Technology, Cost, and Price Finance 510: Microeconomic Analysis
Technology, Cost, and Price
Finance 510: Microeconomic Analysis
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?
Factor Markets
Production Decisions
Product 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
BAF :
A BF
Set of inputs 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
Variable Inputs
Inputs Output
Short Run Long Run
Properties of Production
),( lkFy Labor
Capital (Fixed in the Short Run)
Output
0),( lkF for all lk,
0),( lkFkfor all lk,
0),( lkFl
(Output is positive)
(Production is increasing in all factors)
0),(),( lkFlkF lkklfor all lk, (Factors are complements in
production)
Short Run Properties: Marginal Returns k is fixed
y
l0
0),( lkFll
As labor increases (given a fixed capital stock), labor productivity decreases
),( lkF
y
l0
0),( lkFll
As labor increases (given a fixed capital stock), labor productivity increases
),( lkF
The Technical rate of substitution (TRS) measures the amount of labor required to replace each unit of capital and maintain constant production
k
l
l
k
ylkF ),(
0),(),( dllkFdklkF lk
Marginal Product of Labor
Marginal Product of Capital
),(
),(
lkF
lkF
dk
dlTRS
l
k
Long Run Properties k is variable
k
l
*l
*k
ylkF ),(
)','(),( ** lkMRSlkMRS
'l
'k
If you have a lot of capital relative to labor, then TRS is low)!
0),( lkFll
Long Run Properties k is variable
The elasticity of substitution measures curvature
k
l'
k
l
k
l
TRSkl
%
%
kl
TRS
TRSdkl
d
Long Run Properties k is variable
Long Run Properties k is variable
),(2)2,2( lkFlkF Increasing Returns to Scale
),(2)2,2( lkFlkF Constant Returns to Scale
),(2)2,2( lkFlkF Decreasing Returns to Scale
Cost Minimization
The cost function for the firm can be written as
wlrkTC 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
ylkF
tosubject
wlrkMinkl
),(
,
Cost Minimization: Short Run
ylkF
tosubject
wlkrMinl
),(
k is fixed
Fixed Cost
ylkFwlkrl ,)(
Cost Minimization: Short Run k is fixed
ylkFwlkrl ,)(
0),()( lkFwl ll
First Order Necessary Conditions
),( lkFy
),( lkF
w
l
ylkF ),(
Cost Minimization: Short Run k is fixed
ylkFwlkrl ,),(
),( lkF
w
l
ylkF ),(
Recall that lambda measures the marginal impact of the constraint. In this case, lambda represents the marginal cost of producing more output
0),( lkFll
0),( lkFll
Marginal costs are increasing
Marginal costs are decreasing
Marginal Cost vs. Average Cost
dy
wlkrd
y
wl
y
kr
y
wlkr
y
Costs
MC
ATC
AVC
Minimum ATC
0),( lkFll
Marginal Cost vs. Average Cost
dy
wlkrd
y
wl
y
kr
y
wlkr
y
Costs
MC
ATCAVC
0),( lkFll
Cost Minimization: Long Run
ylkF
tosubject
wlrkMinlk
),(
,
k is variable
ylkFwlrkl ,),(
Cost Minimization: Long Run k is variable
ylkFwlrkl ,),(
0),(),( lkFwl ll
First Order Necessary Conditions
0),( lkFy
0),(),( lkFrl kk ),(
),(
lkF
lkF
w
r
l
k
ylkF
tosubject
wlrkMinlk
),(
,
k
l
*l
*k
ylkF ),(
),(
),(
lkF
lkF
w
r
l
k
),(),( lkF
r
lkF
w
kl
l
k l
wsmall is
small is w
l
k l
wlarge is large is w
Elasticity of Substitution
y
mc
y
mc
Marginal Cost vs. Average Cost
dy
wlrkd y
wlrk
y
Costs MC
),(2)2,2( lkFlkF
AC
Marginal Cost vs. Average Cost
dy
wlrkd y
wlrk
y
Costs
MC = AC
),(2)2,2( lkFlkF
Marginal Cost vs. Average Cost
dy
wlrkd y
wlrk
y
Costs
MC
),(2)2,2( lkFlkF
AC
Estimating Production Functions
lAklkFy ),(
lkyA %%%%
Productivity Growth
Output Growth
Capital Growth
Labor Growth
Example: Estimating Production Functions
lAky A Cobb-Douglas Production function was estimated for the aggregate production sector of the US
30.63. lAky
Average Annual Growth = 1.5%
1
Example: Estimating Production Elasticities
npp llAky
Production LaborNon-Production Labor
IndustryFood/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
Profit Maximization and Industry Dynamics
After the determination of optimal production, the firm is faced with a cost function…
)(yTCTC
Further, the firm faces a demand for its product…
)( pyy
A quick diversion…
y
p
y
p
Demand refers to output as a function of price
)( pyy
Inverse demand refers to price as a function of output
)(ypp
D
Profit Maximization and Industry Dynamics
After the determination of optimal production, the firm is faced with a cost function…
)(yTCTC Further, the firm faces an inverse demand for its product…
)(ypp A firm needs to choose output to maximize profits…
)()()( yTCyypy
Profit Maximization
)()(max yTCyypy
First Order Necessary Conditions
0)(
dy
ydTCpy
dy
dp
Marginal Cost (MC)
MCpydy
dp
MCppp
y
dy
dp
MCpp
1
1
1
MCp
First Order Condition
Multiply and divide the first term by p
A little rearranging
Now, solve for price
MCpydy
dp
y
p
y
p
D
Initially, you are charging price (P) and generating sales equal to Y
Revenue = P*Y
To increase sales, you must lower your price
Cost, Price, and Market Structure
Market Structure Spectrum
Perfect Competition Monopoly
One Producer Supplies the entire Market
The market is supplied by many producers – each with zero market share
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.
Size Rank
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
C
Measuring Market Structure – Concentration Ratios
Size Rank
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
C
4CR Measures the cumulative market share of the top four firms
Concentration Ratios in US manufacturing; 1947 - 1997
Year
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
100CR 200CR50CR
Aggregate manufacturing in the US hasn’t really changed since WWII
Measuring Market Structure: The Herfindahl-Hirschman Index (HHI)
N
iisHHI
1
2
is = Market share of firm i
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
2is
HHI = 2,000
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B HHI = 500
HHI = 1,000
The HHI index penalizes a small number of total firms
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
HHI = 500HHI = 555
The HHI index also penalizes an unequal distribution of firms
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
1
1
MCp
Perfect Competition
Perfectly competitive firms are so small relative to the market that they can’t influence market price – they face a perfectly elastic demand curve
y
p
p
D
MC
*y
ATC
MCp
1
1
MCp
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)
y
p
p
MC = AC
*y
MCp
Perfect Competition
1
1
MCp
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.
MCp *22
Monopoly
y
p
p
D
MC
*y
ATC
MR MC
Example
1
1
MCp
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
MCp *33.14
Monopoly
y
p
p
D
MC
*y MR
MC
Example
Higher market concentration offers the potential for market power. However, does high market concentration guarantee market power?
P
MCPLI
The Lerner index measures the percentage of a
product’s price that is due to the markup
Perfect Competition Monopoly
MCp
0LI
1
1
MCp
1
LI
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
MCPLI
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
AC
MC
TC
y
dy
dTC
y
TC
%
%
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!!
1
S A scale economy index larger than one indicates the potential for a monopoly!
Cost Structure and Market Structure – Does it pay to be big?
y
Costs
MC
ATC
*y
1S
If market demand is always below y*, than this industry could become monopolistic!!
Globally scale economies
Costs
MC
ATC
Costs
MCATC
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.
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.