managerialeconomics 2013 folded

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University of Siegen

Managerial Economics

PD Dr. Hagen Bobzin

University of Siegen

Spring 2013

http://www.hagen-bobzin.de/vorlesungen/index.html

University of Siegen, April 2013 PD Dr. Hagen Bobzin, Managerial Economics 1/111

Contents

EconomicsThe Economic Problem

Market Economy


Demand Analysis

Preferences

Constraints

Utility Maximization

Consumer Behavior

Supply Analysis

Production Theory

Cost Theory

Profit Maximization

Behavior of Firms



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Contents

Market Analysis

Market Equilibrium

Market Structure

Economic Policy

Strategic Behavior of Firms

Interaction with Customers

Interaction with Competitors

Interaction with the Government

Risk and Uncertainty

Investment Behavior


References

Dobbs, I. M. (2000), Managerial Economics: Firms, Markets, and

Business Decisions, Oxford : University Press.

Froeb, L. M., McCann, B. (2010), Managerial Economics: A Problem

Solving Approach, 2nd ed., Cincinnati, OH : South-Western.

Hirschey, M. (2009), Fundamentals of Managerial Economics, 9. ed.,

Cincinnati : South-Western.

Jones, T. (2004), Business Economics and Managerial Decision Making,

Chichester : John Wiley.

Varian, H. R. (2005), Intermediate Microeconomics, 7. ed., New York :

Norton.

Webster, T. J. (2003), Managerial Economics: Theory and Practice,

Amsterdam : Academic Press.

Wilkinson, N. (2005), Managerial Economics: A Problem-Solving

Approach, Cambridge : Cambridge University.



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1Economics1.1The Economic Problem

Economics

The Economic Problem

Market Economy


Demand Analysis

Preferences

Constraints


Consumer Behavior

Supply Analysis

Production Theory

Cost Theory

Profit Maximization

Behavior of Firms



The economic problemis a quantitative conflict:

scarce resources including environment (factors of production) =

scarcityof goods (commodities and services)

Scarcity contradicts unlimited needs!

This trade-off requires decision making:

alternative usage of scarce resources = opportunity cost(give up

benefits of alternatives)



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Economic Agents

Decision Makers(Economic Agents)

households/consumers firms/producers state/government/ society

economic

plans: consumption

: savings: supply of labor

: demand forresources

: investment: supply of goods

: materialinfrastructure

: set, control,enforce rules

: supply of moneytargets utility maximization profit maximization : serving collective

needs: income

redistribution: operational money


1Economics1.2Market Economy

Market Price Mechanism

In amarket economyall actors (players),

: households or consumers,

: firms or producers, and

: the government,

form their individual economic plans on the basis of selfish interests.

The division of labor requires that the actors interact on markets:

: factor markets,

: goods markets.

The coordination of economic plans is made by the market price

mechanism.



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1Economics1.2Market Economy

Circular Flows of Income

: factor markets

: goods markets

households firms

factor services

consumption goods and services

production goods


1Economics1.3Managerial Economics



: Application of economic methods in the managerial decision

process: Quantitative methods (numerical analysis, statistical estimation)

: Firms point of view (e.g., game theory)



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Firms are major economic institutions in market economies.

Common characteristics:

: Owners (e.g., shareholders)

: Managers (executing and organizing units)

: Pool of resources (inputs): labor incl. skills and competences: physical capital, and: financial capital

: Organizational structure

(cf. new institutional economics: governance structure)




Owners, managers and workers may have different objectives

: profit vs. revenue maximization (Baumol, 1959), see p. 56.: short vs. long run targets: difficulties in performance assessment (principal agent problems,

moral hazard etc.)

Examples:: corporations including share holders and managers: wage bargaining between labor unions and management



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Overall assessment of firms by markets:

: factor cost: value of resources used up: revenue: value of generated goods (commodities and services): profit revenue cost: decision regarding firms via markets

: pofit 0: stay at the market, go on with activities: pofit < 0: leave the market


2Demand Analysis

Demand Analysis

EconomicsThe Economic Problem

Market Economy


Demand Analysis

Preferences

Constraints


Consumer Behavior

Supply Analysis

Production Theory

Cost Theory

Profit Maximization

Behavior of Firms



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2Demand Analysis2.1Preferences

Objective.

Explain how consumers make choices (consumer behavior)

People perceive a lack of many things and they have the desire to

correct this situation wantsand needsHouseholds consume baskets of commodities and services (goods) to

satisfy their needs.

Preferencesof a person explain how the person assesses alternative

consumption bundles(x1,x2).

Example: (x1,x2) (x1,x2

)means that(x1,x2)is not worse than

(x1

,x2

).

The well-being induced by consumption is calledutility.



Utility Function

Theutility function u(x1,x2)is a mathematical tool indicating the utility

level or degree of satisfaction resulting from the consumption bundle

(x1,x2).

Remark: It can be shown that a continuous utility function exists if the

preferences hold good the following conditions:

1. Reflexivity: x

xfor all x

2. Completeness: [x x orx x] for everyx= x

3. Transitivity: [x x and x x] = x x

4. Continuity: All sets {x| x x} are closed.



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Utility Function

Graphical representation of a utility function U= u(x1,x2)and of

indifference curves; anindifference curvedescribes all consumption

bundels yielding the same utility level (similar to contour lines of a hill).



Marginal Utility

Holdingx2 fixed (here x 2andx2 ) and varying x1, we gain other cuts ofthe graph of the utility function.

marginal utilityofx1 = u(x1,x

2)

x1

U

x1(x2 fixed)

1. Gossens Law: the increments of utility decrease (or diminishing

marginal utility)



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Marginal Utility

Consuming more of both commodities, i.e. (x1, x2), indicates that

the utility level is increased byU. In reality, however, we cannot

measureUnumerically, but we knowU> 0.

Rule of thumb: the more we consume, the better we feel, the higherthe utility level is.



Marginal Utility

Analyticsregarding the utility function U=u(x1,x2):

ComputeUwhen varying x1 and x2by discrete amountsx1and

x2, respectively.

Thetotal diffentialrefers to infinitesimally small changes:

dU= u

x1dx1+

u

x2dx2

Movements along an indifference curve require dU= 0as the utilitylevel is constant! Such movements describe a substitution process (give

dx2to get dx1).

dx1 =u/x2

u/x1dx2

The fraction of marginal utilities is calledmarginal rate of substitution.



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Opportunity Cost

Themarginal rate of substitution (MRS) dx2/dx1denotes the

(negative) slope of an indifference curve at some point.

x1

x2

P

Q

RS

U= u(x1,x2)= konst.

xa2x1 > xb2x1

> xc2x1

x1x1x1

xa2

xb2

xc2

The graph indicatesdiminishing MRS: the relative scarcity ofx2

increases with each additional unit x1 ( P Q R S).The forced waiver ofx2 for additional units ofx1 is calledopportunity

cost.



Total Differential

Mathematical Results

: utility function: U=u(x1,x2)

: marginal utilities: u(x1,x2)

x1and

u(x1,x2)

x2

: total differential: dU= u

x1

dx1+ u

x2

dx2

: indifference curve: U= const. or dU=0

: marginal rate of substitution: MRS =dx2

dx1=

u/x2

u/x1



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2Demand Analysis2.2Constraints

Budget Constraint

Household would like to climb on top of the utility mountain, but in

reality they cannot go as far as they want to.

What situations are feasible?: restricted amount of money/income (budget constraint)

y p1x1+ p2x2 (income expenditure)

: time constraint (e.g., working/leisure time per day)

: family, mobility etc.


2Demand Analysis2.2Constraints

Budget Constraint

Budget line

y= p1x1+ p2x2 x2 = y

p2

p1

p2x1

Parametric variations (effects on the budget line)

x1

x2p1

x1

x2p2

x1

x2y



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2Demand Analysis2.3Utility Maximization

Utility Maximization(no technical analytics here)

Find the most preferred situation (commodity bundle (x1, x2)) among

all feasible actions determined by a given budget!

maxx1,x2

{u(x1,x2)| y p1x1+ p2x2, x1 0,x2 0}

x1

x2

x2

x1

U

Theoptimum consumption bundle( x1, x2)(demand)depends besides

preferences on the commodity prices p1, p2 and the income y.


2Demand Analysis2.4Consumer Behavior

Varying the parameters (p1,p2,y) of the utility maximization problem

forces the houshold to adjust its consumption according to the new

situation and its preferences.

Thebehavior of householdscan now be described by (Marshallian)

demand functions

xD1 (p1, p2,y) and x

D2 (p1, p2,y).

In what follows we practice aceteris paribus analysis, that is we vary

one parameter (e.g., p1) while holding the others (i.e. p2and y) fixed.



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Price Consumption Curves

price consumption curve (PCC): p2 = x1,x2 ?

All geometric points of household optima when varying one price.

: p2 = x2 (usual case)

p2 = x2 possible (Giffen good)

: p2 = (x2 = ) x1 (substitutes)p2 = (x2 = ) x1 (complements)



Demand Curve

graphical derivation of ademand curve xD1 (p1, p2,y)

x1

x2

p1 > p1 > p

1

p1

p1

p1

y

p1

y

p1

y

p1

x1

p1

Law of demand:

p1 = xD1

(almost always)



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Income Consumption Curves

Income consumption curve (ICC): y = x2 ?



Income Consumption Curves

Criticism of indifference curve analysis

: No explaination how preferences are formed or changed.

: Consumers frequently do not behave rationally but they use rules

of thumb or follow their instincts.

: Consumers do not make marginal calculations explicitly. One may

argue, however, that the results are reasonable approximations.

: Consumers are not sufficiently well informed to make rational

choices between products (cost of information).: A hierarchy of needs with some goods being more important than

others is difficult to implement (lexicographic ordering).

: Utility functions may not be independent and one consumers

utility may be influenced by the actions of another (cf. income

distribution below, external effects).

: Refinements of theory not presented here.



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Aggregation

Individual demand functionsfor every householdh = 1,,H

xDjh = xDjh (p1,,pj,, pn,yh )

Market demand functionsfor every good jare derived byaggregation:

xDj = xDj1(p1,,pn,y1)+ +x

DjH(p1,, pn,yH)

Caveat:

The market demand functions depend on the distribution of income

among households. We ignore this problem here and note simply

xDj = xDj (p1,, pn )



Aggregation

Graphical aggregationof the demand for commodity jregarding twohouseholds.

Note: Only the first households demand is positive above the upper

dashed line.

Note: Ifpj = xDjh for all households, we obtain the law of

demandfor the whole market; pj = xDj .

Note: different results for price discimination, see p. 83.



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Elasticities

: Elasticitiesdenote the relative (or percentage) change of a variable

y(effect) in response to the relative change of an independent

variable x (reason)

xy =

y/y

x/x

dy

dx

x

y =

rel. change ofy

rel. change ofx

: own price elasticityx1p1 = dx1

dp1

p1

x1

: cross price elasticityx1p2 = dx1

dp2

p2

x1

: income elasticityx1y = dx1

dy

y

x1

As firms do not know the preferences of their customers, they have toobserve their behavior (revealed preferences) and to forecast their

reaction by estimated elasticities refer to market demand functions.



Elasticities

Example: a linear price-demand function p= a bx

price elasticityxp = dx

dp

p

x=1

a

bx

x

p

xp =0

totally price inelastic

x

p

xp =

totally price elastic

x

p

ab

a2b

xp =

xp = 1

xp =0

The steeper the line, the more comfortable for the firms.



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Other Decision Problems

Choice between leisure F/labor time Land consumption x

maxx, F

{u(x,F)|wL px, L + F=16}

Thedemand for leisure timecorresponds to thesupply of labor.Both functions, the supply of labor and the demand for consumption,

depend on the factor prices (here the wage rate w) and commodity

prices (here p).

Choice between present consumption c1 and savings s1 (or future

consumptionc2)

maxc1,c2

{u(c1, c2)| y1 = c1+ s1, y2+ (1 + r)s1 =c2}



Remarks on Managerial Economics

: Firms need to know the preferences of their customers and to

adapt to these preferences best possible.: demand estimation (quantitative methods, statistical estimation): promotion / advertisement (take influence on preferences): price discrimination (spatial separation of markets, separation of

consumer groups, see p. 83): differentiated commodities (similar goods with different

combinations of characteristics (houses, cars ...) hedonistic

prices, cf. Lancaster (1966)



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3Supply Analysis

Supply Analysis

Economics

The Economic Problem

Market Economy


Demand Analysis

Preferences

Constraints


Consumer Behavior

Supply Analysis

Production Theory

Cost Theory

Profit Maximization

Behavior of Firms


3Supply Analysis3.1Production Theory

Supply Analysis

Firms transformfactors of production

: labor, land (original factors) and capital (derived factor): more precisely, v1,, vm

intooutputs

: consumption goods, investment goods: commodities and services

: x1,,xn

As long as the economy values the outputs higher than the

corresponding inputs (both at market prices), the transformation

process is rewarded aprofit. Otherwise the respective firms make a

lossand they have to leave the market.



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Production Process



Production Function

Production plansdenote technically feasible input output combinations.

(v1, v2,x) = (2inputs, 1output)

Technically efficientproduction plans denote actions without any waste

neither of inputs nor of outputs.

Theproduction function

f(v1, v2)= x

denotes themaximumoutput x given the inputs (v1, v2)and, almost

always, theminimuminputs needed to produce x. The problem of

technical efficiency is solved, e.g., by engineers.



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Production Function

Isoquantsdenote all input combinations (v1, v2)providing the same

(maximum) outputx.

Cobb-Douglas production function x= av1

v

2



Production Function

Linear limitational production function

x= min

v1

a1,

v2

a2

production process



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Production Function

a production function representing thelaw of returns( next page)



Law of returns

Thelaw of returnsrefers usually to just one variable input, sayv2,

while all other inputs are fixed, herev1.

x = f(v1, v2)



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Law of returns

above: partial variationof inputs

now: total variationof inputs (walk along a production process)

The analysis ofreturns to scalevaries all inputs by the same factor.

f(v1, v2)= x>1= f(v1, v2) x

increasing returns to scale

constant returns to scale

decreasing returns to scale

Example: constant returns to scale say that doubling all inputs (= 2)

also doubles the output.



(back to partial variations of inputs)

Theaverage productivityx/v1 denotes the output per unit of input v1.

v1

x

x= x(v1, v2)

v1

x

x

v1

=tan



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Themarginal productivityof an input v1denotes the additional output

dxwith respect to the last additional (infinitesimally small) unit ofv1,

e.g., dv1.

v1

x

x= f(v1, v2)

v1

xdv1

v1

x dx dx= f(v1, v2)

v1 tan

dv1

x

v1

dx

dv1=

f(v1, v2)

v1



law of returns

x= f(v1, v2)

average productivityx

v1

marginal productivityf(v1, v2)

v1



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3Supply Analysis3.2Cost Theory

Cost Function

Production cost= used quantities of inputs(v1, v2)times their given

factor prices (q1, q2)

q1v1+ q2v2

Cost function= minimumcost to produce a given output x at given

factor pricesq1,q2with respect to the known production technology.

c(q1, q2,x) minv1,v2

{q1v1+ q2v2|x = f(v1, v2)}

Variables of the minimization problem: inputsv1,v2Parameters: factor pricesq1,q2, outputx

Technical efficiency guaranteed by the production function.



Cost Functions in the Short Run

Production function x = f(v1, v2)with a fixed input ( short run)

Cost function

c(q1, q2,x)= minv1

q1v1+ q2v2| x = f(v1, v2)

= q1f

1(x, v2) + q2v2

= cv(x) + cF

v1

x capacity limit

q1 = 1/2 +cF flip

q1v1

x

c F x

c(x)

cFcapacitylimit



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Cost Functions in the Short Run

cost functionc(x)= cv(x) + cF

average costc(x)

x =tan

marginal costdc(x)

dx =c(x)

average variable cost

cv(x)/x= tan

average fixed costq2v2

x

= cF

x... to be continued on p. 59.

x

c

cF

x

c

x, c c

(x)

c/xcv/x

cF/x



Cost Functions in the Long Run

Production function x = f(v1, v2)with all inputs variable ( long run)

The cost function

c(q1, q2,x)= min

v1,v2 q1v1+ q2v2|x= f(v1, v2)denotes the minimum factor cost for a given output x(and given factor

pricesq1,q2).



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Constrained Programming

Mathematical solution (constrained programming)

Lagrangean function

L(v1, v2, ) = q1v1+ q2v2+ x f(v1, v2)Necessary optimum conditions

L

v1=q1

f(v1, v2)

v1=0

L

v2=q2

f(v1, v2)

v2=0

L

= x f(v1, v2)= 0

This is a system of 3 equations with 3 variables.



Marginal Rate of Substitution (MRS)

Remember: The slope of an isoquant x = f(v1, v2)= constant can be

calculated by the total differential.

dx= 0 = f(v1, v2)

v1dv1+

f(v1, v2)

v2dv2

dv2

dv1=

f/v1

f/v2

v1

v2

x= f(v1, v2)= const.

v1 v1

=dv1

v2

v2

dv2

marginal rate of technical

substitution (MRS)

MRS=dv2

dv1

v2

v1



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Minimum Cost Combination (MCC)

Graphical determination of aminimum cost combination (v1, v2)for

the production of a given amountx.

: red isoquant given: x= f(v1, v2)= const.: iso-cost line: ciso =q1v1+ q2v2

: cost minimum (green line): minimum cost combination (v1, v2)

v1

v2

x= f(v1, v2)

v2

v1

ciso


3Supply Analysis3.3Profit Maximization

Remark:

Economist analyze almost alwaysprofit maximizationas the relevant

problem. Complex problem: profit maximization necessarily requires

cost minimization.

But many firms persue some sort ofrevenue maximization(Baumol,

1959)

: Compatible if all costs are fixed or if the revenues grow faster

than production cost.

: Revenue is easier to measure (profit is a residual); managers

prefer short-term goals.

: A revenue target is easier to use when motivating staff.



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The Problem in General

Profit Maximization

Find the most preferred production plan(v1, v2,x)among all

technically feasible actions!

profit revenue cost

maximumprofit

(q1, q2, p) maxv1,v2,x

{px q1v1 q2v2| x = f(v1, v2)}

(q1, q2, p)= maxx

px c(q1, q2,x)

(q1, q2, p)= maxv1,v2

p f(v1, v2) q1v1 q2v2



Short Run Analysis

Profit maximizing output x( supply) in the short run

(x)= px c(x) != max

= ( x)= 0 p= c ( x) (price = marginal cost)

und ( x) 0

x

c(x)= cv(x) + cF

x

r= px

x

c, r, rc

x



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Short Run Analysis

All curves have been derived on p. 51.

p

p

x

c

x,

c

x

c

x

c/x

cv/x

cF/x

profit

lossfirms optimum (break even point)

firms minimum (production barrier)


3Supply Analysis3.4Behavior of Firms

Supply Functions

Supply functionsfor the outputs stem from profit maximization

maxx

r(p,x) c(q1, q2,x) = r(p,x)

x = p=

c(q1, q2,x)

x

Different notation if we drop given factor pricesq1andq2

maxx

px c(x) = p= dr(x)

dx=

dc(x)

dx

M R r (x)= c (x) MC

Solving themarginal cost pricing rule p= c (x)forxyields the

supply function

x= xS(p) (or more precisely = xS(q1, q2,p))



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Law of Supply

By plausibility (no mathematical proof here)

p = profit per unit = x= xS(p)

If each firm behaves this way, market supply does the same

(aggregation).

Thelaw of supplystates that if the price of a commodity increases, the

market supply increases, too.

x

p xS



Demand Functions

Demand functionsfor inputs stem from profit maximization

maxv1,v2

p f(v1, v2) q1v1 q2v2 = pf(v1, v2)

v1=q1

and pf(v1, v2)

v2=q2

Factors are paid according to theirmonetary marginal productivity.

Solving forv1andv2is more difficult than before (a system of 2equations for 2 inputsv1,v2). The result denotes the demand functions

v1 =vD1 (q1, q2, p ) and v2 = v

D2(q1, q2, p)

The demand for inputs is directly connected to the supply of outputs via

the production function!



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Demand Functions

Graphical determination of factor demand (cf. page 48)

v1

x

law of returns x = f(v1, v2)

v1

f

v1

q1

v1

f

v1

p f

v1with p> 1

factor demand viaq1= p f

v1



Parametric Variations

Parametric variations(reactions by plausibility)

p = x (law of supply) = v1 , v2

q1 = profit per unit = x = v1 , v2

The usual reaction (q1 , v1 ) is called thelaw of demand.

Caveat:

q1 (e.g., wage rate),v2 (e.g., capital stock) also plausible

(substitution of factors of production)



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Elasticities

elasticity of the demand forv1with respect to the price p

vD1

(q1, q2,p)

p

p

v1

v1/v1

p/p

effect

reason

own price elasticity

vD1(q1, q2, p)

q1

q1

v1

v1/v1

q1/q1

cross price elasticity

vD1

(q1, q2, p)

q2

q2

v1

v1/v1

q2/q2



Long Run Analysis

Up until now fixed inputs possible (e.g., physical capital stock)

short runanalysis

c(q1, q2,x; v2)= maxv1

{q1v1+ q2v2| x = f(v1, v2)}

In thelong runall inputs are variable! ( optimal sizev2of an

enterprise)

c(q1, q2,x)= maxv1,v2

{q1v1+ q2v2| x = f(v1, v2)}

The long run cost functionc(q1, q2,x)is the envelope of all short run

cost functionsc(q1, q2,x; v2)(mathematical proof dropped).

Graphics in Schumann (1999, pp. 183 ff.)



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Denote short run cost functions

c(s) c(q1, q2,x; v2 (s))

wherev2(s) is a given physical capital stock (firms size) with fixed costs

c(s)

F

=q2v2(s)

x

c

c(1)F

c(1)

c(2)F

c(2)

c(3)F

c(3) c



production function x = av21

(v2 v1)(b v2)

v1

xlaw of returnsv250

v1

xvariation of the capital stock



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v1

xlaw of returnsv250

x

cxcost function for v250



x

cxcost functions for variation of v2

x

cxlong run cost functionred envelope



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graphical presentation of

: average cost curves (short and long run)

: marginal cost curves (short and long run)

: optimum choice ofv2and xgiven a market price p

: supply curve in the long run (increasing part of the marginal cost

curve starting in the minimum of the long run average cost curve)

: adjustment of capital stocks (fixed in the short run) by investments


4Market Analysis

Market Analysis

Market Equilibrium

Market Structure

Economic Policy






Investment Behavior



37/56

4Market Analysis4.1Market Equilibrium

Price Formation

Price formation on markets: On all goods markets (j= 1,, n)

and on all factor markets (i= 1,, m) an equilibrium price (supply =

demand) is to be determined simultaneously.

1. individual demand and supply curves (all agents behave as pricetakers, i.e. market prices are seen as given)

2. aggregation of individual behavior (generates market demand and

market supply curves)

3. price formation (price adjustment until some equilibrium is found)

xD > xS = p and vice versa

4. go back to step 1. with new market price

These processes are to be repeated permanently (new commodities,

new market agents, technical progress, inflation, etc.).



price formationxS > xD p

xS < xD p

market demand

p xD

market supply

pxS

individual demand individual supply

aggregation aggregation

new price p new price p



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Market equilibrium: situation where market demand and market

supply match (coordination by market prices)

: demand xDj = xDj (p1,,pj,, pn )

: supplyxS

j = xS

j (p1,

, pj,

, pn ): equilibrium xDj = x

Sj = x

j , equilibrium price p

j

xj

pjxSjx

Dj

pj

xj

excess supply, pj

excess demand, pj



Comparative Statics

Variations of parameters

: parameters here p1,, pn without pj

: changes in preferences, technical progress

: variations of the number of households and firms

: shocks external to the market (taxes, earth quakes, etc.)



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4Market Analysis4.2Market Structure

Market structure: Classification of markets by von Stackelberg

supply sidenumber

of agents one few many

one bilateralmonopoly

constraineddemand

monopoly

demandmonopoly

(monopson)

few

constrained

supply

monopoly

bilateral

oligopoly

demand

oligopoly

many supply

monopoly

supply

oligopoly polypoly

demandside

: market structure and market power are closely related

: firms try to get rid of competition and to gain market power: differentiated commodities (a monopoly with close substitutes)


4Market Analysis4.2Market Structure

Perfect Competition

Idea: In thepolypoly, buyers and sellers are so numerous that nobody

has the power to influence market prices. Thisreference caseis

referred to as perfect competition provided a list of prerequisites

constitutes anideal situationwithout any market power:

: no barriers to entry (or exit): homogeneous goods (perfectly divisible, equal quality,...)

: complete information (about prices and quality): no preferences with respect to time, location, or persons: unlimited ability to react to changes in a timely manner

If one of these conditions fails to hold true as almost always in reality

there are starting points of market power, which can be expected to

be abused.



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4Market Analysis4.3Economic Policy

Economic Policy

The government has to fix, to control, and to enforce rules valid for

the market system (fair play, shelter the society including households

and firms from an abuse of market power).Example: control of mergers and acquisitions, anti-trust law

Other government interventions are to be taken into account (e.g.,

taxes, rules, laws, price floors or ceilings, social legislation etc.)

Summary: The economic constitution is the outcome of interactions

between households (weakest group), firms (frequently organized as

powerful lobbies), and the government.


5Strategic Behavior of Firms


Market Analysis

Market Equilibrium

Market Structure

Economic Policy






Investment Behavior



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5Strategic Behavior of Firms5.1Interaction with Customers

Price Discrimination

Price discrimination

two groups of consumers (e.g., two regions) with different demand

functions

maxx1,x2

p1(x1)x1+ p2(x2)x2 c(x1+ x2)

optimum conditions withx = x1+ x2

p1(x1)x1+ p1(x1)= c(x) (note: dx/dx1 =1)

p2(x2)x2+ p2(x2)= c(x) (note: dx/dx2 =1)

therefore

p1(x1)

1 +

1

x1p1

= p2(x2)

1 +

1

x2p2

The group with the more inelastic demand is charged the higher price.

p1 > p2 0 > x1p1 > x2p2




example for linear demand curves (cf. p. 32)

x1

p1

x2

p2

x= x1+ x2

p c(x)

Cp0p

1

p2

Problem: the groups must be distinguishable from each other.

Otherwise members of the first group can argue to belong to the

second group.



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Examples of price discrimination

: Children, old people, students etc. pay less than normal.: Cheaper hotel rooms on weekends.: Cheaper flight tickets if a weekend is included in the trip

(holidaymakers vs. businessmen): Different prices in the home country and foreign countries (avoid

re-importation)



Strategies to Gain Market Power

Strategies of firms to establish a niche with monopoly power up to

some degree:

: differentiated commodities (get rid of homogeneous commodities

and competitors providing the same good): promotion, advertisement (try to reshape the preferences of

customers, the steeper the demand curve the better): consumers tend to stick to commodities (are willing to pay a

higher price) due to cost of information;

avoid market transparency and hide information (fish food: price

per liter rather than price per kilogram, small and large balls in

different colors, best hiding strategy: price per 743 ml for big

multi-colored balls): lazy consumers implicitly accept the market power of firms,

however, only up to a certain degree (do not lose them)



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5Strategic Behavior of Firms5.2Interaction with Competitors

Differentiated commodities indicate already that firms do not only

interact with their customers but also with competitors.

: Game theory, especially, gives a vast literature on the behavior of

interacting competitors (product strategies, pricing strategies,

threat strategies, etc.): Monopolies: monopolist (incumbent) vs. potential competitors: Duopolies: autonomous or heteronomous/conjectural behavior

setting either prices or quantities: Oligopolies: monopolistic competition with differentiated

commodities: Cartels (e.g., cooperating duopolists or collusion): ... many more scenarios

Problem of legal authorities: what is fair and what is a provable (!)abuse of market power?



Cournot-Nash solution in aduopoly

: two firms producing one commodity (x= x1+ x2) with individual

cost functionsc1(x1)and c2(x2): a common price-demand-curve p= p(x1+ x2): individual profit functions; both assume that the output of the

competitor is given.

1(x1)= p(x1+ x2)x1 c1(x1)

2(x2)= p(x1+ x2)x2 c2(x2)

: Thereaction curvesdenote the best (i.e. profit maximizing)

answer of each duopolist given the output of his opponent.

x2 x1and x1 x2: TheCournot-Nash solutiondenotes an intersection point of the

two reaction curves. Such a point represents a reciprocally best

answers to the opponents strategy. x1 = x1 x2 = x2



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Analytical solution

Necessary optimum conditions

1(x1)= p (x1+ x2)x1+ p(x1+ x2) c

1(x1)= 0

2(x2)= p (x1+ x2)x2+ p(x1+ x2) c2(x2)= 0

These are the two reaction curves; renaming gives

x1 = R1(x2) (optimum answer of the 1st duopolist to x2)

x2 = R2(x1) (optimum answer of the 2nd duopolist to x1)

Any intersection point with x1 = R1( x2)and x2 = R2( x1)denotes a

mutually best answer.

None of the two duopolists will change its behavior.



: price demand function: p(x1+ x2)= a b(x1+ x2): cost function firm j: cj(xj )= cxj with (j= 1, 2): profit function firm j: j =[a b(x1+ x2)]xj cx jwith

(j= 1, 2)

2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2



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2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2isoprofit curves of firm 1

2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2isoprofit curves of firm 2



2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2CournotNash solution



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Asymmetric solution of von Stackelberg

: Same duopoly as before, but:: One of the duopolists can act independently of the other.

: The duopolists in the dependent position takes the output x1ofhis opponent as given. Reaction curve: x2 = R2(x1)

: New asymmetric solution:

The 1st independent duopolist computes the reaction function

x2 = R2(x1)of his competitor and maximizes with this additional

information his own profit:

1(x1)= p

x1+ R2(x1)

x1 c1(x1) max



: firm 1 in the independent position (leader): firm 2 in the dependent position (follower)

2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2

von Stackelberg solution



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Collusion (symmetric cartel solution)

2 4 6 8 10 12 14 x1

2

4

6

8

10

12

14

x2cartel solution



Problems with reaction functions:

: Is there a unique intersection point? (no, one, more than one

intersection points): Does some intersection point represent a stable solution?

Adjustment processes to the intersection point?: How does the independent duopolist know the reaction curve of

his opponent?: Is the independent position always profitable (first mover

advantage)?: What information do legal authorities need to shelter the society

from an abuse of market power?



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5Strategic Behavior of Firms5.3Interaction with the Government

Regulation

: The government has to fix rules for the market systems

(regarding, e.g., fair trade).

: Governments need many information about: the behavior of market participants (consumer preferences),: production techniques and/or cost functions,: competitive strategies (market power),: consequences of new rules (who wins, who loses): and many more.

: Many safeguarding actions of the government do not show the

results wanted. They have direct and indirect effects (no market,

but policy failure)



Regulation in a monopoly

example: supply monopoly (compare Cournots solution with

as-if-competition)

x

c, r

r, p

p(x)r (x)

c/x

c (x)

r = c

x

p Cournots solution (r = c

)

as-if-competition (p = c )



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Result: In the Cournot solution, the monopolist sells a smaller amount

at a higher price compared to the solution with as-if-competition.

Possible solution: Regulation by government (enforce the marginal

cost pricing rule)

Problem: If average cost per unit exceeds the marginal cost price, the

firm operates at a loss. In the long run it would have to leave the

market.

Other possible solution: allow prices to exceed marginal cost, but

the firm has to operate at zero (or reasonable) profit.

Other problem: hidden information, dynamic investment behavior of

firms, cross subsidies (e.g., letter and parcel services), etc.



lobbyingof members of parliament

example: protectionism by a tariff

: firms profit (higher prices and profits per unit at home): households lose (cheaper imports no longer available): governments tend to play that game due to customs revenues

Caveat: The strategy is usually performed under the pretence to

protect jobs, but the economy as a whole suffers a net loss in welfare.



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5Strategic Behavior of Firms5.4Risk and Uncertainty

Risk and Uncertainty, cf. Frank Knight (1921)

: Riskis the kind of randomness that can be modeled by

quantitative methods (e.g., mortality rates, casino gambling,

equipment failure rates).A set ofprobabilitiesassigned to a set ofpossibilities.

: a priori probabilities (by logic; e.g., rolling any number on a die): objective orstatisticalprobabilities (by empirical evaluation): subjective orpersonalprobabilities (by individual estimates): Possibilities denote outcomes, states or values (alternatives).

: Uncertaintyis immeasurable, not possible to calculate.

(unknown possibilities and/or unknown probabilities)

No insurance without risk (rather than uncertainty).


5Strategic Behavior of Firms5.4Risk and Uncertainty

Some sources of risk (examples)

: changing market demand (tastes, income, expectations on the

future): changing supply consitions (factor prices, competitors): inventions, innovations: macroeconomic risks (business cycle, inflation, exchange rates): political changes (regulation, tax system, environmental

protection)

Some sources of uncertainty

: irrational behavior of agents (customers, competitors), e.g., panic: processes after some desaster, e.g., earth quake or maximum

credible accident (MCA) in an atomic power plant



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5Strategic Behavior of Firms5.5Investment Behavior

Investment Behavior

dynamic aspects of managerial decision making

: short run: fixed capital stock, given capacities, fixed cost: long run: adjustment of the capital stock by investments

Kt+1 = Kt+ Int where I

nt = I

gt Dt

: under certainty: optimal firms size indicated by someKAny investment with a positive NPV is advantageous.

Find the investment with the highest NPV.: at risk: revised decision making concerning risk



Net Present Value (NPV)

: timeline (t=0,1,2,3): sequence of net investments (I0,I1,I2): sequence of revenues (r1, r2, r3): sequence of operating costs (c1, c2, c3)

N PV= I0+ 1

1 + i(r1c1I1)+

1

(1 + i)2(r2c2I2)+

1

(1 + i)3(r3c3)



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Decision Tree Analysis



Exercise

Demand analysis:

Households maximize their utilityu(x1,x2)with respect to a given budget y.

(x1and x2denote commodities).

(a) What is the technical budget constraint and what does it express? Depict

the budget constraint graphically and show the effects if one of the prices

inceases and if the budget increases! 6 points

(b) How are the terms indifference curve, income consumption curve and

normal good defined? 4.5 points(c) What does a demand function express and what determines the demand?

If the behavior of consumers is based on their preferences, what might be

useful from a managerial point of view? 9.5 points

Total: 20 points



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Exercise

Supply analysis:

The figure describes the cost situation of a firm whose production function

corresponds to the law of returns.

p

p

p

x

p

. . . to be continued.University of Siegen, April 2013 PD Dr. Hagen Bobzin, Managerial Economics 107/111


Exercise

(a) Identify the curves and explain them! 6 points

(b) What necessary and sufficient conditions of profit maximization are

relevant for the firm with respect to perfect competition? What are the

optimum choices of the firm if the prices p, p or p are given? What

do we know about the profit? 8 points

(c) How are the terms firms optimum and firms minimum defined?

Denote the short-term and long-term supply curve of the firm. 6 points

Total: 20 points



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Exercise

Perfect Competition

: How is perfect competition defined?: Why is perfect competition frequently used a reference case in

economics?: Why do managers try to get rid of perfect competition?: Give examples how firms try to gain market power by destroying

preconditions of perfect competition.



Exercise

Consider a monopoly with a linear price demand function

p(x)= a bx and a cost function c(x)= kx2 (a, b, kare constants).

: Compute Cournots solution.: Visualize Cournots solution in a corresponding graph.: Indicate the difference between Cournots solution and perfect

competition.: Explain how advertisement could improve Cournots solution.

(too long for 20 minutes)



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Exercise

Suppose that there are two firms competing on a market by means of

quantities.

: Explain the concept of reaction curves.: How is the Cournot-Nash solution defined? How is the

Cournot-Nash solution related to reaction curves?: In an asymmetric setting as used by von Stackelberg how does the

leader profit?: What characterizes the cartell solution?


managerialeconomics 2013 folded

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