Download Finance 510: Microeconomic Analysis

Finance 510: Microeconomic
Analysis
Technology, Cost, and Price
Oil prices are currently hovering around
$60/barrel. This is a 50% increase from one
year ago! How will this rise impact the prices
of final goods?
Production
Decisions
Product
Markets
Factor
Markets
Supply/Demand
Determines Factor
prices
Factor
Usage/Prices
Determine
Production Costs
Supply/Demand
determine markup
over costs
Production theory begins with the assumption that every
producer has a technology available to convert various
inputs into output. Its usually convenient to represent this
technology with a production function
F : AB
F
A
Set of inputs
B
Output
Short Run vs. Long Run
It is important in production theory to distinguish the short run
from the long run. In the short run, some of the inputs into
production are fixed. In the long run, all inputs are changeable.
“Fixed”
Inputs
Output
Inputs
Output
Variable
Inputs
Short Run
Long Run
Properties of Production
y  F (k , l )
Labor
Output
F (k , l )  0
Fk (k , l )  0
Fl (k , l )  0
for all
for all
k, l
k, l
Fkl (k , l )  Flk (k , l )  0
Capital (Fixed in the
Short Run)
(Output is positive)
(Production is increasing in all
factors)
for all
k, l
(Factors are complements in
production)
Short Run Properties: Marginal Returns
As labor increases (given a
fixed capital stock), labor
productivity decreases
Fll (k , l )  0
is fixed
As labor increases (given a
fixed capital stock), labor
productivity increases
Fll (k , l )  0
y
0
k
y
F (k , l )
F (k , l )
l
l
0
k
Long Run Properties
is variable
Fk (k , l )dk  Fl (k , l )dl  0
l
Marginal Product of
Capital
Marginal Product of
Labor
Fk (k , l )
dl
TRS 

dk
Fl (k , l )
l
F (k , l )  y
k
k
The Technical rate of substitution (TRS) measures the amount of labor required
to replace each unit of capital and maintain constant production
Long Run Properties
k
is variable
Fll (k , l )  0
MRS (k , l )  MRS (k ' , l ' )
*
*
l
If you have a lot of capital relative to labor,
then TRS is low)!
l*
F (k , l )  y
l'
k*
k'
k
Long Run Properties
l
l
 
k
k
is variable
'
l
%  
k


%TRS
l
 
k
k
The elasticity of substitution measures curvature
l
d 
k  TRS


d TRS   l 
 
k
Long Run Properties
Increasing
Returns to Scale
Constant
Returns to Scale
Decreasing
Returns to Scale
k
is variable
F (2k ,2l )  2 F (k , l )
F (2k ,2l )  2 F (k , l )
F (2k ,2l )  2 F (k , l )
Cost Minimization
The cost function for the firm can be written as
TC  rk  wl
Given the costs of the firm’s inputs, the problem facing the firm is to
find the lowest cost method of producing a fixed amount of output
Min rk  wl
l ,k
subject to
F (k , l )  y
Cost Minimization: Short Run
Fixed Cost
Min rk  wl
l
subject to
k
is fixed
F (k , l )  y
(l )  rk  wl   F k , l   y 
Cost Minimization: Short Run
k
is fixed
(l )  rk  wl   F k , l   y 
First Order Necessary Conditions
 l (l )  w  Fl (k , l )  0
y  F (k , l )
w

Fl ( k , l )
F (k , l )  y
k
Cost Minimization: Short Run
is fixed
(l ,  )  rk  wl   F k , l   y 
w

Fl ( k , l )
F (k , l )  y
Recall that lambda measures the
marginal impact of the constraint.
In this case, lambda represents the
marginal cost of producing more
output
Fll (k , l )  0
Fll (k , l )  0
Marginal costs
are increasing
Marginal costs
are decreasing
Fll (k , l )  0
Marginal Cost vs. Average Cost
d rk  wl 
dy
rk  wl  rk   wl 
     
y
 y  y 
Costs
ATC
Minimum ATC
MC
AVC
y
Fll (k , l )  0
Marginal Cost vs. Average Cost
d rk  wl 
dy
rk  wl  rk   wl 
     
y
 y  y 
Costs
ATC
AVC
MC
y
Cost Minimization: Long Run
Min rk  wl
k ,l
subject to
k
is variable
F (k , l )  y
(l,  )  rk  wl   F k , l   y 
Cost Minimization: Long Run
k
is variable
(l,  )  rk  wl   F k , l   y 
First Order Necessary Conditions
 l (l ,  )  w  Fl (k , l )  0
 k (l ,  )  r  Fk (k , l )  0
y  F (k , l )  0
r Fk (k , l )

w Fl (k , l )
Min rk  wl
k ,l
subject to
F (k , l )  y
l
r Fk (k , l )

w Fl (k , l )
w
r


Fl (k , l ) Fk (k , l )
l*
F (k , l )  y
k*
k
Elasticity of Substitution
 is small
l
mc
w
 w is small
l
y
l
k
w
 is large
k
mc
 w is large
l
y
Marginal Cost vs. Average Cost
d rk  wl 
dy
Costs
F (2k ,2l )  2 F (k , l )
rk  wl
y
MC
AC
y
Marginal Cost vs. Average Cost
d rk  wl 
dy
F (2k ,2l )  2 F (k , l )
rk  wl
y
Costs
MC = AC
y
Marginal Cost vs. Average Cost
d rk  wl 
dy
F (2k ,2l )  2 F (k , l )
rk  wl
y
Costs
AC
MC
y
Estimating Production Functions
 
y  F (k , l )  Ak l
%A  %y   %k    %l 
Labor Growth
Capital Growth
Output Growth
Productivity Growth
Example: Estimating Production Functions
 
y  Ak l
A Cobb-Douglas Production function was estimated for the
aggregate production sector of the US
y  Ak l
.63 .30
Average Annual Growth = 1.5%
   1
Example: Estimating Production Elasticities
  
y  Ak l p lnp
Non-Production Labor
Production Labor



Food/Beverage
.555
.439
.076
1.070
Textiles
.121
.549
.335
1.004
Furniture
.205
.802
.103
1.109
Petroleum
.308
.546
.089
.947
Stone, Clay, etc.
.632
.032
.366
1.029
Primary Metals
.371
.077
.509
.958
Industry
   
Profit Maximization and Industry Dynamics
After the determination of optimal production, the firm is faced
with a cost function…
TC  TC ( y )
Further, the firm faces a demand for its product…
y  y ( p)
A quick diversion…
Demand refers to output as a function of price
y  y ( p)
p
Inverse demand refers to price as a function of
output
p  p( y)
p
D
y
y
Profit Maximization and Industry Dynamics
After the determination of optimal production, the firm is faced
with a cost function…
TC  TC ( y )
Further, the firm faces an inverse demand for its product…
p  p( y)
A firm needs to choose output to maximize profits…
 ( y )  p( y ) y  TC ( y )
Profit Maximization
max p( y) y  TC ( y)
y
First Order Necessary Conditions
dp
dTC ( y )
y p
0
dy
dy
Marginal Cost (MC)
dp
y  p  MC
dy
First Order Condition
dp y
and divide the
p  p  MC Multiply
first term by p
dy p
1
A little rearranging
  p  p  MC
 
Now, solve for price
MC
p
 1
1  
 
dp
y  p  MC
dy
p
Initially, you are charging
price (P) and generating
sales equal to Y
p
Revenue = P*Y
To increase sales, you
must lower your price
D
y
y
Cost, Price, and Market Structure
Market Structure Spectrum
Perfect Competition
The market is supplied by many
producers – each with zero market share
Monopoly
One Producer Supplies
the entire Market
Measuring Market Structure – Concentration Ratios
Suppose that we take all the firms in an industry and raked them by
size. Then calculate the cumulative market share of the n largest
firms.
Cumulative Market
Share
100
A
C
80
B
40
20
0
01
Size
Rank
2
3
4
5
6
7
10
20
Measuring Market Structure – Concentration Ratios
Cumulative Market
Share
100
A
C
80
B
40
20
0
01
CR4
Size
Rank
2
3
4
5
6
7
10
20
Measures the cumulative market share of the top four firms
Concentration Ratios in US manufacturing; 1947 - 1997
Year
CR50
CR100
CR200
1947
17
23
30
1958
23
30
38
1967
25
33
42
1977
24
33
44
1987
25
33
43
1992
24
32
42
1997
24
32
40
Aggregate manufacturing in the US hasn’t really changed since WWII
Measuring Market Structure: The Herfindahl-Hirschman
Index (HHI)
N
HHI   s
i 1
2
i
si = Market share of firm i
s 2i
Rank
Market Share
1
25
625
2
25
625
3
25
625
4
5
25
5
5
25
6
5
25
7
5
25
8
5
25
HHI = 2,000
The HHI index penalizes a small number of total firms
Cumulative Market
Share
100
A
HHI = 500
80
B
HHI = 1,000
40
20
0
01
2
3
4
5
6
7
10
20
The HHI index also penalizes an unequal distribution of firms
Cumulative Market
Share
100
80
HHI = 500
HHI = 555
A
40
B
20
0
01
2
3
4
5
6
7
10
20
Concentration Ratios in For Selected Industries
Industry
CR(4)
HHI
Breakfast Cereals
83
2446
Automobiles
80
2862
Aircraft
80
2562
Telephone Equipment
55
1061
Women’s Footwear
50
795
Soft Drinks
47
800
Computers & Peripherals 37
464
Pharmaceuticals
32
446
Petroleum Refineries
28
422
Textile Mills
13
94
Perfect Competition
p
MC
p
 1
1  
 
Perfectly competitive firms are so small
relative to the market that they can’t
influence market price – they face a
perfectly elastic demand curve
MC
ATC
p
D
y*
y
 
p  MC
Perfect Competition
p
MC
p
 1
1  
 
As we move from the short run to the
long run, firms adjust their capital
structure (move from short run cost
functions to long run cost functions)
 
p
MC = AC
y*
y
p  MC
Monopoly
p
MC
p
 1
1  
 
Monopolies by definition face the entire
market demand. Therefore, monopolies
charge a markup over marginal cost – as
the elasticity of demand increases, the
markup decreases.
MC
Example
ATC
p
  2
p  2 * MC
MC
D
MR
y*
y
Monopoly
p
MC
p
 1
1  
 
As we move from the short run to the
long run, firms adjust their capital
structure (move from short run cost
functions to long run cost functions).
Typically, demand also becomes more
elastic as consumers find substitute
products
MC
Example
  4
p
D
p  1.33 * MC
MC
y*
y
MR
Higher market concentration offers the potential for market
power. However, does high market concentration
guarantee market power?
P  MC
LI 
P
Perfect Competition
p  MC
LI  0
The Lerner index measures the percentage of a
product’s price that is due to the markup
Monopoly
MC
p
 1
1  
 
LI 
1

Lerner index in For Selected Industries
Industry
LI
Communication
.972
Paper & Allied Products
.930
Electric, Gas & Sanitary Services
.921
Food Products
.880
General Manufacturing
.777
Furniture
.731
Tobacco
.638
Apparel
.444
Motor Vehicles
.433
Machinery
.300
P  MC
LI 
P
Cost Structure and Market Structure – Does it
pay to be big?
The output elasticity of costs is defined as the percentage
increase in total costs for every 1% increase in production
%TC dTC y
MC



%y
dy TC AC
If the output elasticity is less than one, then total costs are
growing at a rate that is lower than output (Average Costs are
declining) – It pays to be big!!
S
1

A scale economy index larger than one
indicates the potential for a monopoly!
Cost Structure and Market Structure – Does it
pay to be big?
Costs
ATC
If market demand is always
below y*, than this industry
could become monopolistic!!
MC
y*
S 1
y
Globally scale economies
Globally scale economies (S>1 for all y) are known as natural
monopolies (the market should – and will – be serviced by one
producer). This can happen if production exhibits increasing
returns to scale, or if there are large fixed costs.
Costs
Costs
ATC
MC
ATC
MC
Monopoly Market Characteristics
Scale economies (Natural Monopolies)
Small market size
Network Externalities
Government Policy (Protected Monopolies)
Any one of these characteristics suggest that the long
run market structure should be monopolistic.