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


The elasticity of substitution measures curvature

k

l'

k

l

k

l

TRSkl

%

%

kl

TRS

TRSdkl

d



),(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


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


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


dy

wlrkd y

wlrk

y

Costs MC

),(2)2,2( lkFlkF

AC


dy

wlrkd y

wlrk

y

Costs

MC = AC

),(2)2,2( lkFlkF


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


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


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


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


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.

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Technology, Cost, and Price Finance 510: Microeconomic Analysis