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					APPENDIX TO CHAPTER 2
Market Equilibrium,
Efficiency & Taxes
                        Main Ideas
 Market  Equilibrium
 Efficiency
   Social Surplus
   Pareto Efficiency
   Dead-weight loss

 Market    Interventions
     Price Ceilings & Price Floors
 Taxes   and Tax Incidence
             Market Equilibrium

 Equilibrium:  A situation where there is no
 incentive for change.

 Market Equilibrium: A market is in equilibrium
 when total quantity demanded by buyers equals
 total quantity supplied by sellers
   In a market equilibrium, buyers have no incentive to
    offer a higher price, and..
   Sellers have no incentive to offer a lower price
         Excess Supply
  Market         Market
p
  demand         supply
                     q=S(p)
                      D(p’) < S(p’); an excess
p’                    of quantity supplied over
p*                    quantity demanded.
                      q=D(p)

     D(p’)       S(p’)    D(p), S(p)
Market price must fall towards p*, i.e.
sellers must offer a lower price to buyers
       Market Equilibrium
  Market          Market
p
  demand          supply
                      q=S(p)
                      D(p”) > S(p”); an excess
                      of quantity demanded
p*                    over quantity supplied.
p”                    q=D(p)

     S(p”)    D(p”)      D(p), S(p)
Market price must rise towards p*, i.e.
buyers must offer more to sellers
     Market Equilibrium
  Market        Market
p
  demand        supply
                    S(p) = c+dp
                   What are the values
p*                 of p* and q*?

                    D(p) = a-bp

           q*         D(p), S(p)
          Market Equilibrium
             D(p)  a  bp
               S(p)  c  dp

At the equilibrium price p*, D(p*) = S(p*).
That is,           *           *
           a  bp  c  dp
which gives      * ac
                p 
                    bd
          Market Equilibrium
             D(p)  a  bp
               S(p)  c  dp

At the equilibrium price p*, D(p*) = S(p*).
That is,           *           *
           a  bp  c  dp
which gives      * ac
                p 
                    bd
          *        *
   and q  D(p )  S(p )  ad  bc
                            *
                                   .
                            bd
            Market Equilibrium
      Market        Market
    p
      demand        supply
                        S(p) = c+dp
*
p 
ac
bd
                        D(p) = a-bp
          ad  bc          D(p), S(p)
      q 
        *
           bd
       Summary: Market Equilibrium
 We have learnt that a Demand Curve reflects a
 consumer’s marginal utility from consumption,
 as captured by his WTP. He buys QD: P = MU

 Supply  Curve: Later in the course, we will see
 that firms (in a competitive market) sell a quantity
 such that the price received for the last unit is just
 above (or equal to) its cost, i.e.
      QS: P = MC (as long as P > min AC)

 AtMarket Equilibrium, P*: QD = QS = Q* =>…
 Market Equilibrium results in an output level Q*,
  such that at Q*: MU=MC
                        Efficiency
   Economists are very concerned with the goal of “efficiency”
      i.e. to minimize waste of resources
   E.g. Gasoline taxes are a more efficient way of collecting
    taxes than Income Taxes: Why?
      No govt. resources spent on collection
      Scope for fraud is zero, hence no expenses on audits
   When a competitive market produces an output level Q*:
    MU = MC, it is efficient, why?
      The benefit of the marginal unit produced is at least as
       high as its cost.
      If Q’: MU > MC? Too little output
   There are two different concepts of efficiency. We will
    focus more on one here, but I will mention the second.
                      Economic Surplus
 Social  Surplus = Consumer surplus + Producer
    surplus
     measures the benefits of economic activity in monetary units.
     where Consumer surplus is the benefit obtained by
      consumers and producer surplus is the benefit obtained by
      producers.


   Pareto efficiency An outcome/situation is termed
    pareto efficient if nothing can be done to change it
    without making at least one person worse off
       If things can be changed such that no one is worse off, and at
        least one person is better off, then the change is a Pareto
        improvement over the initial outcome (which is not pareto
        efficient).
             A double blind-date story…
   Pete has a blind date with Jenny and his friend David has
    a blind date with Michelle on a Friday night..

   The dates are both disasters  …

   As the pairs are walking back to their dorms they bump into
    each other….
      David and Jenny are thunder-struck by one another,
       and…
      Pete and Michelle are totally bedazzled by the other’s
       witty remarks.
      Half an hour after they get to their dorms, Jenny and
       Michelle have already exchanged the guys’ cell phone
       numbers and [censored]…

   Economists say this outcome is a Pareto improvement
    over the original outcome (which is not pareto optimal)
            Blind Date Story – Take 2
 The    David-Michelle pair did not really hit it off,
  and
      Jenny thought Pete was really cool and..
      Michelle thought Pete was really cool too!
      (Pete feels he’d be just happy going out with either
       of them)…
 Is   a Pareto-improvement possible?
      Michelle can’t be better off without making Jenny
       worse off..
      So a Pareto improvement is not possible..
      (although a cat-fight may be ;)
 Here,  is the initial outcome pareto
  efficient?
      Yes 
Example: Market for Apartment Rentals
 The       market:
    demand
                                      Market Demand & Supply
   supply




                               Price
   equilibrium price                                           S
   equilibrium quantity
 Consumer surplus (CS)                 CS
 Producer surplus (PS)
 Social surplus (SS)
                         P*
                                        PS
  SS = CS + PS                                                  D

   The area SS measures the size of the Pareto Q* Quantity
    improvement created by the market.

    Equilibrium & Efficiency                             p 15
         Surplus with Competitive Equilibrium
 Surplus   is maximized in
  competitive equilibrium.
 All units that generate
                                         Market Demand & Supply
  positive CS and PS (to
  the left of Q*) are




                                 Price
  produced and sold.                                               S
 But units that would create
   negative CS …                         CS
   and negative PS
                                 P*
  are not produced or sold.               PS
 Policies that interfere with
  the competitive equilibrium                                      D
  reduce surplus.                                      Q* Quantity



      Equilibrium & Efficiency                              p 16
                   Price Ceilings: Rent Control
   Price Ceiling: Upper bound              Market Demand & Supply
    on price (below market price)
   Price Floor: Lower bound
    on price (above market
    price)




                                    Price
   The market:                                                       S
      controlled rent PC                             CS Lost
      transacted quantity QC               CS            PS Lost
      excess demand QX
   Suppose consumers with
    highest WTP get apartments. P*
   Rent controls cause transfer of PC
    surplus from producers to           PS                          D
    consumers,                                            QX
   but controls also cause both
    consumers and producers to                       QC        Quantity
    lose surplus (dead-weight loss).
   Total surplus has decreased. Surplus Transferred

        Equilibrium & Efficiency                               p 17
              Example: Dead Weight Loss

            is a retired guy who lives in sunny Florida and
  owns an apartment in NYC
 There is a rent ceiling of $500 on the apartment.
 At any price under $1000, Mr. Wilson prefers to keep the
  apartment locked up and use it for a few weeks a year
  when he visits his kids in NYC
 The Jones are a family of four who are willing to pay up
  to $1200 for the apartment.
 Deadweight loss because of $500 rent ceiling:
    Mr. Wilson is willing to rent out for $1000, but cannot
    The Jones are willing to rent for $1000, but cannot




Equilibrium & Efficiency                              p 18
      Effects of Abolishing Rent Control
                                             Market Demand & Supply
   If controls are removed…
      the dead-weight loss
        disappears,…




                                     Price
                                                                         S
      but so does the surplus transfer.
      Surplus has increased, but           CS
        some renters will be worse off.
   Thus, removing price controls is P*                DWL
    normally not a Pareto            PC
    improvement.                         PS                              D

   The market with price controls may
    be Pareto efficient,                             QC          Quantity
    even though surplus isn’t
    maximized.                       Surplus Transferred



      Equilibrium & Efficiency                                    p 19
                        Rationing with Prices
 Every economic system
  has a process for deciding
  who gets what.                Market Demand & Supply
 This process is called




                                Price
  rationing.
 In free markets, rationing
                                                      S
  is done with prices.
 Consumers with                WPT > P*
  WTP > P* …
                             P*
 acquire goods with
                                MC < P*
  MC < P*.                                             D
 Consumers with lower
  WTP do not acquire any                     Q* Quantity
  goods.


    Equilibrium & Efficiency                     p 20
      Who gets rent-controlled apartments?
 With controlled prices and excess demand, buyers are
  attempting to acquire more goods than are available.
 Therefore, nonprice rationing must be used.
 What nonprice-rationing mechanisms determine who
  gets rent-controlled apartments?
   first-come, first-served
   bribery and “under-the-table” payments
   connections




  Equilibrium & Efficiency                       p 21
Nonprice rationing is not Efficient
 People  with lower WTP may get more of the rationed
   good than those with higher WTP.
        This lowers consumer surplus.

 Non-price                rationing mechanisms are costly to use.
      For example, renters may waste a lot of time trying to
       convince landlords to let them have apartments.
      These costs are called transactions costs.
      Transactions costs also lower consumer surplus


 Are  these additional costs captured on the rent-control
   diagram we saw earlier?
        No!
        So actual dead-weight loss is bigger than in diagram
Equilibrium & Efficiency                                      p 22
                                    Taxes
 Governments                tax goods and services for a number of
 reasons:
   for revenue to finance government activities,
   to discourage the consumption of certain goods and services,
   or to increase equity.

 In most cases, taxes reduce efficiency,…
 though some taxes (e.g. on gasoline) may increase
  efficiency.




  Equilibrium & Efficiency                                     p 23
           The Effect of Taxes on Markets
 An  excise tax is a tax of a fixed size applied to
   each unit of a good sold, e.g.
        a tax of £2 on each pack of cigarettes
 Suppose             you buy a £4-pack of cigarettes.
      as you are handing the 4 dollar to the seller,…
      the government reaches out and snatches 2 of the bills
       away.
      Result: you pay £2 more than the seller receives.




Equilibrium & Efficiency                                  p 24
Quantity Taxes & Market Equilibrium
    Market         Market
  p
    demand         supply
                            An sales tax (paid
                            by buyer) lowers
 pb                         the market demand
 p*                         curve by £t, lowers
 ps                         the sellers’ price and
                t=2         reduces the quantity
                            traded.
          qt q*    D(p), S(p)
  And buyers pay pb = ps + 2
Quantity Taxes & Market Equilibrium
   Market           Market
 p
   demand           supply
                             An excise tax
                     £t      (paid by seller)
pb                           raises the market
p*                           supply curve by $t,
ps                           raises the buyers’
                             price and lowers the
                             quantity traded.
          qt q* D(p), S(p)

 And sellers receive only ps = pb - t.
Quantity Taxes & Market Equilibrium
   Market             Market
 p
   demand             supply
                               A sales tax levied at
                               rate £t has the same
pb               £t            effects on the
p*                             market’s equilibrium
ps                             as does an excise tax
                 £t            levied at rate £t.

         qt q*        D(p), S(p)
Quantity Taxes and Market Equilibrium
 To compute the equilibrium price and quantity
  under taxes, we need to remember two things:
 (1) Buyer’s price exceeds Seller’s price by tax

                 pb = ps+t
 (2) Quantity bought by buyer at price he pays =
  Quantity sold by seller at the price she receives
               Qd(pb) = Qs(ps)
  Quantity Taxes & Market Equilibrium
   D(pb )  a  bpb and S(ps )  c  dps .
                                   3
With the tax, the market equilibrium satisfies

      pb  ps  t and D(pb )  S(ps ) so 2
      pb  ps  t and a  bpb  c  dps .
                     1
 Substituting for pb gives
                                     a  c  bt
     a  b(ps  t )  c  dps  ps             .
                                       bd
                              Taxes and Surplus
 After QT, PD and PS
  are determined,…                           Market Demand & Supply
 we see the dead-




                                    Price
  weight loss,                                                        S
 the taxes collected,                      CS
 the consumer surplus             PD       PD

 and the producer
                                            $2
                                             Taxes    DWL
  surplus.                         PS       PS
                                            PS                        D

                                                     QT       Quantity



   Equilibrium & Efficiency                                    p 30
                   Tax and No-Tax Comparisons
   As compared with the no-tax
    price P*,                            Market Demand & Supply
   we have a larger demand
    price and smaller supply




                                 Price
    price,
   which pushes the quantity                                       S
    demanded and supplied                CS
    below the surplus-
    maximizing level.            PD              PD
   This creates the DWL,                        $2
                                 P*      Taxes        DWL
   reduces the consumer
    surplus                      PS              PS
   and reduces the producer             PS                         D
    surplus.
   The left-over surplus takes                   QT        Quantity
    the form of taxes collected.



      Equilibrium & Efficiency                               p 31
               Taxes and the Size of the DWL
 Ifsupply is very inelastic,…
                               P
 then when a tax is
  imposed,…                              S
 the quantity transacted
  doesn’t change much.
 Therefore, the dead-weight  P*
  loss will be small.
                                                      D
 The same thing happens if
  demand is very inelastic.
 In general, lower elasticity of
  demand/supply=> smaller                                 Q
                                      QT Q*
  DWL
       Equilibrium & Efficiency                p 32
                  Who bears the tax burden?
 Here we have a very          P
  elastic demand curve,…             Taxes from
                                     the buyer
 and an ordinary supply                                       S
  curve.
                               PD
 After a tax is imposed,…
                               P*
 the quantity, demand price                                   D
                                    Taxes from
  and supply price all change.      the seller
 The taxes from the buyer…
                               PS
 are small compared with the
  taxes from the seller.                                           Q
                                                           *
                                                  QT   Q

    Equilibrium & Efficiency                           p 33
            Tax Incidence with Elastic Supply
 Here we have a very
  elastic supply curve,…       P
 and an ordinary demand
  curve.
 After a tax is imposed,…

 the quantity, demand price
                               PD
  and supply price all change.      Taxes from
 The taxes from the seller…
                                    the buyer                 S
 are small compared with the  P*
                               PS
  taxes from the buyer.                                       D

                                                 QT       *       Q
                                    Taxes from        Q
                                    the seller

    Equilibrium & Efficiency                          p 34
                   Tax Incidence in General
 The  tax incidence is the relative amount of the tax
  burden that is borne by the buyer and the seller.
 Tax incidence is unrelated to which party hands over
  the money to the government.
 In general, the larger the elasticity of demand,
    the greater the tax incidence on the eller,
    and the small the share from the buyer.
 The larger the elasticity of supply,
    the greater the share of taxes that comes from the
     buyer,
    and the smaller the share from the seller.
 Here’s why…

  Equilibrium & Efficiency                         p 35
    Tax Incidence 2



                                    Tax Incidence
Taxes from
the buyer
                 QT PD
Taxes from
the seller
                 QT PS
        QT PD
Ratio                         PD
        QT PS                      Taxes from
                                                                    S
                                    the buyer     PD
       PD   S                P*
                                                     Q
                                  Taxes from     PS
       PS   D                PS
                                    the seller
                                                                    D
 Can  you prove this from                                               Q
                                                              *
  the definition of                              QT       Q
  elasticity?

    Equilibrium & Efficiency                                      p 36
         Elasticity and Tax Incidence

              Q * QT     PD     Q PD
                        .           .
       PD
             Q*          P*
                                 Q P*
       PS Q * QT        PS     Q PS
                        .           .
                Q*        P*      Q P*
           Q PD
                          S
         Q . P*        
           PS Q         D
           P*    Q
• More elastic supply=> greater tax incidence on buyer
• More elastic demand=> greater tax incidence on seller
• It matters little whom the govt. levies the tax on, buyer
or seller
                 Main Ideas

 Social  Surplus & Pareto Efficiency
 Deadweight loss

 Price vs. Non-price Rationing

 Efficiency vs. Equity

 Taxes and DWL

 Elasticity, the size of DWL & Tax Incidence

				
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