Lectures Intermediate Microeconomicsweb.hallym.ac.kr/~cxj183/Intermediate Microeconomics I... · 2014. 1. 13. · Thorstein Veblen and Harvey Leibenstein (1950) Bandwagon, Snob, and

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Intermediate Microeconomics Prof. C. Jo 1

Lecture 01 - Overview of Microeconomic Theory 1. Economics: A Study of (rational) Choice under the condition of Scarcity cf) Opportunity Cost 2. Microeconomic Theory (a.k.a. Price Theory) Macroeconomic Theory (a.k.a. Income Theory) 3. Methodologies Economic Model: Assumptions and Propositions Deductive Method (Theory) vs. Inductive Method (Empirical Studies) Positive vs. Normative Economics 4. Rationality: Economic agents use rational means to achieve their goals. cf) bounded rationality 5. Optimization Problem: Minimization vs. Maximization cf) maximize profit with minimum amount of inputs? No way! cf) duality problem 6. Equilibrium: Existence, Stability, and Uniqueness cf) Not Balance? Why equilibrium? 7. Mathematical Equations Easy to understand, interpret and forecast the economic phenomenon. 8. Market Mechanism = Price Mechanism Rationing Function of Price Allocative Function of Price (“Invisible Hand” by Adam Smith, 1776) Mixed Economy=Market System + Government intervention “Economic behaviors only for self-Interest but eventually for public-good.” Consumer Sovereignty vs. Dependence Effect (K. Gallbraith) 9. Market Demand Law of Demand (no exceptions? Think about this) Q f P P M N T LD R= ( ), , , , , , L : Market Demand Function ceteris paribus “Other Things Being Equal” (Alfred Marshall) cf) movement along the curve vs. shift of a curve


10. Elasticity Arc elasticity vs. point elasticity Ex) Q aP b= − Elasticity and Total Revenue Determinants of Price Elasticity of Demand Classification of goods based on Income Elasticity Cross Elasticity of Demand 11. Equilibrium revisited baPQD +−= and βα −= PQS Static Stability vs. Dynamic Stability (See another lecture note on Stability of Equilibrium) 12. Price Control Price Floor vs. Price Ceiling 13. Conspicuous Demand Thorstein Veblen and Harvey Leibenstein (1950) Bandwagon, Snob, and Veblen Effects


Lecture 02 – Stability of Equilibrium 1. Static Stability a. Walrasian Adjustment Process If excess demand (supply) exists, the market price will go up (down). Excess supply (demand) price above (below) equilibrium price.

)()()( PSPDPED −= : Excess Demand Function

0)( <dP

PdED

(Try to draw diagrams with stable and unstable conditions) b. Marshallian Adjustment Process Housing market has very steep supply curve. It’s hard to adjust price to eliminate any existence of excess demand or supply.

)()()( QsQdPPQEDP SD −=−= : Excess Demand Price Function

0)( <dQ

QdEDP

(Try to draw diagrams with stable and unstable conditions) 2. Dynamic Stability a. Discrete time (Cobweb Process) baPD tt +−= (demand) (1)

βα −= −1tt PS (supply) (2) ( βα ,,, ba are all positive numbers).

Equilibrium condition implies that tt SD = . So we get 01 =−−+ − βα bPaP tt (3). And finally, rewriting w.r.t. tP ,

a

bPa

P ttβα +

+−= −1 (4) (Difference Equation)

b. Continuous time (Differential Equation)

demand of slopesupply of slope > (condition for dynamic stability)


Lecture 03 – Consumer Preference Theory 1. Consumer preferences will tell us how an individual would rank (i.e. compare the desirability of) any two consumption bundles (or baskets), assuming the bundles were available at no cost. Of course, a consumer’s actual choice will ultimately depend on a number of factors in addition to preferences. 2. Assumptions about the consumer preferences a. completeness: BAf , BA p , or BA ≈ b. transitivity: If BAf and CB f , then CAf c. continuity: gradual change in preference with gradual change in consumption d. monotonicity: strong non-satiation or “more is better” → continuous utility function 3. Cardinal vs. Ordinal Utility Jeremy Bentham “the greatest happiness of the greatest number” Jevons, Menger, and Walras “Marginal Revolution” Pareto’s ordinal utility through indifference curve Hicks and R.G.D. Allen 4. Utility Surface U xy= MUy U U = 4 MUx y x

8 8 4 4 2 2 5. Diminishing MU? Ex) U H R= + , where H is number of hamburgers and R is number of root beer. 6. Properties of Indifference Curves a) Downward sloping. b) Convex to the origin (see MRS). c) Indifference curves cannot intersect. d) Every consumption bundle lies on one and only one indifference curve (everywhere dense). e) Indifference curves are not “thick.” f) The farther from the origin, the more utility it has.


7. Marginal Rate of Substitution (MRS) y y 8 G C

Δy H D 5 Δx J F K 2 i Δx 2 5 8 x x

− = − − =slope of I.C. or ΔΔ

yx

dydx

MRSx y,

U U x y= ( , ) . Totally differentiating to get dU MU dx MU dyx y= + = 0 (why?).

− = =dydx

MUxMU

MRSy

x y, . dMRS

dxx y, < 0 or

d ydx

2

2 0> (MRS is diminishing)

cf) Can you draw an indifference curve with increasing MRSx y, ? 8. Special Utility Functions a) Perfect Substitutes b) Perfect Complements Pancakes Right Shoe c) One Good and one Bad d) One Good and one neuter (neutral good) Corn Sandwich

Waf

fles

Left

Shoe

Pollu

tant

Use

d cl

othe

s


e) Cobb-Douglas Utility Function (by Charles Cobb & Paul Douglas, 1928) U Ax y= α β , where A, , and α β are positive constants. Cobb-Douglass utility function has three properties that make it of interest in the study of consumer choice. (1) MU’s are positive. Check it out. (2) Since MU’s are all positive, the indifference curves will be downward sloping. (3) It also exhibits a diminishing MRS f) Quasi-Linear Utility Function (imperfect substitution, No income effect on x) It can describe preferences for a consumer who purchases the same amount of a commodity regardless of his income. Ex) toothpaste and coffee U x y v x by( , ) ( )= + , where v x( ) is a function that increases in x and b is positive constant. The indifference curves are parallel, so for any value of y, the slopes of I.C. will be the same. Ex) U x y= + 9. Budget Constraint P x P y Mx y+ ≤ From this constraint we can derive the budget line (or price line) to visualize in 2-D space.

yPP

x MP

x

y y= − + , where −

PP

x

yis slope and

MPy

is vertical intercept.

y

MPy

x

MPx

10. Change in Income and Change in Price Ex) M0 = $800 , P Px y= =$20 $40, . Draw the budget lines in each case. 1) Income rises from $800 to $1,000 2) Px rises to $25, holding initial income and Py constant. 3) Now, income rises from $800 to $1,000 and Px rises to $25 and Py rises to $50.

Feasibility Set or

Opportunity Set


11. Optimal Choice max U

x yx y

,( , ) : “choose x and y to maximize utility”

subject to: P x P y Mx y+ ≤ : “expenditures on x and y must not exceed the consumer’s income” If the consumer likes more of both goods, the marginal utilities of good x and y are both positive. At an optimal basket all income will be spent. So, the consumer will choose a basket on the budget line P x P y Mx y+ = . y B A U2 U1 U0 x 12. Lagrangean Function (by Joseph-Louis Lagrange) max U

x yx y

,( , )

subject to: P x P y Mx y+ ≤

We define the Lagrangean ( L ) as L x y U x y M P x P yx y( , , ) ( , ) ( )λ λ= + − − , where λ is a Lagrange multiplier. The first-order necessary condition (FOC) for an interior optimum (with x > 0 and y > 0 ) are

∂∂

= ⇒∂

∂=

Lx

U x yx

Px0( , ) λ (1)

∂∂

= ⇒∂

∂=

Ly

U x yy

Py0( , ) λ (2)

∂∂

= ⇒ − − =L M P x P yx yλ

0 0 (3)

We can combine (1) and (2) to eliminate the Lagrange multiplier, so FOCs reduce to:

MUMU

PP

x

y

x

y= or MU

PMU

Px

x

y

y= (4)

P x P y Mx y+ = (5) From the above equations, we can derive demand function of x and y. Ex) You are given U x y x y x y( , ) / /= + = +1 2 1 2 and P x P y Mx y+ = . Now derive demand functions of x and y when the consumer is maximizing his utility.

At point A,

− = = =dydx

MUMU

MRS PP

x

yx y

x

y,

At point B,

MUMU

PP

MUP

MUP

x

y

x

y

x

x

y

y> > or


MU xxx

= =−12

12

1 2/ and MU yyy

= =−12

12

1 2/ . So MRSMUMU

yxx y

x

y, = =

And FOC of utility maximization is MUMU

y

x

PP

x

y

x

y= =

*

*, where x y* * and are utility-maximizing

quantities demanded.

By squaring both sides of above equation and rearranging terms, we find that y x PP

x

y

* *=2

2 .

Plugging the last expression into budget equation and simplifying, we get

MPP

xPxPy

xyx =⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛+ 2

2**

MP

PPPx

PP

PxPP

xxPy

xyx

y

xx

y

xx =⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛ +=⎟

⎟⎠

⎞⎜⎜⎝

⎛+=+

2*

2*

2** . So, x

P MP P P

y

x y x

* =+ 2

(1)

.223

2

2

2

22

2**

yxyx

xy

y

x

xyx

y

y

x

PPPP

MPP

PP

PPP

MP

PP

xy+

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+== So, y

P MP P P

x

x y y

* =+ 2

(2)

13. Change in Income and Optimal Choice y y ICC ICC x x Income (M) Income (M) Engel Curve Engel Curve x x

(Normal Good, η > 0 ) (Inferior Good, η < 0 )


14. Change in Price and Optimal Choice y PCC (or Offer Curve) Px x Demand X 15. Change in Price: Revisited y E ′E ′′E i1 i0 x0 ′′x ′x ( / )M Px ( / )M Px′ x

cf) What would be the shape of PCC if the price elasticity of demand is 1 (unitary elastic)? cf) Think about the shape of PCC if the quantity is reduced with price hike. And also think about the shape of demand for that good.

* Price Effect ( )E E→ ′ ( ):E E→ ′′ Substitution Effect due to price change ( ):′′ → ′E E Income Effect In this case, good x is a normal good. cf) Derive substitution and income effect if good x is neither a normal nor an inferior good. cf) Derive substitution and income effect if good x is an inferior good. Maybe you can think of two different cases.


16. Slutzky Equation (Slutzky Decomposition) ′ − = ′′ − + ′ − ′′x x x x x x0 0( ) ( ) (1)

Dividing both sides by ΔPx , we get the following equation, ′ −

=′′ −

+′ − ′′x x

Px x

Px x

Px x x0 0

Δ Δ Δ (2)

l.h.s. can be explained ΔΔ

xPx M

. And the first term on r.h.s. is equal to ΔΔ

xPx U

.

And the second term on r.h.s. is now rewritten as follows, ′ − ′′

= ⋅x x

PxR

RPx xΔ

ΔΔ

ΔΔ

, where R means real income. (3)

ΔΔ

RPx

means the change in real income w.r.t. change in price.

So, ΔΔ

RP

xx= − (Shepard’s lemma) (4)

And ΔΔ

ΔΔ

xR

xM

= (why? Think about the definition of income effect!) (5)

Plugging (4) and (5) in (3) and then in (2), we can get

ΔΔ

ΔΔ

ΔΔ

xP

xP

x xMx M x U

= − ⋅ (Slutzky Equation)

17. Labor Supply and Leisure (Application) H L+ = 24 , where H is hours worked and L is amount of leisure activities. And hourly wage is given at w0 and non-labor income is given at V0 . The utility function is now U U L M= ( , ) (1) The budget equation is M w H V w L V w w L V= + = − + = − +0 0 0 0 0 0 024 24( ) (2)

Rewriting (2), we can get M w L w V+ = +0 0 024 (full-income constraint) (3) If we assume the price level of goods (composite good) is PC = $1 , then M on l.h.s would equal total number of goods that this consumer buys. Can you interpret terms in equation (3)? 1) Now, can you draw the budget line? 2) Find the utility-maximizing point. 3) Suppose wage rises. Overlap new optimal points on the original budget line. 4) Connect those optimization points to get PCC. And labor supply curve. 5) Why do you think is it a backward bending supply curve?


Lecture 04 – Production Theory 1. How to define a ‘Firm’? – Roles, Objectives, and more a) Specialization in production. b) Team production is more efficient than individual production in many aspects. Less transaction costs but more monitoring costs in firm. c) Internal control than external market transactions with much transaction cost. Opportunistic behaviors due to asset specificity. But, is internal control always reasonable? Not really. Why? Ex) Vehicle brand owner d) Profit-maximizers? e) Ownership and management are separated. 2. Production Technology: Basic Analysis a) Time periods SR with at least one fixed input / LR with all variable inputs b) Production function (total product curve)

Q f L K= ( ), (1) Q: is maximum amount of output a firm could get from a given combination of inputs. So, inefficient management could reduce output from what is technologically possible. If we invert the equation (1) to get L g Q= ( ) , which tells us the minimum amount of labor L required to produce a given amount of output Q, this function is labor requirement function. 3. TP MP APL L L, , and Q TP R I A L MP, AP J B S C AP MP L

A P QLL

= MPdQdLL

=

Up to I (inflection point), MPL is increasing (increasing marginal returns to labor), and after that MPL starts diminishing. Up to S, APL is increasing, so APL < MPL .

After S, APL is decreasing, APL > MPL

Law of Diminishing Marginal Returns:Principle that as the usage of one input increases, the quantities of other inputs being held fixed, a point will be reached beyond which the marginal product of the variable input will decrease.


4. Production Technology: Two Variable Inputs Production Surface (or Total Product Hill)

Q A K O B

L 5. Isoquants A curve that shows all of the combinations of labor and capital that can produce a given level of output. K Ridge Lines R

S C ΔK D ΔL O L 6. MRTS (Marginal rate of Technical Substitution)

MRTS KLL K,

= −ΔΔ

From Q f L K= ( , ) , we can get the following equation by totally differentiating the production function. Δ Δ ΔQ MP L MP KL K= ⋅ + ⋅ = 0. Finally, we can get


MRTS KL

MPMPL K

L

K, = − =

ΔΔ

and d KdL

2

2 0> implies the Law of Diminishing MRTS.

7. Elasticity of Substitution

MRTSMRTSLK

LK

Δ

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛Δ

=−

=KL,MRTSin change percentage

ratiolabor capitalin change percentageσ

K K/L at A = slope of ray OA = 4 MRTS at A = 4 20 A K/L at B = slope of ray OB = 1 MRTS at B = 1 As the firm moves from A to B, the B elasticity of substitution equals 1. 10 Ex) 100== LKQ (left diagram) 0 5 10 L K K K0 K0 K1 K1

L0 L1 L L0 L1 L (σ is relatively small) (σ is relatively big) “Little” opportunity to substitute between inputs “Big” opportunity to substitute between inputs


8. Special Production Functions a) Linear Production Function (Perfect Substitutes, σ = ∞ ) Q cL dK= + , c and d are positive constants. Ex) natural gas or fuel oil in manufacturing process. company data storage b/w high-capacity and low-capacity computers. b) Fixed-proportions Production Function (Perfect Complements, σ = 0 , Leontief Function)

),min( bKaLQ = , a and b are positive constants. Ex) fixed portions of oxygen and hydrogen atoms to make water molecules. One frame with two tires for bicycle. One chassis with four tires for a car. c) Cobb-Douglas Production Function

Q AL K= α β , A, , are positive constantsα β . d) Constant Elasticity of Substitution (CES) Production Function

σ is independent of MRTSL K, or input ratio ( K L/ ) or even output Q .

Q A aL a Kr

= + −− −−ρ ρ ρ( )1 , where A a> < < ≥ −0 0 1 1, , ρ .

r is the degree of homogeneity. σ ρ=

+1

1

a) If ρ σ= − = ∞1 ( ) , Q A aL a K r= + −[ ( ) ]1 (isoquant is a straight-line).

Homogeneous Function of degree r y f x z= ( ),

If we k-fold all the independent variables x and z, f kx kz k f x z k yr r( ) ( ), , ≡ = If r = 1 , the function is also known as linear homogeneous function. Ex) Identify the following functions.

a) y x xz z= + −3 22 2 b) y xz

= +3

5 c) y x za a= −1

Returns to scale for a Cobb-Douglas Production Function Let L1 and K1 denote the initial quantities of labor and capital, and let Q1 denote the initial output, so Q AL K1 1 1=

α β . Now let’s increase all input quantities by the same proportional amount λ , where λ > 1, and let Q2 denote the resulting volume of output: Q A L K AL K Q2 1 1 1 1 1= = =

+ +( ) ( )λ λ λ λα β α β α β α β . From this, we can see that if: a) α β+ >1, then λ λα β+ > , and so Q Q2 1> λ (increasing returns to scale, IRS) b) α β+ = 1 , then λ λα β+ = , and so Q Q2 1= λ (constant returns to scale, CRS) c) α β+ < 1, then λ λα β+ < , and so Q Q2 1< λ (decreasing returns to scale, DRS)


b) If ρ σ= =0 ( )1 , we need a trick because we can’t define 1∞ .

Taking log on both sides, we can get log log log[ ( ) ]Q A r aL a K= − + −− −ρ

ρ ρ1 .

But the second term of r.h.s. is indeterminate because of 00

. The best way to solve this

problem is to use L’Hospital rule.

Generally, when we have lim ( ) lim ( )ρ ρ

ρ ρ→ →

= =0 0

0 0f g, , lim( )( )

lim ( )( )ρ ρ

ρρ

ρρ→ →

=′′0 0

fg

fg

Let’s define f r aL a K( ) log[ ( ) ]ρ ρ ρ= + −− −1 and g( )ρ ρ= .

lim ( ) lim( )

( log ( ) log )ρ ρ ρ ρ

ρ ρρ→ → − −

− −′ =−

+ −+ −

0 0 11f r

aL a KaL L a K K

= − + − = − −r a L a K r L Ka a1

1 1( log ( ) log ) log( )

lim ( )ρ

ρ→

′ =0

1g

Finally, we know limlog log lim ( )( )

log log( )ρ ρ

ρρ→ →

−= − = +0 0

1Q A fg

A r L Ka a

lim ( )ρ→

−=0

1Q A L Ka a r (Cobb-Douglas Production Function)

(You can check out why Cobb-Douglas has σ = 1) c) If ρ→∞ (σ = 0 ). Leontief Production Function Q aL bK= min[ ], K σ = 0 σ = 01. σ = 1 σ = ∞ σ = 5 L 9. Returns to Scale: revisited f kL kK kf L K( ) ( ), , = : CRS f kL kK kf L K( ) ( ), , > : IRS f kL kK kf L K( ) ( ), , < : DRS


Q CRS K K L L Q IRS K K L L Q DRS K K L L


Lecture 05 – Cost Concepts for Decision Making 1. Costs a) Explicit costs which involve a direct monetary outlay.

Indirect costs that do not involve outlays of cash. b) Accounting Costs (total sum of explicit costs) Economic Costs (sum of explicit and implicit costs) c) Opportunity Costs d) Sunk (unavoidable) costs vs. Non-sunk (avoidable) costs, Initial set-up costs. 2. Cost-Minimization Problem a) iso-cost curve

wL rK TC C+ = = , Kwr

L Cr

= − +

K C1 / r C / r E C0 / r Slope = - (w / r) K* F G Q Q= L* (C0 / w) (C / w) (C1 / w) L b) Cost minimization

At point F, (slope of iso - cost curve) slope of isoquant curve)= ( . So, wr

MRTSL K= ,

And we already know that MRTSMPMP

wrL K

L

K, = = or

MPw

MPr

L K= .

The last expression implies that the additional output per dollar spent on labor services equals the additional output per dollar spent on capital services (“equal bang for the buck”). You can check the condition at points E and G. How about the corner point solutions? Does the above equation hold at the corner solution? Generally, if we have m units of inputs, the cost minimization condition (FOC) is

MPw

MPw

MPw

m

m

1

1

2

2

= = =L

c) Expansion Path Q Q Q0 1 2< <


d) Comparative Statics Analysis of Changes in Input Prices Demand for inputs is Derived Demand depending upon change in quantities of final products. So, we can’t use the method in consumption theory to derive input demand curves. To analyze the effect of change in input prices without considering change in quantities, we need to confine our analysis to change in input combinations that can produce same amount of output (analogous to consumption theory of only substitution effect!).

σ = =ΔΔ

ΔΔ

( / ) / ( / )/

( / ) / ( / )( / ) / ( / )

K L K LMRTS MRTS

K L K Lw r w r

K

0⎟⎠⎞

⎜⎝⎛

rw

A K0 B K1

1⎟⎠⎞

⎜⎝⎛

rw

0 L0 L1 L e) Cost Minimization in SR K A F K Q0 L min

( , )L KwL rK+

subject to: Q f L K= ( ), We proceed by defining a Lagrangean function Λ( ) [ ( ) ]L K wL rK f L K Q, , , λ λ= + + − ,where λ is a Lagrange multiplier.

When the firm’s capital is fixed at K , the short-run cost-minimizing input combination is at point F. If the firm were free to adjust all of its inputs, the cost-minimizing combination would be at point A.


The conditions for an interior optimal solution (L > 0, K > 0) to this problem are

∂Λ∂

= ⇒ =∂

∂=

Lw f L K

LMPL0 λ λ

( , ) (1)

∂Λ∂

= ⇒ =∂

∂=

Kr f L K

KMPK0 λ λ

( , ) (2)

∂Λ∂

= ⇒ =λ

0 f L K Q( ), (3)

From (1) and (2), we can get MPMP

wr

L

K

= (4)

Equations (3) and (4) are two equations with two unknowns, L and K. They are identical to the conditions that we derived for an interior solution to the cost-minimization problem using graphical arguments. The solution to these conditions are the long-run input demand functions, L w r Q K w r Q* *( ( ), , ) and , , . Ex) Production function is Q LK= 50 . What are the demand curves for labor and capital? f) Duality: “Backing Out” The above analysis shows how we can start with a production function and derive the input demand function. But we can also reverse directions: If we start with input demand functions, we can characterize the properties of a production function and sometimes even write down the equation of the production function. This is because of duality, which refers to the correspondence between the production function and the input demand function. Ex) Suppose we are given respective labor demand function and capital demand function

L Q rw

=50

and K Q wr

=50

. Solving for w in terms of Q, r, and L: rL

Qw2

50⎟⎠⎞

⎜⎝⎛=

Plugging the last expression in capital demand function,

LQ

rrLQQK

500,2)50(

50

22/12=⎟

⎟⎠

⎞⎜⎜⎝

⎛= . Finally, Q LK Q LK L K2 0 5 0 52500 50 50= = =, . .

3. Production Cost in the Short-Run The function TC TC w r Q= ( ), , simplifies to TC TC Q= ( ) TC TFC TVC Q AC Q AFC AVC= + = ⋅ = +( )

AC TCQ

TFCQ

TVCQ

AFC AVC= = + = +

MC TCQ

TFCQ

TVCQ

MFC MVC MVC= = + = + =ΔΔ

ΔΔ

ΔΔ

Marginal Cost in SR is Marginal Variable Cost (QMFC = 0 )


$ TC A TVC I I’ 0 $Q ′Q Q Q $ MC AC AVC D C B $Q ′Q Q Q TC Q F VC Q( ) ( )= + . The necessary condition of minimum AVC (at point C) is

d VC Q Q

dQVC Q Q VC Q

QVC Q

QVC Q

Q[ ( ) / ] ( ) ( ) ( ) ( )

=′ −

=′

−2 2

.01)()()(1)( 2 =⎥⎦

⎤⎢⎣

⎡−=−⋅

QQQVC

dQQdVC

QQVC

QdQQdVC

So,

dVC QdQ

VC QQ

MVC AVC( ) ( )= =,

Likewise, can you prove the condition at point D?


4. Production Cost in the Long-Run a) Envelope Curve AC SMCA SMCB SACC LRMC LRAC SACA SACB a b e d c a’ 0 Qa Qc Qe Q

Long-run optimal level of production b) LRMC Curve At point c, LRAC LRMC SAC SMCB B= = = c) Returns to Scale and LRAC Curve AC (3) (1) (2)

Q (1) Constant Returns to Scale (2) Increasing Returns to Scale (Economies of Scale or Scale Economy) →Natural Monopoly (3) Decreasing Returns to Scale (Diseconomies of Scale) d) Economies of Scope TC Q Q TC Q TC Q( ) ( ) ( )1 2 1 20 0, , , < +


ES TC Q TC Q TC Q QTC Q Q

=+ −( ) ( ) ( )

( )1 2 1 2

1 2

, ,

, 0>ES (Scope Economies happen)

Sources of Scope Economies: Shared common inputs, cost complementation (oil and

benzene, oil and natural gas, computer software and computer support etc.) e) Economies of Experience (Learning by Doing) Economies of scale (EOS) and Economies of Experience (EOE) are different. EOS refer to the ability to perform activities at a lower unit cost when those activities are

performed on a larger scale at a given point in time. EOE refer to reductions in unit costs due to accumulating experience over time. EOS may be substantial even when EOE are minimal. This is likely to be the case in mature, capital-intensive production processes, such as aluminum can manufacturing. Likewise, EOE may be substantial even when EOS are minimal as in such complex labor-intensive activities as the production of handmade watches. Firms that do not correctly distinguish between EOS and EOE draw incorrect inferences about the benefits of size in a market. For example, if a firm has low average costs because of EOS, reductions in the current volume of production will increase unit costs. If the low average costs are the results of cumulative experience, the firm may be able to cut back current production volumes without raising its average costs.


Lecture 06 – Profit Maximization 1. Profit maximizing quantity π ( ) ( ) ( )Q TR Q TC Q= − (1) (economic profit) = (sales revenue) – (economic costs) (accounting profit) = (sales revenue) – (accounting costs) $ TR (Q) TC(Q) MC(Q*) π(Q) 0 Q1 Q* Q2 Q 1º : FOC

d QdQ

dTR QdQ

dTC QdQ

MR Q MC Qπ ( ) ( ) ( ) ( ) ( )= − = − = 0 , so MC Q MR Q( ) ( )=

2º: SOC

d QdQ

d TR QdQ

d TC QdQ

TR Q TC Q2

2

2

2

2

2 0π ( ) ( ) ( ) ( ) ( )= − = ′′ − ′′ < . MR Q MC Q′ < ′( ) ( )

2. Deriving Marginal Revenue Curve $ A E B C D F Q Q


Amoroso-Robinson Formula

⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=+=

⋅==

D

PdQdP

PQP

dQdPQP

dQQPd

dQdTRMR

ε111)(

Since demand curve is downward sloping, ε D is always positive. Therefore, MR is lower than AR (average revenue, i.e. Price). MR P< . Ifε D = ∞ (horizontal demand, infinitely elastic demand, or Q = 0), MR AR P= =( ) . 3. Marginal Revenue, Price Elasticity and Total Revenue $ ε > 1 ε = 1 0 1<


Lecture 07 – Market Structure (I) A. Perfect Competition 1. Study Paradigm of Market (Industrial Organization) Market Structure (S) / Behaviors or Conduct (C) / Performance (P) 2. Perfect Competition Conditions or Assumptions a) Many buyers and sellers: fragmented industry so that each company has negligible market share that cannot change the whole structure b) Homogeneous (or identical) product: Consumers will not incur additional costs in collecting additional information. Ex) Gold, silver etc. c) Perfect mobility of inputs: no entry or exit barriers d) Perfect information e) No transaction cost f) Price takers: price is now a parameter * P.C. is an ideal type of market structure with good predictability of market. 3. Profit maximization of a representative firm $ MC

AC C P* MR = D A B AVC E Ps D O Q* Q 4. Industry Supply Curve in SR

Q Q Q Q QM n ii

n= + + + = ∑

=1 2

1L ( )at a given P

*5. Residual Demand Elasticities (amount demanded from i-th firm)=(industry demand) – (amount produced by all other firms)

SDi QQx −= . Differentiating this equation w.r.t. price, dPdQ

dPdQ

dPdx sDi −=

i

ii x

PdPdx

−=εQ( )

Di

DS

S

s

i

D

D

Di

S

S

D

D

i

S

D

D

i

D

i

i

QxQQ

QP

dPdQ

xQ

QP

dPdQ

QQ

QQ

xP

dPdQ

QQ

xP

dPdQ

xP

dPdx

//

+−=⇒+−=−⇒ ε

)1(1

i

iS

iDi k

kek

e −⋅+⋅=⇒ε )1 then ,let and ,( iD

Si

D

i

D

S

D

i

D

D kQQk

Qx

QQ

Qx

QQ

−==+=Q

• Supply curve: MC curve above AVC. • Point D: Shut-Down Point • Point E: Beak-Even Point • Demand curve: MR curve at P* • Total revenue: □ P*OQ*C • Total costs: □ AOQ*B • Economic profit: □ P*ABC • Any points between D and E: A firm should produce some output even though the firm is facing economic losses. Why?


The smaller ik is, the larger iε , which depends on supply elasticities of other firms. In competitive market, i) ik is relatively small. ii) even if ik is not small but if Se is elastic, then iε is elastic. B. Monopoly 1. Sources of Monopoly a) Control of Scarce Inputs (OPEC, DeBeers etc.) b) Patents or Franchise / License Scheme (MD, RN, McDonald’s, Burger King etc.) c) Government Enforced Barriers (MLB, NFL, NBA etc.) d) Large Economies of Scale: Natural Monopoly e) Merger and Acquisition (M&A) f) Illegal ways to sustain monopoly power (Bribe, Lobby, Patent killing, etc.) 2. Short-Run Analysis a) Derivation

MR Q dTR QdQ

P Q dPdQ

( ) ( )= = + and FOC of profit maximization is MR Q MC Q( ) ( )=

So, P MR Q Q dPdQ

MC Q= − >( ) ( ) ( / )QdP dQ < 0

P

MC PM C SAC A B M Demand QM Q MR 3. Marginal cost and price elasticity of demand: Inverse Elasticity Pricing Rule (IEPR) At point M, MR Q MC Q( ) ( )= . According to Amoroso-Robinson formula, we know

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

DPQMCQMR

ε11)()( . So,

P MCP D

* *

*

−=

1ε

(asε D P MC→∞ →, )

The l.h.s. of above equation is the monopolist’s optimal markup of price over marginal cost, expressed as a percentage of the price. For this reason, this equation is called the inverse elasticity pricing rule(IEPR). And l.h.s. is called Lerner Index of market power.


4. Monopolist’s Demand for Inputs If the input market is competitive, then this monopolist should take prices of inputs as given. We can easily derive the relationship using profit as a function of L and K, not Q. Let TR TC( ) ( )⋅ ⋅ and denote total revenue and total cost function, respectively. Then, we know TR TR Q TR f L K= =( ) ( ( )), and TC wL rK= + . Based upon these expressions, we can get π π= = −( ) ( ) ( )L K TR L K TC L K, , ,

1º : ∂∂

=∂∂

=π πL K

0 . So, ∂∂

=∂

∂=

TR L KL

TC L KL

w( , ) ( , ) , ∂∂

=∂

∂=

TR L KK

TC L KK

r( , ) ( , )

∂

∂=∂

∂= ⋅

∂∂

= ⋅TR L K

LTR f L K

LdTRdQ

fL

MR MPL( , ) ( ( , ))

∂

∂= ⋅

∂∂

= ⋅TR L K

KdTRdQ

fK

MR MPK( , )

(some textbooks are using MPP (marginal physical product) instead of MP) So, the final expression can be

MRP L K MR Q MP L K wMRP L K MR Q MP L K r

L L

K K

( , ) ( ) ( , )( , ) ( ) ( , )

= ⋅ == ⋅ =

(1)

where MRP is marginal revenue product, which is similar to VMP (value of marginal product, P MP⋅ ) in perfectly competitive goods market. Now, we need to think how equation (1) is related to MR Q MC Q( ) ( )= . We have total cost function TC Q C f L K wL rK( ) ( ( , ))= ≡ + . Differentiating this function w.r.t L and K,

dTC QdQ

f L KL

w

dTC QdQ

f L KK

r

( ) ( , )

( ) ( , )

⋅∂

∂≡

⋅∂

∂≡

, which can be rewritten as MC Q MP L K wMC Q MP L K r

L

K

( ) ( , )( ) ( , )

⋅ ≡⋅ ≡

(2)

2º : SOC would be MRP MRPLL KK<


From the last expression, we can get important result using Amoroso-Robinson formula

22

21

111111 MRPPMR =⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

εε. So the ratio of equilibrium prices will be

PP

1

2

2

1

2

1

1

2

1 1

1 111

=−

−=

−−

⋅ε

ε

εε

εε

( )( )

. So, If , then If , then ε εε ε

1 2 1 2

1 2 1 2

> <

< >

P PP P

.

. (3rd-degree discrimination)

c) 1st-degree and 2nd-degree Price Discriminations P P A B D D O Qd Q Q d) Price Discrimination using hurdles Using “very cheap” devices that make customers reveal their own price elasticities. Ex) Coupons, Sale, mail-in rebates, matinee etc. 6. Other Sales Strategies a) Two-part Tariff Pricing The consumer pays a fixed (access) fee for service, plus a variable charge per unit purchased. Ex) utilities (electricity and gas), amusement parks and theme parks, sports clubs (racquet courts, aerobic classes, golf clubs etc). b) Tying and Bundling • Tying: a seller’s conditioning the purchase of one product on the purchase of another. Technological ties: specific plug-in interface may be hard to copy or actually protected from copying by IPR. ex) ink-jet printers Contractual ties: consumer is bound by contract to consume both products from the same Source. ex) Harley-Davidson Motorcycles. 7. Quality Discrimination A firm will try to reduce the quality of the lower-quality good (economy air service) so as to reduce the incentive of people with a high willingness to pay to switch from the high-quality good (first or business class) when the firm increases its price. 8. Welfare Issues in Monopoly The major concern is that monopoly misallocates resources by producing the “wrong” amount of a good, where price does not equal marginal cost.


P A Pm P Q A bQ( ) = − MC = c c P=P(Q) MR(Q) Qm QS Suppose we are given the demand function as P Q A bQ( ) = − , and the cost is fixed at c. With this information, we are required to solve the following questions:

a) MR Q A bQ( ) = − 2 b) Q A cbm

=−

2 c) P A cm =

+2

d) π mA c

b=

−( )2

4

e) DWL P c Q Qm S m= − −( )( )2

=−

=−( ) )A c

bQ A c

bS2

8 (Q

f) CS A P Q A cb

m m=−

=−( ) ( )

2 8

2

9. Determinants of DWL

⎟⎠⎞

⎜⎝⎛⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⎟⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛⋅⋅=⋅=

PP

QQ

PP

dPdPdQdPdQdPDWL

21

21

If we assume constant costs, so that dP P cm= − , then upon gathering terms, this is equivalent to

DWL P Q LD m m= ⋅ ⋅ ⋅ ⋅12

2ε , where L is Lerner Index.

This suggests that the inefficiency associated with monopoly pricing is greater, the larger the elasticity of demand, the larger the Lerner index, and the larger the industry (as measured by the firm’s revenues). However, such an interpretation would be incorrect since L depends on the elasticity of demand. As ε increases, a profit-maximizing monopolist responds by decreasing L. Starting with Harberger (1954), estimates of the economy-wide loss from the exercise or market power have been calculated based on the above equation. Harberger estimated that the DWL in the manufacturing sector in U.S. was approximately 0.1% of GDP. The relatively small estimates are due to low observed values of L and his assumption that the elasticity of demand was one. Small values of L are consistent with profit maximizing if demand is relatively elastic, not unity. Cowling and Mueller (1978) observe that if a firm is a monopolist and profit maximizes, then

CS

Monopoly Profit DWL


ε D L= 1 and the equation will be DWL m=π2

. Their estimates based on this equation suggest

that DWL could be on the order of 4% of GNP. However, the use of this assumes that all firms are monopolists, and this is clearly as unsatisfactory as assuming that L is independent of the elasticity of demand. 10. X-inefficiency A monopoly may spend “too much” on advertising, product differentiation, or investment in excess production capacity. Tullock (1967) and Posner (1975) argue that the welfare costs of monopoly include expenditures on lobbying and campaign contributions intended to obtain tariff protection, patent protection, and other preferential government treatment. In the extreme, a firm would be willing to spend an amount up to the potential monopoly profits to become a monopolist. Such rent-seeking activities would increase the welfare costs of monopoly. Cowling and Mueller considered this issue carefully. They used advertising expenditures to approximate the costs of monopolization to society. Adding these costs to their estimate of DWL, they estimated that the welfare cost of monopolization may be as high as 13 percent of GDP. In less competitive markets, there is less pressure on firms to use inputs efficiently. Inefficient monopolists may not be driven out of the market even in the long run. We consider this effect on costs, called X-inefficiency (by Leibenstein, 1966). If monopolization raises costs, the DWL is larger. In addition, the costs of producing the monopoly output level are higher. The important welfare point is that if increasing competition in monopolized markets would lead to reduced costs, then estimates of welfare loss based on DWL triangles such as Harberger’s will be far too low. While the controversy over the welfare cost of market power has not been resolved, it is possible to step back and make three observations. First, even a relatively small percent of GNP represents a considerable amount of resources. Second, any strategic behavior on the part of firms intended to obtain or protect their monopoly positions raises the costs of monopolization substantially. Third, in some industries, the potential gains to society from decreasing monopoly power are large. P C PM MCM=ACM Increase in DWL due to X-inefficiency MCC=ACC PC Demand QM MR QC Q

Increase in costs due to X-inefficiency


11. Benefits of Monopoly a) Scale Economies Oliver Williamson (1968) has suggested that if a merger to monopoly results in a decrease in industry-wide costs, these cost savings could easily compensate for any increase in allocative inefficiency. P Lost CS due to monopoly pricing PM PC MCC MCM P=P(Q) MR(Q) QM QC Q It is the value of the resources that were required under competition to produce QM units, but are not required to produce that output level under monopoly. Williamson’s point is that it does not take very large cost savings to compensate for the allocative inefficiency. b) Research and Development (R&D) Joseph Schumpeter (1965) argued that market power is a necessary incentive for research and development. He contended that without the lure of monopoly profits firms would have insufficient incentives to undertake research and development. Moreover, it was a mistake to focus on allocative inefficiency if that inefficiency made possible innovation of new products and technologies. For it is this kind of innovation that is responsible for economic growth and substantial qualitative increases in living standards. 12. Regulating Monopoly a) Marginal Cost Pricing b) Average Cost Pricing c) Two-tier Pricing d) Rate-of-Return Regulation

Cost Savings due to lower cost of monopoly


Lecture 08 – Market Structure (II) A. Oligopoly 1. Spectrum of market structure Most markets are neither perfectly competitive nor monopolistic but they may fall somewhere in between along the spectrum. Typical market will have more than one seller of the same or similar products, but not enough to justify the assumption that sellers simply take prices as given. Thus, each firm will have an individual, downward sloping demand curve and is said to have “some level” of monopoly power. 2. Oligopoly Oligopoly is from the Greek word “oligospolein” meaning “few to sell.” And it is reflecting the interdependence among firms, which means oligopoly or imperfectly competitive firm must take account of its rival’s actions in making its own pricing decisions. So, studies of oligopoly can give us good information about competitions among firms, strategic reaction or decision- making process and trend of market shares of firms. The most modern approach is to model such firms as choosing “strategies” or playing “games” with one another. This approach is called game theory. 3. Early Generalized Model Assumptions N firms producing homogeneous and standardized products. Input market is perfectly competitive. No entry is allowed. From these assumptions, we can derive several things; 1) Inverse demand function is expressed as

p f Q= ( ) (i)

, where Q qii

N= ∑

=1(market quantity).

2) Profit of each firm will be π i i i ip Q q c q i N= ⋅ − =( ) ( ), , , , 1 2 L (ii)

3) FOC of profit maximization is ddq

p q dpdQ

dQdq

dc qdq

i

ii

i

i i

i

π= + − =

( ) 0 (iii)

cf) dQdqi

means that a change in product of i-th firm can affect the change in total product or

change in products of other firms. 4) We need to know the value of dQ dqi . Rewriting this, we can get

dQdq

dqdq

dQdqi

i

i

i

i= + − ⎟⎟

⎠

⎞⎜⎜⎝

⎛=+== ∑ ∑∑

=≠ =≠−

=

N

ji

N

jijiij

N

ii qQqqqQ

1 11 .Q (iv)

Perfect competition Monopoly

Monopolistic competition Oligopoly


dQdq

i

i

− : the ratio of change in products of other firms to the change in i-th firm.

⇒ Conjectural Variation (C.V.)

So, equation (iv) is now dQdqi

i= +1 λ (v)

(This is the most important factor in Oligopoly. We can figure out different types of oligopoly asλ changes) Putting aside the discussion about λ i , we need to derive the generalized result by assuming that ci (cost structure) and λ i are constant across individual firms. Therefore,

5) From (iii) and (v), we can get p MC q dpdQi i

− = − +( )1 λ

p MCp

qQ

Qp

dpdQ

i i− = − ⋅ ⋅ ⋅ +( )1 λ . Lerner Index =+ki ( )1 λε (vi)

( ki is market share of i-th firm. ε is price elasticity of market demand) From (vi), assuming that every firm has the same size, then k Ni = 1 .

p MCp N

i− =+⋅

( )1 λε

(vii)

6) So, Lerner Index or monopoly power can be determined by N , , and ε λ . Ex) In perfect competition, p MCi= (QN →∞ and ε = ∞ )

In monopoly, N = =1 0, λ . So, p MCp

i− =1ε

For more generalized case, we can relax the assumption that λ is constant. So, assuming that λ i and ki can vary among the firms, then we get

p MCp

ki i i− = +( )1 λε (viii)

7) Let’s think about the industry (But, assume that MC AC= ) Rewriting equation (ii), we can get

π i i i i ip Q q c q q= ⋅ − ′ ⋅( ) ( ) , i N= 1 2, , , L (ix) Let Π denote the industry profit or aggregate profits, then

Π = = ⋅ − ⋅ ′∑∑∑=π i i i i i

i

Np Q q q c q( ) ( )

1 (x)

8) From (viii), multiplying by qi on both sides and summing up from 1 through N, we get

pq c qp

k qi i i i i i− ′∑∑ = +∑ ( )1 λε

. And pq c qpQ

k qQ

ki i i i i i i i− ′∑∑ = +∑⋅

=+∑( ) ( )1 12λ

ελ

ε (xi)

From equation (x) and (xi),


ΠTR

k HHIi i i= +∑ = +2 1 1( ) ( )λε

λε (xii)

, where HHI kii

N= ∑

=

2

1(Herfindahl-Hirschmann Index)

9) From (xii), l.h.s is called Industrial Rate of Return, which can reflect the performance of the industry.

10) If MC ki i i, , and λ are constant, HHI k Nii

N= =∑

=

2

1

1 (why?)

ΠTR N

p MC QpQ

LI= + = − =( ) ( )1 λε (xiii)

In conclusion, 1. As N →∞ , Conjectural variation ( )λ i → 0

Negligible market share ( )ki → 0

Low HHI ( )HHI → 0

Therefore, from (xii), the value on r.h.s. will go to zero, which is analogous to the perfect

competition with p MC= .

2. If monopoly, N k HHIi i= = = =1 100%) 10000 0, 1 or , 1 or , and ( ( ) λ .

∴(Price-cost margin in monopoly) = (industrial rate of return)

p MCp TR

−= =

1ε

Π

4. Cournot Duopoly (Augustine A. Cournot, 1838) 1) Assumptions * λ i i idQ dq= =− / 0 * Each firm determines products that maximize their profits taking the products of rivals’ constant. * Market demand is QaP −= ( )0>a and 21 qqQ += (Q is the total quantity of spring water sold in the market per unit of time). * For simplicity, cACMC == . 2) Model * Firm 2 assumes that firm 1 is producing 1q and it produces 2q as the best response to 1q . * So, the economic profit for firm 2 is as follows, 22122 )()( qqqcaqcP −−−=−=π .

02 212

2 =−−−=ΔΔ

qqcaqπ

(i). From (i), we get the best response of firm 2 to 1q of firm 1,


2

12

qcaq

−−= (ii): Reaction Curve of firm 2

* In the same way, we get reaction curve of firm 1.

2

21

qcaq

−−= (iii): Reaction Curve of firm 1

2q )( ca − Firm 1

2/)( ca − C

3/)( ca − M Firm 2 3/)( ca − 2/)( ca − )( ca − 1q * Cournot-Nash Equilibrium

3

** 21caqq −==

3

2*2* 1caqaP +=−=

*)*(9

)(1

2

qcPcac −=−

=π

* Suppose firm 1 and firm 2 decide to make a Cartel and act as “collective monopolist.” Then what are the profits of two firms? And what is the monopolistic product? (MR = MC) Given demand curve is QaP −= . .)( QQaPQTR −== And ,2QaMR −= and cMC =

MCcQaMR ==−=∴ 2 . So, 2

)( caQm−

=

If these two firms produce the same quantities, then 4

)(21

caqq −== .

And ,2

caPm+

=8

)( 2cam

−=π , which is bigger than profit at point C (

9)( 2ca

c−

=π ).

* If the two firms make a Cartel and determine their quantities cooperatively, then their economic profits are higher than those of Cournot-Nash equilibrium. Therefore, there is a good reason and motive to cartelize or to collude.


* But, why do we call C as an equilibrium point, not M? Or, why is not M an equilibrium? Because there is another motive to cheat by increasing quantity to earn more profit at point M.

* If firm 1 produces 41

caq −= and keeps the Cartel but firm 2 does not, then the profit function

of firm 2 is as follows: 22222 ))(43()

4( qqcaqqcaca −−=−−−−=π .

02)(43

22

2 =−−=ΔΔ

qcaqπ

.

),(83**2 caq −= which maximizes economic profit of firm 2. Hence, firm 2 breaks the cartel

and produces more. Market price of firm 2’s products is 8

532

caP += and

222 )(81)(

649 caca −>−=π .

* Firm 2 has a motive to cheat firm 1. Vice versa. So, one-shot cartel is unstable. * Cartel is easy to collapse. But, if the cartel is made among few firms for relatively long periods, then it can be sustained longer with efficient and severe punishment or penalty on the violators. 5. Generalization to Oligopoly P a Q a= − >, 0 .

Q qii

n= ∑

=1

π i i i i n ip c q a c q q q q q q= − = − − + + + + + ++( ) [ ( )]1 2 1L L

ddq

a c q q q q q qii

i i i nπ

= − − − − − − − − − =− +[ ]1 2 1 12 0L L

⇒ + + + + + + = −− +q q q q q a ci i i n1 1 12L L Assuming that c c MC AC ii i i= = = ∀, ( *)q qj =

q a cn

p a ncn

a cn

* * * ( )( )

=−+

=++

=−+1 1 1

2

2, , π

If n = 2 , we get the same results in Cournot Duopoly. 6. Bertrand’s Paradox 1) Assumptions * Each firm is assuming that the prices of other firms are constant in deciding the quantities. * So, in this model we can think about the motive to set a lower price than any other firm. * Price-undercutting and finally up to most competitive level. 2) Model Unlike Cournot model, firms will determine the price. And quantity is decided in accordance with the price. * Market Demand: P a Q= − or Q a P= − ( a > 0 ) Suppose there are two flash memory (USB) companies TDK and Maxell. Assuming that the USBs are entirely identical in every aspect, then consumers try to purchase a cheaper one.


If P PT M< , Q a P QT T= − = and QM = 0

If P PT M= , Q a P QT T M= − =12

( )

If P PT M> , QT = 0 and Q a P QM M= − = , where Q Q QM T= + . The unique (Nash) equilibrium is accomplished if P P cT M= = , and at this level

π πT M c c a c= = − × − =( ) ( )12

0 .

* The rationale is as follows; At P P cT M= = , no firm can set a price lower than c. If P cT > , then Maxell can dominate the market by setting P PM T< even slightly. If P PT M> , π T TP c= − × =( ) 0 0

If P PT M= , π T T TP c a P= − × −( ) ( )12

If P PT M< , π T T TP c a P= − × −( ) ( ) * For example, if TDK sets P PT M= − ε ( ε > 0 ), then its profit will be ( )( )P c a PM M− − − +ε ε . Simply, as ε approaches to zero, its profit will go to

( )( )P c a PM M− − . If TDK sets P PT M= , profit is 12

( )( )P c a PM M− − ,

which is about half of ( )( )P c a PM M− − − +ε ε . Ex) Suppose a = 2000 , c = 800 , PM = 1000 , and PT = =999 1, ε . Maxell earns 0, and TDK earns ( ) ( ) ,999 800 2000 999 199 199− × − = .

If P PT M= =1000, π T = − − =12

1000 800 2000 1000 100 000( )( ) ,

7. Product Differentiation 1) Model * Small Car Market (Oligopoly) Two Firms: Ford (Firm 1) and Toyota (Firm 2) with Focus and Echo, respectively. * For simplicity, assume that MC AC c AC MCF F T T= = = = .

Demand facing Ford is assumed to be Q a P PF F T= − + ⋅β (i). * If β > 0, the increase in PT will increase QF . It means Focus and Echo are substitutes. * If β < 0, two products are complements. 2) Analysis Let’s get best response of Ford to PT . π βF F F F F TP c Q P c a P P= − = − − + ⋅( ) ( )( ) (ii)

ddP

a c P PFF

F Tπ

β= + − + ⋅ =2 0 (iii)


The reasonable price PF is Pa c P

FT=

+ + ⋅β2

(iv) (Ford’s reaction curve to Toyota’s price)

For example, if Toyota sells Echo at P cT = , then Ford’s best way to maximize its profit is to

sell Focus at P a c cF =+ + β

2.

Suppose the demand facing Toyota is Q a P PT T F= − + ⋅β (v)

In the same way, we can get P a c PT F=+ + ⋅β

2 (vi)

PT Ford Toyota B d c a b PF

Point a and c: a c+2

Point b and d: a c+−2 β

If 0 2<


1) Hotelling’s Model (1929) * Consider a long, narrow city with only one street which is 1 mile long. * Consumers are uniformly distributed between 0 and 1. * Each has to purchase one unit of product. * Two stores are selling almost identical product at the same price and try to maximize profits. * Consumers will purchase at the nearest store because they have to incur transaction cost (travel, time, waiting, …). store 1 store 2 Location 0 a 1 - b 1 a ( )1− −a b b * Suppose two stores have to locate at the same time before they start to sell. Consumers living on the left of store 1and half of consumers living between store 1 and 2 will choose store 1. * Store 1’s market share = + − − = + −a a b a b05 1 0 5 1. ( ) . ( ) Store 2’s market share = + − − = − +b a b a b0 5 1 0 5 1. ( ) . ( ) * The equilibrium in this location game is where two stores are located in the center of this linear city. a b= = −0 5 1. ( ) * Intuitively, if store 1 is at a = 0 5. , then the best response of store 2 is to locate at b = 0 5. to maximize its share. But, if store 2 is at ( ) .1 0 5− >b , then it has less 50% of total share. If store is at a = 0 3. , store 2 can maximize its share by locating at ( ) .1 0 3− =b , right next to store 1. The equilibrium when there are two firms suggested to Hotelling that “Buyers are confronted everywhere with an excessive sameness” (1929). The result that two firms in either product or geographic space will locate in the middle is often referred to as the principle of minimum differentiation (K. Boulding, 1966). The principle does not hold strictly when there are more than two firms. However, even when there are more than two firms, the equilibrium market configuration is characterized by “bunching.” * Economic Implication: Adopting this model to product Differentiation Two competitive firms in duopoly will have a strategy for medium consumers as main target in design, character or quality. And the degree of differentiation is trivial. Ex) Even in political science, U.S. has two party politics system. Democrats and Republican. They take public pledge or commitments which are so similar or vague which are not easily distinguishable. 9. Stackelberg’s Duopoly (Leader-Follower Model) In Cournot’s duopoly, we assumed that λ = 0 . But, if the decision on production is sequential or if there is a gap in competitive power, then one firm acts as a leader and the others as followers. Stackelberg showed another duopoly model with leader and followers. In his model, leader acts as if the other firm’s output is constant, and followers, however, choose optimal products in response to leader’s output. 1) If leader/follower are predetermined * Firm 1 (leader) and Firm 2 (follower). Identical in almost every aspect.


* Market demand: P a q q= − +( )1 2 , same demand in Cournot model. * MC AC c AC MC1 1 2 2= = = =

* If q1 is determined, q2 that maximizes π 2 will be: qa c q

21

2=

− − (i)

* And, Firm 1 (leader) can expect that Firm 2 will produce q a c q2 12=

− − if Firm 1 produces q1 .

So, plugging the reaction curve of Firm 2 into π 1 ,

π 1 1 1 2 1 1 1 1 12

2 212

= − = − − − =− −

× =−

−( ) ( )p c q a c q q q a c q q a c q q (ii)

ddq

a c q q a cπ 11

1 120

2=

−− = =

−, * (iii)

* By the way, the Firm 2 (follower) will produce q2 in response to qa c

1 2* = − .

qa c a c a c

22

2 4* =

− −−

=−

(iv)

* So, market product Q q q a c= + = −1 23

4* * ( ) (v)

* Market price is P a a c a c* ( )= − − = +34

34

(vi)

* 8

)(2

)(4

3)(2

*1

**1

cacaccaqcP −=−⋅⎟⎠⎞

⎜⎝⎛ −

+=−=π (vii)

*16

)(4

)(4

3)(2

*2

**2

cacaccaqcP −=−⋅⎟⎠⎞

⎜⎝⎛ −

+=−=π (viii)

2) If leader/followers are not certain We know every firm wants to be a leader because the leader’s profit is always bigger than that of follower. So, if the leader and follower are not determined before they start game, we might expect different results. Each firm has two strategies; Lead and Follow. * If two firm act as leaders ad produce q1 and q2 ,

q q a c1 2 2* *= = − , P a q q c= − + =( )1 2 , π π1 1 2 2 0= − = − = =( ) ( )P c q P c q

Identical to Perfect Competition (Stackelberg Warfare) * If two firms act as followers and produce q1 and q2 ,

q q a c1 2 3′ = ′ =

− , ′ = +P a c23

,π π1 221

9′ = ′ = −( )a c

It is Cournot Duopoly


q2 Firm 1 S2 W a c−

2

C a c−

3

S1 a c−

4 M

Firm 2 a c−

4 a c−

3 a c−

2 q1

C: Cournot-Nash Equilibrium Point S1: If Firm 1 is a leader S2: If Firm 2 is a leader W: Stackelberg Warfare

10. Kinked Demand Curves (by Paul Sweezy) P MC1 A MC2 PA

B C Demand

MR QA


Another hypothesis about how oligopolistic rivals may respond says that rivals match price cuts but do not respond to price increases. In this situation, an oligopolist believes that it will not gain much in sales if it lowers its price, because rivals will match the price cuts, but it will lose considerably if it raises its price, since it will be undersold by rivals who do not change their prices. The demand curve facing such an oligopolist appears kinked. The curve is very steep below the current price, 1p , reflecting the fact that few sales are gained as price is lowered. But it is relatively flat above that price, indicating that the firm loses many customers to its rivals, who refuse to match the price increases.

The figure also presents the MR curve, which has a sharp drop at the output level corresponding to the kink. Why does the MR curve have this shape, and what are the consequences? Consider what happens if the firm wants to increase output by one unit. It must lower its price by a considerable amount since, as it does so, its rivals will match that price. Accordingly, the MR it garners is small. If the firm contemplates cutting back on production by one unit, it needs to raise its price only a little since rivals will not change their price. Thus, the loss in revenue from cutting back output by a unit is much greater than the gain in revenue from increasing output by a unit. With a flat demand curve, price and MR are close together.

The drop in MR means that at the output at which the drop occurs, extra revenue lost from cutting back production is much greater than the extra revenue gained from increasing

production. This has one important implication. Small changes in MC, from MC1 to MC2, have no effect on output or price. Thus, firms that believe they face a kinked demand curve have good reason to hesitate before changing their price. 11. Advertising (Non-price competition) 1) Types of Advertising • Persuasive advertising of experience goods: focusing on image making for the company • Informational advertising of search goods: focusing on information of products 2) Optimal Advertising Model TR TR Q= ≥( ), , where α α 0 (advertising expenses) π α α= − −TR Q TC Q( ) ( ), . To solve for Q *andα * that can maximize profit, FOCs will be

∂∂

=∂∂

− = − =

∂∂

=∂∂

− = − =

π

πα α α

QTRQ

dTCdQ

TR MC

TR TR

Q 0

1 1 0

Can you interpret the result?


Lecture 09 – Market Structure (III) B. Monopolistic Competition (MC) and more 1. Product Differentiation Revisited Product differentiation by their characteristics or attributes. Ex) Automobile models are distinguished by their attributes: number of cylinders; type of upholstery; number of doors; horsepower; length; width; and weight; front-, back- or four- wheel drive; air conditioning; stereo system; transmission type; fuel efficiency; exterior styling; and so on. Products are horizontally differentiated if consumers have heterogeneous preferences regarding the most preferred mix of different attributes – there is no agreement among consumers regarding which particular product or brand is the best. When the tastes of consumers are asymmetric and prices identical, a wide range of substitutable products are demanded. Ex) light vs. regular beer; thin- vs. thick-crust pizza. Products are vertically differentiated if consumers unanimously agree on which product or brand is preferred. Vertical differentiation corresponds to situations where consumers agree on a quality index so that if all products had the same price, consumers would all purchase the identical brand. Automobile brands within a class are horizontally differentiated. But automobile classes are vertically differentiated – if the price of a Ford Focus were the same as a Saab Turbo 900, all consumers would purchase the Saab. There are two common approaches to the specification of consumers’ preferences when products are horizontally differentiated. The address branch assumes that consumers have preferences over the characteristics of products. The goods branch assumes that consumers have preferences over goods and a taste for variety. These different approaches to specifying the preferences of consumers give rise to different modeling approaches, address models and monopolistic competition.

2. Monopolistic Competition The “goods are the goods approach” dates from Edward Chamberlin’s publication of The Theory of Monopolistic Competition in 1933.

1) Preference Specification Two key assumptions typically underlie the specification of preferences in models of MC. • There is a very large set of possible differentiated products over which the preferences of consumers are defined. • The preferences of consumers over the set of all possible differentiated brands are symmetric → close substitutability among the goods within the group 2) Monopolistic Competition: Equilibrium The focus of MC models is not (typically) on the strategic decisions regarding product specification or design, since the products of all firms are equally differentiated by assumption. Instead the analysis is used to focus on the issue of the extent of variety – the number of products available in the market.

• Equilibrium Conditions a) Profit-Maximization. b) Free-Entry Condition.


• Determinants of MC Equilibrium Elasticity of substitution and scale economies • Excess-Capacity Results Price exceeds marginal cost, so that firms are exercising market power. Firms are not producing where their average costs are minimized.

P LMC LAC F P* D* MR* Q Q* QM Excess capacity


Lecture 10 – Market Structure (IV) C. Game Theory 1. Foundations and Principles 1) Basic Elements of a Game • Players: the identity of those playing the game, N ≥ 2 • Rules: the timing of all players’ move; the actions available to a player at each of her moves; the information that a player has at each move. • Outcomes: It depends on what each player does when it is her turn to move. The set of outcomes is determined by all of the possible combinations of actions taken by players. • Payoffs: It represents the players’ preferences over the outcomes of the game. 2) Types of Games • Static (strategic) games of complete information • Dynamic games of complete information • Static (strategic) games of incomplete information • Dynamic games of incomplete information 3) Equilibrium Concepts We want to focus on how to solve games. An equilibrium concept is a solution to a game. By this we mean that the equilibrium concept identifies, out of the set of all possible strategies, the strategies that players are actually likely to play. Solving for equilibrium is similar to making a prediction about how the game will be played. The focus is on defining commonly used equilibrium concepts and illustrating how to find strategies consistent with each concept. 4) Fundamental Assumptions • Rationality: Players are interested in maximizing their payoffs. • Common Knowledge: All players know the structure of the game and that their opponents are rational, that all players know that all players know the structure of the game and that their opponents are rational, and so on. Static Games of Complete Information “Static” means that players have a single move and that when a player moves, she does not know the action taken by her rivals. This may be because players move simultaneously. “Complete information” means that players know the payoffs of their opponents. 5) Normal Form Representation • A set of players, identified by number: { }I , 2, 1, L

• A set of actions or strategies for each player i , denoted Si . This is the “list” of permissible actions player i can take. • A payoff function for each player i , π i s( ) , where s s s sI= ( )1 2, , , L and s Si i∈ (strategy vector). • In addition, the descriptions of some games require delineation of who knows what, when, and order of play, etc. 2. One Shot Game If a game is played only once and the players move simultaneously or at least no player knows any of the other players’ moves before choosing his. Thus we fully characterize a one-shot

game by a list of the available strategies and payoffs { }IISSK ππ ,,;,, 11 LL=


1) Strategic Form It is called the strategic (or normal) form representation of a game. For starters, let’s consider the strategic form of a one-shot game with only two players, A and B, each with two strategies, 1 and 2. (The players could be two firms, an employer and employee, a parent and child, etc.) The payoffs for each player are collected in the following two matrices. These are combined into a single game matrix:

Player B 1 2

1 π A11 ,π B

11 π A12 ,π B

12 Player A

2 π A21 , π B

21 π A22 ,π B

22 ,which fully summarizes the strategic form of the game. The game matrix is useful for depicting the strategic form of games with few players (usually two or three) and a finite number of strategies. A game is symmetric if π πA

jkB

kj= for all j and k. If π πAjk

Bkj c+ = , where c is a constant, for

each pair of strategies (j, k), then the game is constant sum; if c = 0, then it is a zero-sum game. Most generally, games are variable sum. We are looking for a solution to such games. If each player is rational, what is her optimal strategy? This is given by the best response function. Player i’s best response to other player’s strategies is the solution to the following maximization problem:

max ( , ),S i i i i Iis s s s sπ 1 1 1L L, , , , − + (i)

given the strategies of the ( )I −1 other players. So the best response function is s R si i i= ( ) , which can also be expressed as R s s s si i i I( )1 1 1, , , , , L L− + ; that is, i’s best strategy is generally a function of the strategies of all other players. If each player plays her optimal strategy, what happens? That is, what is the equilibrium of such a game? 2) Eliminating Dominated Strategies One feature of best response functions is that they never reflect dominated strategies. For

player i, strategy si ′ dominates strategy si ′′ if the payoff to si ′ exceeds the payoff to si ′′ for every combination of other players’ strategies si ; that is, if

π πi i i i i is s s s( , ) ( , )′ > ′′ (ii)

for all si . Rational players never play dominated strategies si ′′ , so we can frequently eliminate some strategies as candidates for solutions.

Player B Player B 1 2 1 2

1 π A11 π A

12 1 π B11 π B

12 Player A

2 π A21 π A

22

Player A

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