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					ECON6021 (Nov 2004)


Price Taking, Price Setting, and
Competitive Market
This lecture will introduce:

   Profit maximization
   Price Taking Firm
    – Supply curve
    – Application: multi-plant firm
   Price Setting Firm
    – Price-cost margin
    – Price discrimination
   Competitive Market
    – Efficiency of Competitive Market
Marginal Analysis
   Firm’s objective
    – to maximize profit π=TR-TC

   If MR > MC, the extra revenue from selling
    one more unit exceeds the extra cost.

   If MR < MC, the extra revenue from selling
    one more unit is less than the extra cost.

   If MR = MC economic profit is maximized.
Profit Maximization

   π is maximized if
    – MR = MC and MR cuts MC from above
    – So long as it is worthwhile producing
   This holds for whatever market structure
    such as
    – Perfect competition (price taking firm)
    – Monopoly (price setting firm)
        Price Taking Firm
Total revenue & total cost
         (dollars per day)


                                                           TR

                             300

                             225
                                                    Economic
                             183                    profit =
                                                    TR - TC
                             100
                                   Economic
                                   loss

                               0   4          9    12
                                        Quantity (sweaters per day)
Profit-Maximizing Output for a
Price Taking Firm(dollars per day)
 Marginal revenue & marginal cost

                                          Profit-
                                          maximization
                                                                  MC
                                     30   point

                                     25                                D=AR=MR

                                     20



                                     10


                                                     8 9 10
                                                    Quantity (sweaters per day)
        Total Revenue, Total Cost,
        and Economic Profit for a Price
        Setting Firm
Total revenue & total cost
         (dollars per day)




                             300

                             225

                             183

                             100



                               0   4       9      12
                                       Quantity (sweaters per day)
                                    A Price Setting Firm’s Profit
                                    Maximizing Output
Price and cost (dollars per hour)

                                                                    MC
                                     20



                                                                                        dP(Q )
                                     14                             MR (Q )  P(Q )  Q
                                                                                         dQ

                                     10
                                                                                  D

                                                            MR
                                      0   1    2      3        4           5
                                                   Quantity (haircuts per hour)
Price Taking
Firm
Characteristics of Perfect
Competition
     – Many firms, each selling an identical product
     – Many buyers
     – No restrictions on entry into the industry
     – Firms in the industry have no advantage over potential new
       entrants
     – Firms and buyers are well informed about prices of the
       products of each firm in the industry
   As a result of these characteristics, perfect competitors are price
    takers.
   Price takers -- firms that cannot influence the market price
A Firm’s Supply Curve                                       MC curve
                 (dollars per day)
 Marginal revenue & marginal cost

                                                            = Supply curve

                                     31                      MR2


                                     25                       MR1
                                                           AVC
                                          s
                                     17                      MR0



                                          7    9 10
                                           Quantity (sweaters per day)
A Firm’s Supply Curve
                 (dollars per day)
 Marginal revenue & marginal cost

                                                         S
                                     31



                                     25


                                          s
                                     17



                                          7    9 10
                                           Quantity (sweaters per day)
Application: Multi-plant firm

   Suppose a perfectly competitive firm has two
    plants producing identical goods with
    marginal cost functions MC1(Q1) and
    MC2(Q2).
   It is straightforward to show that it show
    produce Q1 and Q2 in the two plant so that
                MC1(Q1) = MC2(Q2) = P
    where P is market price.
Price Setting
Firm
Price Setting Firm and How
Monopoly Arises
   The simplest form of price setting firm is
    monopoly
   A monopoly is an industry that produces
    a good or service
    – for which no close substitute exists and
    – in which there is one supplier that is
      protected from competition by a barrier
      preventing the entry of new firms.
Barriers to Entry

   Key input owned by a firm
    – DeBeers, a South African firm that controls
      more than 80 percent of the world’s supply
      of natural diamonds.
   But most monopolies arise from two
    other types of barrier: legal barriers and
    natural barriers
Barriers to Entry
   Legal Barriers to Entry
    – In a legal monopoly competition and entry is restricted by the
      granting of a public franchise, government license, patent, or
      copyright.
    – E.g. Microsoft is the only firm that is allowed to produce
      Window 98, etc. HK Town gas. China light
   Natural Barriers to Entry
    – A natural monopoly results from a situation in which one firm
      can supply the entire market at a lower price than two or
      more firms can.
    – Example: Electric utility
    – A market used to be thought as a natural monopoly may turn
      out to be no longer the case as technology progresses
Natural Monopoly
  Price (cents per kilowatt-hour)
                                    15



                                    10



                                     5                                      ATC

                                                                        D

                                    0    1      2       3          4
                                             Quantity (millions of kilowatt-hours)
Monopoly Price-
Setting Strategies
   Price discrimination is the practice of
    selling different units of a good or
    service for different prices.
   A single-price monopoly is a firm that
    must sell each unit of its output for the
    same price.
Single-Price Monopoly

   The firm’s demand curve is the market
    demand curve.
   Marginal revenue is not the same as the
    market price.
   There is no supply curve for a
    monopoly.
Price and Output Decision

   The competitive firm is a price taker, whereas
    the monopoly influences its price.
   For the monopoly, price exceeds marginal
    revenue, thus price exceeds marginal cost.
   Profit is maximized where MC = MR
   Monopolists can earn economic profits--firms
    cannot enter due to barriers to entry.
A Monopoly’s Output and Price
Price and cost (dollars per hour)

                                                                           MC
                                    20
                                                                                     Profit = $12
                                                                                     ($4 x 3 units)

                                    14
                                         Economic                                   ATC
                                         profit $12
                                    10
                                                                                         D

                                                                   MR
                                    0        1        2      3        4           5
                                                          Quantity (haircuts per hour)
An example: Linear Demand Q =
100 – 2P; AC=MC=10
   Inverse demand: P = 50 – Q/2
   TR = P*Q = (50 – Q/2) Q = 50Q – Q2/2
   MR = 50 – Q
    – Remark: if P = A – BQ, then MR = A – 2BQ
   MR = MC → 50 – Q = 10 → Q = 40
   Substituting Q = 40 into inverse
    demand, P = 50 – 40/2 = 30
Optimal output, profit margin, and
profit
      P

          AR = P(Q) =50 – Q2/2

 30                 Profit = profit margin X Q*
                            = (P* - AC) Q*

                                   MC = AC
 10
                MR = 50 – Q2
                                         Q
           40
Price-cost Margin and Elasticity
               dTR                dP(Q )
        MR           P (Q )  Q
               dQ                   dQ
                          Q dP(Q ) 
                      P 1 
                                      
                             P dQ    
                          dP(Q ) / P 
                      P 1 
                                      
                               dQ / Q 
                                       
                                1 
                        P1       
                                     
                            ex ,Px 
                              1 
                       P 1 
                           | e |
                                      
                              x , Px 
Price-cost market and
    Equating MC with MR, we have

                                      1 
         MC           MR  P1 
                              | e |
                                              
                                     x , Px 
                        P  MC        1
 price - cost margin          
                           P      | e x ,Px |
     The more elastic the demand, the smaller the
      price-cost margin
     Price-cost margin, a.k.a. price-cost markup, or
      Lerner Index of market power (1934).
Competition and Efficiency

   Efficiency is achieved when all the gains
    from trade have been realized (social
    welfare is maximized).
 Monopoly and
 Competition Compared
Price

        PA    Single-price
              monopoly
              restricts output,
              raises price
                                  MC
        PM
                                  Equilibrium
        PC                        in competitive
                                  industry




              MR                     D


         0   QM    QC             Quantity
 Inefficiency of Monopoly
Price

                   Consumer
        PA         surplus                       Monopoly

                                    MC
        PM
                                    Deadweight
        PC                          loss
             Monopoly’s
             gain


                              MR       D


         0                QM   QC    Quantity
Gains from Monopoly

   Economies of Scale and Scope
    – Lowers average total cost and a greater
      range of goods produced

   Incentives to Innovate
    – The attempt to apply new knowledge in the
      production process and obtain a patent
Price Discrimination
   Arcadia Publisher is planning to publish a book.
    – loyalty to the author is fixed at $2M
    – production cost=$0 per copy
    – two groups of buyers
        • 100K group 1 readers--each willing to pay up to $30
        • 400K group 2 readers--each willing to pay up to $5
   If p= $30, only group 1 readers will buy the book.
    Arcadia obtains $30x100K =$3M (gross of loyalty)
   If p= $5, both groups of readers will buy the book.
    Arcadia obtains $5x500K=$2.5M (gross of loyalty)
   Hence, charging $30 is better.
Price Discrimination

   Now suppose Arcadia knows that all
    group 1 readers are in HK and group 2
    readers are in Chile. Then it can
    charges a fee of $30 for a book sold in
    HK and $5 for a book sold in Chile.
   Price discrimination leads to
    – greater profits
    – greater social welfare!!
Determination of differentiated
prices under constant marginal cost
                                       A



          2 segmented markets, 2
          separate price in general.




      b                 b/2                B/2       q
                                                 B
More generally, the problem is
    max Q1 ,Q2 P1 (Q1 )Q1  P2 (Q2 )Q2   TC (Q1  Q2 )

   Optimal output for the two markets are given by
              P1 (Q1 ) TC
      P1  Q1               0
                Q1      Q1
                P2 (Q2 ) TC
      P2  Q2                  0
                  Q2      Q21
                    P1 (Q1 )           P2 (Q2 )
      MC1  P1  Q1            P2  Q2            MC2
                      Q1                 Q2

Equalizationof marginal cost and marginal revenue
in each segment
Evidence of Geographic Price
Discrimination
   Parallel imports--unauthorized flows of
    genuine products across countries that
    compete with authorized distribution channels
    (ranging from deluxe cars to cheap beer)

   It is often thought that parallel imports of HK
    made movie and music products back into HK
    market adversely affects the very survival of
    HK movie and music industry.
Price Discrimination: How to
separate different customers
   Coupons--those people who have lower time cost will
    collect and use coupons to get a discount; they are
    likely to have lower maximum willingness to pay as
    well (Sincere VIP card works similarly)
   In 1999, CTI charged different fees for its registered
    IDD users--37cents/min to US for smart users who
    made a double registration; $2.9 /min for not-so-
    smart users who did not (c.w. HKTC’s 001 and 0060).
   Educational edition--software companies charge a
    substantial lower price to teachers and students for
    their software
Price Discrimination: How to
separate different customers
   Hardcover vs paperback--readers of lower maximum
    willingness to pay are more patient; hence publishing
    a paperback later attract these buyers without
    affecting sale to hardcover buyers (compared w.
    seasonal sales in department stores)--production
    differentiation in general
   Different prices for different geographic locations
     – golf clubs are much more expensive in HK than in
        the US (HK$4.5K vs US$250)
     – tennis ball--HK’s price is two or three times that in
        the US
Competitive Markets
Market Equilibrium

       Equilibrium is defined as the price at which the
        quantity demanded equals the quantity supplied
        (so markets clear)
    –     While all five conditions for perfect competition are
          (obviously) never fully satisfied, the model is still useful
          as frame of reference.
       When a market is out of equilibrium, market
        forces push the price towards equilibrium
       Excess supply (a.k.a., surplus) -- This triggers a
        price decrease
       Excess demand (a.k.a., shortage) --This
        triggers a price increase
Market Equilibrium (cont.)
   Price ($ per ton-mile)



                                 a           surplus when
                                             market price = 22
                                                                   supply

                            22
                                                    b
                            20                                    equilibrium


                                 c                               demand
                             0              8       10     11


                                     Quantity (Million ton-miles a year)
Invisible Hand
   Social welfare (SW) = net gains from production and
    trade
   In the absence of tax, SW = buyer surplus + seller
    surplus
   In the presence of tax, SW = buyer surplus + seller
    surplus + tax revenue
   An outcome is efficient if the SW cannot be further
    increased. [taxation cannot increase SW, to be
    shown shortly]
   Perfect competition is efficient, in which
    – marginal benefit = price
    – marginal cost = price
    – single price in market
Price Ceiling

Upper limit that sellers can lawfully charge
and buyers can lawfully pay
 rent control

 regulated price for electricity
Price Floor

Lower limit that sellers can charge and
buyers can pay
 minimum wage

 agricultural price supports
Minimum Wage: Equilibrium
                                          Net inc. in seller surplus = fdge -ghb
                                          Net inc. in buyer surplus = - (fdge +egb)
                                          Net inc. in SW = - (ghb + egb)
                           a
Wage ($ per hour)




                                          excess supply     supply
                           f      e
                    4.20
                           d          g        b
                    4.00
                                                           equilibrium
                                           h
                           c                               demand
                       0              8        10     11


                               Quantity (Billion worker-hours a week)
Minimum Wage: Losses

   deadweight losses -- sellers willing to
    provide item at price that buyers willing
    to pay, but provision doesn’t occur
   price elasticities of demand and supply
                       Can tax improve SW?
                                                    Net   inc.   in   buyer surplus = -(fdge + egb)
                                                    Net   inc.   in   seller surplus = -(djhg + ghb)
                                                    Net   inc.   in   tax revenue = fdge + djhg
                                                    Net   inc.   in   SW = -(egh + ghb)
Price ($ per ticket)




                       804 f                                  $10
                                            e                         supply
                       800 d                 g            b
                       794
                             j                  h                        demand




                         0                 900       920

                                 Quantity (Thousand tickets a year)
Tax: Does it matter whom the tax is
imposed upon: sellers or buyers?
   If an excise tax of $10 is levied on sellers, the
    sellers will be willing to supply the same quantity as
    before only when the price is increased by $10.
    [upper shifting of supply, demand unmoved]

   If an excise tax of $10 is levied directly on buyers,
    the buyers will buy the same quantity as before only
    when the price charged by sellers is reduced by
    $10. [downward shifting of demand, supply
    unmoved.]

   The outcomes under the two scenarios are the
    same

				
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