice of technology
Producers optimization problem
Max: f(L, K)
S.t. C = wL + rK
Or its dua
Managerial Economics
Module II
Session 8
Short-run production function,
Marginal and average products as
measures of productivity;
BM - Term I AY 2015-16
Sumit Sarkar, XLRI
Fundamental questions of a
firm
Product selection
Market selection and segmentati
(ZFC) brbrbr Let B , +, ,
be a Banach space.
Dene B = B , +, ,
.
Dene B0 = B . For all non-negative integers n, br dene
Bn+1 to be the Banach space that is the continuous dual of Bn .
Dene the relation on cfw_0, 1, 2, 3, 4, 5, . . . by brm n if
and only
*Original question* (see also the revised, possibly simpler,
version below): Let g > 1, r > 1 be integers. Playing around with
the Verlinde formula (see below), I came across the expression
r 1
2 /r
sin(n/r)22g (e2in
1).
n=1
My goal is to reduce the comp
Somewhat in contrast to [this question][1].
Lets say the Supreme Court has just issued a ruling that the
upper and lower roads of an overpass need not be in the same
congressional district. This makes states with lots of overpasses
into high-genus surface
On the other hand, the three classical consequences of the Baire
category theorem in basic functional analysis mdash; the [open
mapping
theorem](http:/en.wikipedia.org/wiki/Openm appingt heorem
Each of these results has a more or less direct proof from th
The goal of the [four fours][1] puzzle is to represent each natural
number using four copies of the digit 4 and common
mathematical symbols.
For example, 165 = ( 4 +
44! ) 4.
If we remove the restriction on the number of fours, let f (N ) be
the number of
The sequence cfw_bn is monotonic and bounded, so it converges to
some number C . Assume, without loss of generality, that the
sequence cfw_bn is increasing, and write bn = C dn , where
dn 0. We have
an bn = C
an
an dn .
The rst series on the right is c
Lecture: Two-Sided Markets
BB
BUYE
BUYERS
RS
per transaction
fee aB
PLATFOR
PLATFORM
M
per transaction
fee a
S
Membership
fee AB
Examples
(1) Telecom
End User
(2) Apple
End User
SS S
SELLERS
SELLERS
Membership
fee AS
Broadband
Service Provider
Core
Networ