Lecture 5

Transcript Lecture 5

Applications of Cost Theory

• • • Topics in this Chapter include: Estimation of Cost Functions using regressions » »

Short run

-- various methods including polynomial functions such as cubic or quadratic functions

Long run

-- various methods including • Engineering cost techniques • Survivor techniques Linear Break-Even Analysis and Operating Leverage Business Risk and Risk Assessment

Slide 1

Estimating Cost Functions

• • • Firms want to know what their costs are now, what their costs will be, and what they would be at different output levels.

Costs issues involve the type of cost (fixed, variable, average, etc.) and issues of time depreciation.

» Items often depreciate with use » Items can also depreciate with passage of time Because prices of inputs change with inflation, must consider deflating or detrending cost data.

Slide 2

Short Run Cost-Output Relationships

• • • Typically use TIME SERIES data for a plant or for firm, regression estimation is possible.

Typically use a functional form that “fits” the presumed shape.

SRTC is often CUBIC

•

SRTC = a+bQ+cQ 2 +dQ 3

STAC is often QUADRATIC SRAC = a+bQ+cQ 2

cubic

is S-shaped or backward S-shaped

quadratic is U-shaped or arch shaped.

Slide 3

• • • • •

Empirical Cost-Output Polynomial:

In Theory

Short run cost functions can be represented by a cubic relationship

TC = a + bQ + cQ 2 + dQ 3

From this we can find ATC (average total cost)

ATC = TC/Q = a/Q + b + cQ + dQ 2

We can also find MC (marginal cost)

MC = dTC/dQ = b + 2cQ + 3dQ 2

Notice that both ATC and MC are U-Shaped as represented by quadratic equations (to the power of 2) Notice also that if “d” is insignificant, the form is even simpler as the last term is zero in each of the above examples

Slide 4

• •

Estimating Short Run Cost Functions:

In Practice

Example: TIME SERIES data of total cost

Cubic

Total Cost (to the power of three)

TC = C 0 + C 1 Q + C 2 Q 2 + C 3 Q 3

Regression Output: Predictor Coeff Std Err T-value

Time Series Data: TC Q Q 2 Q 3 900 800 834

 20 400 8,000 15 19  225 3,375 361 6,859   Constant 1000 800 1.25

Q 50 20 2.5

Q-squared -10 2.5 -4.0

Q-cubed 2 1 2.0

R-square = .91

Adj R-square = .90

N = 35

Slide 5

PROBLEMS: 1.

Write

the cost regression as an equation. 2.

Find

the AC function. What is MC at Q=10?

3. Find the MC function. What is MC at Q=10?

1. TC = 1000 + 50 Q - 10 Q 2 + 2 Q 3 (1.25) (2.5) (4) (2) t-values in the parentheses 2.

AC = 1000/Q + 50 - 10 Q + 2 Q 2 3.

MC = 50 - 20 Q + 6 Q 2 NOTE: Total cost is S-shaped Average cost is U-shaped And even MC is U-shaped Find AC at Q=10. AC = 1000/

+ 50 – 10(

) + 2(

) 2 = 250 Find MC at Q=10. MC = 50 – 20 (

) + 6 (

) 2 = 100 = 450

Slide 6

Estimating LR Cost Relationships

• • • Use a CROSS SECTION of firms » SR costs usually uses a time series Assume that firms are near their lowest average cost for each output A quadratic curve of a cross section of ACs for various firms can be used.

LRAC

Slide 7

Economies of Scope in Banking

• • • • • •

Economies of scope

occur when producing two or more products jointly by one firm is less than the cost of producing them separately.

Banking offers economies of scope through offering people who can help customers with checking, savings, credit cards, mortgages, car loans, trust accounts, and many other services. Banks are expanding into other fields, including brokerage, insurance, bill paying, foreign exchange hedging, and other services expanding economies of scope.

Work by Jeffry Clark used a logarithmic cost function such as:

Ln TC

= a + b•

Consumer Lending + c •

Mortgage Lending He found evidence for Economies of Scope in banking up to about $100 million in assets.

Slide 8

Engineering Cost Approach

• • • •

Engineering Cost Techniques

offer an alternative to fitting lines through historical data points using regression analysis.

It uses knowledge about the efficiency of machinery. Some processes have pronounced economies of scale, whereas other processes (including the costs of raw materials) do not have economies of scale.

Size and volume are mathematically related, leading to engineering relationships. Large warehouses tend to be cheaper than small ones per cubic foot of space.

Slide 9

• • • •

Survivor Technique

The

Survivor Technique

tending to succeed over time, and what sizes are declining. examines what size of firms are This is a sort of Darwinian survival test for firm size.

Presently many banks are merging, leading one to conclude that small size offers disadvantages at this time.

Dry cleaners are not particularly growing in average size, however.

Slide 10

Break-even Analysis

Total Cost Total Revenue • • • We can have multiple B/E (break-even) points with non-linear costs & revenues.

If linear total cost and total revenue: » TR = P•Q » TC = F + V•Q • where V is Average Variable Cost • • F is Fixed Cost Q is Output

cost-volume-profit analysis

Q B/E B/E

Figure 9.5

Slide 11

• •

The Break-even Quantity: Q

B/E

At break-even: TR = TC » So, P•Q = F + V•Q PROBLEM : As a garage

Q b = F / ( P - V)

= F/CM » where contribution margin is: CM = ( P - V) contractor, find Q B/E if: P = $9,000 per garage V = $7,000 per garage & F = $40,000 per year

Slide 12

Answer

: Q = 40,000/(2,000)= 40/2 = 20 garages at the break-even point.

• •

Break-even Sales Volume

Amount of sales revenues that breaks even P•Q b = P•[F/(P-V)] = F / [ 1 - V/P ]

Ex:

Q = 20

, B/E Sales Volume is $9,000•20 = $180,000 Sales Volume Variable Cost Ratio

Slide 13

Target Profit Output

  Quantity needed to attain a target profit If  is the target profit,

target



= [ F +



] / (P-v) Q

Suppose want to attain $50,000 profit, then, Q target  = ($40,000 + $50,000)/$2,000 = $90,000/$2,000 = 45 garages

Slide 14

• •

Contribution Analysis

Another variation is to find if added sales through a ad campaign or new product is justified. It looks at the incremental contributions and incremental additions to cost.

Do the project if: » Added Contribution > Added Cost » (

P – v)

Q >

Direct Fixed Cost

» When this inequality holds, the project adds more to revenues than it adds to cost.

Limitations of B/E & Contribution Analysis Sometimes the assumptions do not hold 1.

Costs may be semi-variable Many times firms sell multiple products or small, medium, and large varieties There is uncertainty as to the P, V, and F in the problem 4.

Inconsistency in the planning horizon

Slide 15

Degree of Operating Leverage

Operating Profit Elasticity

• DOL = E  » sensitivity of operating profit (EBIT) • to changes in output Operating  = TR-TC = (P-v)•Q - F • Hence, DOL = 

•( Q/  ) =

(P-v)

•( Q/  ) =

(P-v)•Q / [(P-v)•Q - F]

A measure of the

importance of Fixed Cost

Business Risk

to fluctuations in output

Slide 16

Suppose the Contractor Builds 45 Garages, what is the D.O.L?

• • • DOL = (9000-7000) • 45 . {(9000-7000)•45 - 40000} = 90,000 / 50,000 = 1.8

A 1% INCREASE in Q 

1.8%

INCREASE in operating profit.

At the break-even point, DOL is INFINITE. » A small change in Q increase EBIT by astronomically large percentage rates

Slide 17

• • • •

Break-Even Analysis and Risk Assessment

One approach to risk, is the probability of losing money.

Let Q b be the breakeven quantity, and Q is the expected quantity produced.

is the number of standard deviations away from the mean z = (Q

b - Q )/ ^

 • 68% of the time within 1 standard deviation • 95% of the time within 2 standard deviations • 99% of the time within 3 standard deviations

Problem:

If the breakeven quantity is 5,000, and the expected number produced is 6,000, what is the chance of losing money if the standard deviation is 500?

Answer:

z =(5000 – 6000)/500 = -2. There is less than 2.5% chance of losing money. Using table B.1, the exact answer is .0228 or 2.28% chance of losing money.

Slide 18

Prices, Output, and Strategy:

Pure Competition and Monopolistic Competition

• •

Pure competition is a standard against which other market structures are compared. In it, there are many firms and the product is perfectly undifferentiated.



There are industries where are many firm, but the products or service are heterogeneous or differentiated. Monopolistic competition is when there are many firms, but the product or service is differentiated.



This brand competition may involve advertising campaigns and large promotional expenditures to stress often minor distinctions among products © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Slide 19

Competitive Strategy Analysis

• • • Many industries are already competitive, but firms need to find ways to

stay competitive Core Competencies

– technology-based expertise or knowledge on which a firm can focus its strategy.

Value Proposition

– basis for customer willing to pay more than cost-covering prices » Find value in the

value chain

» Find value in

Slide 20

The Strategy Process

Figure 10.1

Slide 21

Generic Types of Strategies

to Attain Sustainable Profits • • •

Product Differentiation Strategy

» A strategy that relies upon differences in products or processes affecting perceived customer value. » For example, Coca-Cola or Nestlé

Cost-based Strategies

» A strategy that relies upon low-cost operations, marketing, or distribution. For example, Southwest Airlines & Dell Computers

Information Technology Strategy

» Use IT capabilities to distinguish yourself from others » For example, Allstate Insurance & GPS tracking to offer lower insurance rates to those who don’t drive their best cars to work

Slide 22

The Relevant Market Concept

• • • A

market

is a group of economic agents that interact in a buyer seller relationship. The number and size of the buyers and sellers affect the nature of that relationship. A popular measure of concentration is the percentage of an industry comprised of the top 4 firms. Similarly, the market share held by the top 4 buyers is a popular measure of buyer concentration.

The relationship among firms is affected by: a. the number of firms and their relative sizes.

b. whether the product is differentiated or standardized.

c. whether decisions by firms are independent or coordinated (collusion).

Slide 23

Michael Porter’s Five Forces of Competitive Advantage The forces that determine competitive advantage are:

The Threat of Substitutes

can be offset by brands, complementors, and special functions served by the product.

The Threat of Entry

economies, restriction of access to distribution channels, or product differentiation.

can be reduced by high fixed costs, scale

The Power of Buyers

from the threat of concentration of buyers.

The Power of Suppliers

for the threat when concentrated suppliers of key inputs affect profitability.

The Intensity of Rivalry

impact profitability via market concentration, price competition tactics, exit barriers, ratio of FC to TC (

cost fixity

), and industry growth rates.

Slide 24

Figure 10.2

Slide 25

Break-even Sales Change Analysis

The

price-cost margin

percentage (PCM) is defined as P

CM = ( P – MC )/P.

A price cut may help or hurt profitability depending on price elasticities and price cost margins. We can ask how much quantity must change after a price cut to breakeven (from before the price cut)?

If we cut prices 10%, to breakeven, the percentage change in quantity ( D Q/Q) must be large enough to satisfy the equation to breakeven: P

CM / (PCM – .10) < (1 +

Q/Q )

The larger is the price-cost margin percentage, the smaller will be the necessary quantity response to justify cutting price.  If PCM is

80%,

then .8/(.8-.1) = 1.14. Hence, a 10% cut in price must be offset by only a 14% increase in quantity to breakeven.

 If PCM is only

20%,

then .2/(.2-.1) = 2. Hence, a 10% cut in price must be offset by at least a 20% increase in quantity to breakeven. So with

Hanes underwear

and low PCM discourages discounting.

Slide 26

There is a continuum of market structures:

Pure Competition Monopoly Monopolistic Competition Oligopoly



Best

Pure Competition assumes:

a very large number of buyers and sellers homogeneous product (standardized) complete knowledge of all relevant market information free entry and exit (no barriers) These assumptions imply several things about competitive markets, including price equals average cost in the long run.

Slide 27

 1.



Monopoly assumes:

Only one firm in the market area Low cross price elasticity with other products.

No interdependence with other competitors.

Substantial entry barriers These assumptions imply that the monopoly price is well above marginal cost. Monopoly is discussed in full in Chapter 11.

Monopolistic competition assumes:

A large number of firms, some of which may be dominant in size Differentiated products Independent decision making by individual firms Easy entry and exit These assumptions imply several things about monopolistic competition, including that the price in the long run is equal to average cost.

Slide 28



Oligopoly assumes:

1. Only a few firms in the market area 2. Products may be differentiated or undifferentiated • • 3. There is a large degree of interdependence with other competitors These assumptions imply several things about monopolies, including that the monopoly price is well above marginal cost. After going briefly over these four market structures, this chapter examines: » Pure Competition » Monopolistic Competition

Slide 29

CHARACTERISTICS OF DIFFERENT MARKET ORGANIZATIONS Although not every industry fits neatly into one of these categories, the categories do provide a useful and convenient framework for thinking about industry structure and behavior.

Slide 30

Price-Output Determination Under Pure Competition

Competitive firms attempt to maximize profits.

Competitive firms cannot charge more than the market price of others, since their product is identical to all others.

Hence, competitive firms are

price takers

Total revenue, TR, is P·Q, where price is given. Therefore, marginal revenue, MR, is price, P. Profit (  ) is total revenue minus total cost, that is: 

= TR TC.

Slide 31

• • Profit maximization implies that each firm produces an output where Price = Marginal Cost (

P = MC

). » To produce more than this quantity implies that P < MC, which is not the most profitable decision. » To produce less than where P=MC, implies that P > MC, and the firm could increase profits by expanding output.

In short run, a competitive firm may earn economic profits

In long run, entry pushes price down to the minimum point of the average cost curve, so that economic profits are zero.

Slide 32

A Competitive Market in the Short Run

• 1.

If P = MC for each firm, then each firm is doing what it thinks maximizes profits. Firms are in equilibrium.

Equilibrium for the industry if: Demand equals Supply at the going price In this example, the firm is earning » economic profits as P SR > AC.

When both (1) & (2) occur, the market is in a

Competitive Equilibrium P SR a firm Q MC 1 AC



MC D the industry CAN EARN ECON PROFITS IN THE SHORT RUN © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Slide 33

A Competitive Market in the Long Run

• • Industries which have economics profits draw entry and shift the  MC 1 curve out to  MC 2 where there is no reason for more firms to enter or firms to exit the industry Price covers all cost, so in the LR,

P=AC

which means that Economic Profits are zero.

P LR AC MC



MC 1



MC 2 entry D a firm the industry ZERO ECON PROFITS IN THE LONG RUN © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Slide 34

Persian Gulf Oil

Long Run Competitive Markets with external diseconomies of scale

•

Figure 10.5

$/barrel for oil Mexican Oil Brazilian Ethanol D2

• • • As demand rises for products, we find that inputs become more expensive. The rising cost is not due necessarily to the productivity of the firms, but higher prices for what they purchase.

One example is the rising price for crude oil. As demand in the world increases, the marginal seller of oil is ever pricier.

Slide 35

Long Run Equilibrium in an Increasing Cost Industry

As demand shifts from D1 to D2, the price rises to P2 and the long run supply curve is upward rising. The cause is the upward shift in AC that firms experience.

posted to a publicly accessible website, in whole or in part.

Slide 36

• •

Price-Output Determination Under

Monopolistic Competition

Monopolistic Competition » MARKET STRUCTURE • • • Many Firms and Many Buyers Easy Entry & Exit PRODUCT DIFFERENTIATION ! ! !

Historical Background » Joan Robinson “Economics of Imperfect Competition,” 1933 » Edward Chamberlin, “Theory of Monopolistic Competition,” 1933 • Small Groups & Large Groups

Slide 37

Product Differentiation

• • •

Differentiation

occurs when consumers perceive that a product differs from its competition on any physical or nonphysical characteristic, including price.

Examples:

restaurants, dealer-owned gas stations, video rental stores, book & convenience stores,

etc

Assumptions of the Model:

» Large number of firms » Differentiated Product » Conditions of Cost and Demand are Similar » Easy Entry & Exit

Slide 38

Basic Model of Monopolistic Competition

• • In the Short Run » » produce where MR= MC price on the demand curve NOTICE: » P > MC » economic profits exist P > AC » there exists incentives for entry into this industry

P M

MC AC

Slide 39

Profits in the SR Induces Entry

• • • Entry in this industry “steals” customers.

Demand curve shifts

inward RESULTS »

MR = MC

(like monopoly) »

P = AC

(like competition) » »

Profits in LR are zero

monopoly) (like competition)

P MC

AC

Slide 40

D D’

Properties of Monopolistic Competition

•

Inefficient Production

» »

EXCESS CAPACITY

•

not at least cost point of AC curve

Could Avoid Excess Capacity by

JOINTLY PRODUCING

at the same plant • • • • Kroger Salt & Morton Salt produced at the same plant

Sears’

Kenmore and Whirlpool dishwashers are built at same factory.

Does the expectation of zero profits in the future

stifle

innovation?

Is there

too much

product differentiation?

Slide 41

Selling and Promotional Expenses

• • Suppose that the price is determined outside of the model, as with liquor prices in some States.

We will expand promotional activities until the extra profit associated with the activity equals the extra cost of the promotion. • This decision rule for

Optimal Advertising

is when: Contribution Margin = Marginal Cost of Advertising • or

expand or

P – MC =

• D A/ D Q advertising whenever (P – MC)( D Q/ D A) >

where,

contribution

(P – MC) is the marginal profit contribution ( of an additional sale, and the

marginal cost of advertising

k •

D A D Q).

Slide 42

Example:

Radio Advertising

• • • To sell one more unit of output will cost the price of the added message,

, divided by the

marginal product of a dollar of advertising

( D Q/ D A). If a radio message costs $1000, and if that message yields 5 new items sold, then the marginal cost of advertising is $200, ($1000 /marginal product of advertising).

If it costs $200 to sell one more car (MCA=$200), and if the contribution of another car sold is $300 to profits, then we

should

expand promotional expenses.

Slide 43

Competitive Markets Under Asymmetric Information • Used car: who knows what about it? The buyer or the seller?

• •

Asymmetric Information

-- unequal or dissimilar knowledge among market participants.

Incomplete Information

-- uncertain knowledge of payoffs, choices, or types of opponents a market player faces.

Slide 44

Search Goods

versus

Experience Goods

• • • • •

Search goods

are products or services whose quality is best detected through a market search.

Experience goods

are products and services whose quality is undetected when purchased.

Warranties and firm reputations are used to assure quality.

But if someone is selling his or her car, isn't it likely that the car is no good? Is it

a lemon?

» This is an explanation why used car prices are new car prices.

so much lower than If one firm defrauds customers, how do the reputable firms signal that they are NOT like the fraudulent firm?

Slide 45

Adverse Selection and the Notorious Firm

• • • Suppose that a firm may decide to produce a

High Quality

Low Quality

product, and the buyer may decide to offer a

High Price

or a

Low Price

. Since the firm fears that if it offers a High Quality product but that buyers only offer a Low Price, they only produce Low Quality products and receive Low Prices. This is the problem of adverse selection

Slide 46

Notorious Firm Analysis

Payoffs in the boxes are for the seller only

• • • Simultaneous decisions of buyer & seller A risk averse decision by the firm is to make a

Low Quality

product

High Quality SELLER BUYER Hi Price Low Price 130 70

Best for the buyer is a low price, but a high quality good. Worst for the buyer is a high price but a low quality good.

Low Quality 150 90 We end in a trap of only poor quality goods at low prices.

Slide 47

• • • •

Solutions to the Problem of Adverse Selection

Regulation (Disclosure Laws, Truth in Lending) Reliance Relationships are long term, mutually beneficial agreements, often informal. Brand names (a form of a “ hostage ” to quality) Nonredeployable assets are assets that have little value in another other use 

Example

Dixie Cups

made with paper-cup machinery which cannot be used for other purposes — if Dixie Cups leak, the company is in trouble

Slide 48

Credible Commitments

• A

credible commitment

is a conditional strategy for establishing trust by promising to make the promise-giver worse off by violating that trust » such as a promise of product replacement if the product ever fails.

Examples : 1.

Dooney & Bourke promise life-time replacement of handbags 2.

Other firms have sometime promised: If any of my products fail to work, I will pay the buyer three-times their purchase price in recompense! Clearly, this commitment makes the firm worse off if they sell shoddy goods.

Brand names are a “bond” or “hostage” lost if products fail to live up to promises.

Slide 49

Mechanisms for commitments

• • • Use of

nonredeployable assets

such as reputation. Once lost, a good reputation is hard to rebuild.

Entering into

alliance relationships

which would fall apart if any party violated their commitments.

using a "

hostage mechanism

" that is irreversible and irrevocable can deter breaking commitments. » Examples are "double your money back guarantees," and "most favored nation" clauses.

Slide 50

Lecture 5

Transcript Lecture 5

Applications of Cost Theory

Estimating Cost Functions

Short Run Cost-Output Relationships

Empirical Cost-Output Polynomial:

In Theory

Estimating Short Run Cost Functions:

In Practice

Estimating LR Cost Relationships

LRAC

Economies of Scope in Banking

Engineering Cost Approach

Survivor Technique

Break-even Analysis

The Break-even Quantity: Q

Answer

: Q = 40,000/(2,000)= 40/2 = 20 garages at the break-even point.

Target Profit Output

Contribution Analysis

Degree of Operating Leverage

Operating Profit Elasticity

Suppose the Contractor Builds 45 Garages, what is the D.O.L?

Break-Even Analysis and Risk Assessment

Competitive Strategy Analysis

The Strategy Process

Generic Types of Strategies

The Relevant Market Concept

Figure 10.2

Break-even Sales Change Analysis

There is a continuum of market structures:

Pure Competition assumes:

Oligopoly assumes:

Price-Output Determination Under Pure Competition

In short run, a competitive firm may earn economic profits

A Competitive Market in the Short Run

A Competitive Market in the Long Run

Long Run Competitive Markets with external diseconomies of scale

Long Run Equilibrium in an Increasing Cost Industry

Price-Output Determination Under

Monopolistic Competition

Product Differentiation

Basic Model of Monopolistic Competition

MC AC

Profits in the SR Induces Entry

AC

Properties of Monopolistic Competition

Inefficient Production

not at least cost point of AC curve

Selling and Promotional Expenses

Example:

Radio Advertising

Search Goods

Experience Goods

Adverse Selection and the Notorious Firm

Notorious Firm Analysis

Solutions to the Problem of Adverse Selection

Credible Commitments

Mechanisms for commitments

Directory