International economic ch10

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  • 1

    Chapter 10THE PARTIAL EQUILIBRIUM

    COMPETITIVE MODEL

    Copyright 2005 by South-Western, a division of Thomson Learning. All rights reserved.

  • 2

    Market Demand Assume that there are only two goods

    (x and y) An individuals demand for x is

    Quantity of x demanded = x(px,py,I) If we use i to reflect each individual in the

    market, then the market demand curve is

    =

    =n

    iiyxi ppxX

    1),,( for demand Market I

  • 3

    Market Demand To construct the market demand curve,

    PX is allowed to vary while Py and the income of each individual are held constant

    If each individuals demand for x is downward sloping, the market demand curve will also be downward sloping

  • 4

    Market Demand

    x xx

    pxpxpx

    x1* x2*

    px*

    To derive the market demand curve, we sum thequantities demanded at every price

    x1

    Individual 1sdemand curve

    x2

    Individual 2sdemand curve

    Market demandcurve

    X*

    X

    x1* + x2* = X*

  • 5

    Shifts in the MarketDemand Curve

    The market demand summarizes the ceteris paribus relationship between X and px changes in px result in movements along the

    curve (change in quantity demanded) changes in other determinants of the

    demand for X cause the demand curve to shift to a new position (change in demand)

  • 6

    Shifts in Market Demand Suppose that individual 1s demand for

    oranges is given byx1 = 10 2px + 0.1I1 + 0.5py

    and individual 2s demand isx2 = 17 px + 0.05I2 + 0.5py

    The market demand curve isX = x1 + x2 = 27 3px + 0.1I1 + 0.05I2 + py

  • 7

    Shifts in Market Demand To graph the demand curve, we must

    assume values for py, I1, and I2

    If py = 4, I1 = 40, and I2 = 20, the market demand curve becomes

    X = 27 3px + 4 + 1 + 4 = 36 3px

  • 8

    Shifts in Market Demand If py rises to 6, the market demand curve

    shifts outward toX = 27 3px + 4 + 1 + 6 = 38 3px

    note that X and Y are substitutes

    If I1 fell to 30 while I2 rose to 30, the market demand would shift inward toX = 27 3px + 3 + 1.5 + 4 = 35.5 3px note that X is a normal good for both buyers

  • 9

    Generalizations Suppose that there are n goods (xi, i = 1,n)

    with prices pi, i = 1,n. Assume that there are m individuals in the

    economy The j ths demand for the i th good will

    depend on all prices and on Ijxij = xij(p1,,pn, Ij)

  • 10

    Generalizations The market demand function for xi is the

    sum of each individuals demand for that good

    ),,...,( 11

    jn

    m

    jiji ppxX I

    =

    =

    The market demand function depends on the prices of all goods and the incomes and preferences of all buyers

  • 11

    Elasticity of Market Demand The price elasticity of market demand is

    measured by

    D

    DPQ Q

    PP

    PPQe

    = ),',(,I

    Market demand is characterized by whether demand is elastic (eQ,P eQ,P > -1)

  • 12

    Elasticity of Market Demand The cross-price elasticity of market

    demand is measured by

    D

    DPQ Q

    PP

    PPQe ''

    ),',(,

    = I

    The income elasticity of market demand is measured by

    D

    DQ Q

    PPQe III

    I = ),',(,

  • 13

    Timing of the Supply Response In the analysis of competitive pricing, the

    time period under consideration is important very short run

    no supply response (quantity supplied is fixed) short run

    existing firms can alter their quantity supplied, but no new firms can enter the industry

    long run new firms may enter an industry

  • 14

    Pricing in the Very Short Run In the very short run (or the market

    period), there is no supply response to changing market conditions price acts only as a device to ration demand

    price will adjust to clear the market the supply curve is a vertical line

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    Pricing in the Very Short Run

    Quantity

    PriceS

    D

    Q*

    P1D

    P2

    When quantity is fixed in thevery short run, price will risefrom P1 to P2 when the demandrises from D to D

  • 16

    Short-Run Price Determination The number of firms in an industry is

    fixed These firms are able to adjust the

    quantity they are producing they can do this by altering the levels of the

    variable inputs they employ

  • 17

    Perfect Competition A perfectly competitive industry is one

    that obeys the following assumptions: there are a large number of firms, each

    producing the same homogeneous product each firm attempts to maximize profits each firm is a price taker

    its actions have no effect on the market price information is perfect transactions are costless

  • 18

    Short-Run Market Supply The quantity of output supplied to the

    entire market in the short run is the sum of the quantities supplied by each firm the amount supplied by each firm depends

    on price The short-run market supply curve will

    be upward-sloping because each firms short-run supply curve has a positive slope

  • 19

    Short-Run Market Supply Curve

    quantity Quantityquantity

    PPP

    q1A q1B

    P1

    To derive the market supply curve, we sum thequantities supplied at every price

    sA

    Firm Assupply curve sB

    Firm Bssupply curve

    Market supplycurve

    Q1

    S

    q1A + q1B = Q1

  • 20

    Short-Run Market Supply Function

    The short-run market supply function shows total quantity supplied by each firm to a market

    =

    =n

    iis wvPqwvPQ

    1),,(),,(

    Firms are assumed to face the same market price and the same prices for inputs

  • 21

    Short-Run Supply Elasticity The short-run supply elasticity describes

    the responsiveness of quantity supplied to changes in market price

    S

    SPS Q

    PPQ

    PQe

    ==

    in change %supplied in change %

    ,

    Because price and quantity supplied are positively related, eS,P > 0

  • 22

    A Short-Run Supply Function Suppose that there are 100 identical

    firms each with the following short-run supply curve

    qi (P,v,w) = 10P/3 (i = 1,2,,100)

    This means that the market supply function is given by

    31000

    310100

    1

    100

    1

    PPqQi i

    is === = =

  • 23

    A Short-Run Supply Function In this case, computation of the

    elasticity of supply shows that it is unit elastic

    13/10003

    1000),,(, ==

    =P

    PQP

    PwvPQe

    S

    SPS

  • 24

    Equilibrium Price Determination

    An equilibrium price is one at which quantity demanded is equal to quantity supplied neither suppliers nor demanders have an

    incentive to alter their economic decisions An equilibrium price (P*) solves the

    equation:),*,(),'*,( wvPQPPQ SD =I

  • 25

    Equilibrium Price Determination

    The equilibrium price depends on many exogenous factors changes in any of these factors will likely

    result in a new equilibrium price

  • 26

    Equilibrium Price Determination

    Quantity

    PriceS

    D

    Q1

    P1

    The interaction betweenmarket demand and marketsupply determines theequilibrium price

  • 27

    Market Reaction to aShift in Demand

    Quantity

    PriceS

    D

    Q1

    P1

    Q2

    P2 Equilibrium price andequilibrium quantity willboth rise

    If many buyers experiencean increase in their demands,the market demand curvewill shift to the right

    D

  • 28

    Market Reaction to aShift in Demand

    Quantity

    PriceSMC

    q1

    P1

    This is the short-runsupply response to anincrease in market price

    q2

    P2

    If the market price rises, firms will increase their level of output

    SAC

  • 29

    Shifts in Supply and Demand Curves

    Demand curves shift because incomes change prices of substitutes or complements change preferences change

    Supply curves shift because input prices change technology changes number of producers change

  • 30

    Shifts in Supply and Demand Curves

    When either a supply curve or a demand curve shift, equilibrium price and quantity will change

    The relative magnitudes of these changes depends on the shapes of the supply and demand curves

  • 31

    Shifts in Supply

    Quantity Quantity

    PricePriceS

    SS

    S

    DD

    PP

    Q

    P

    Q

    P

    QQ

    Elastic Demand Inelastic Demand

    Small increase in price,large drop in quantity

    Large increase in price,small drop in quantity

  • 32

    Shifts in Demand

    Quantity Quantity

    PricePrice

    S

    S

    D D

    P P

    Q

    P

    Q

    P

    Q Q

    Elastic Supply Inelastic Supply

    Small increase in price,large rise in quantity

    Large increase in price,small rise in quantity

    D D

  • 33

    Changing Short-Run Equilibria Suppose that the market demand for

    luxury beach towels isQD = 10,000 500P

    and the short-run market supply isQS = 1,000P/3

    Setting these equal, we find P* = $12

    Q* = 4,000

  • 34

    Changing Short-Run Equilibria Suppose instead that the demand for

    luxury towels rises toQD = 12,500 500P

    Solving for the new equilibrium, we find P* = $15

    Q* = 5,000 Equilibrium price and quantity both rise

  • 35

    Changing Short-Run Equilibria Suppose that the wage of towel cutters

    r