SlideShare a Scribd company logo
1 of 28
Lecture PowerPoint® Slides
           to accompany




                  Prepared by
     Marc Prud‘Homme, University of Ottawa   1
Chapter 7

Consumers, Producers, and the
    Efficiency of Markets


         Copyright © 2011 Nelson Education Limited   2
WTP and the Demand Curve
Q: If price of iPod is $200, who will buy an iPod, and
   what is quantity demanded?

                    A: Anthony & Flea will buy an iPod,
                       Chad & John will not.
  name     WTP
                           Hence, Qd = 2
Anthony $250
                           when P = $200.
Chad        175
Flea        300
John        125

                  Copyright © 2011 Nelson Education Limited   3
WTP and the Demand Curve
 Derive the
                          P (price
 demand                                                     who buys   Qd
                          of iPod)
 schedule:
                       $301 & up nobody                                0

 name    WTP           251 – 300 Flea                                  1

Anthony $250           176 – 250 Anthony, Flea                         2
Chad      175                    Chad, Anthony,
                       126 – 175                                       3
Flea      300                    Flea
                                    John, Chad,
John      125               0 – 125                                    4
                                    Anthony, Flea
                Copyright © 2011 Nelson Education Limited              4
WTP and the Demand Curve
       P
$350
                                                               P       Qd
$300
$250                                                       $301 & up   0

$200                                                       251 – 300   1
$150                                                       176 – 250   2
$100
                                                           126 – 175   3
 $50
                                                             0 – 125   4
  $0                                                Q
       0   1    2           3            4
               Copyright © 2011 Nelson Education Limited               5
About the Staircase Shape…
       P        This D curve looks like a staircase
$350            with 4 steps – one per buyer.
$300                       If there were a huge # of buyers,
                           as in a competitive market,
$250
                                         there would be a huge #
$200
                                         of very tiny steps,
$150                                                     and it would look
$100                                                     more like a smooth
                                                         curve.
 $50
  $0                                                   Q
       0    1      2           3            4                             6
                  Copyright © 2011 Nelson Education Limited
Consumer Surplus (CS)
Consumer surplus is the amount a buyer is willing
to pay minus the amount the buyer actually pays:
       CS = WTP – P

  name    WTP            Suppose P = $260.

Anthony $250             Flea’s CS = $300 – 260 = $40.

Chad       175           The others get no CS because
                         they do not buy an iPod at this
Flea       300           price.
John       125           Total CS = $40.

                 Copyright © 2011 Nelson Education Limited   7
CS and the Demand Curve
       P
                 Flea’s WTP                                    P = $260
$350
                                                               Flea’s CS =
$300                                                           $300 – 260 = $40
$250                                                           Total CS = $40
$200
$150
$100
 $50
  $0                                                Q
       0     1      2           3            4                                  8
                   Copyright © 2011 Nelson Education Limited
CS and the Demand Curve
       P
                 Flea’s WTP                                    Instead, suppose
$350                                                           P = $220
$300                Anthony’s WTP
                                                               Flea’s CS =
$250                                                           $300 – 220 = $80
$200                                                           Anthony’s CS =
                                                               $250 – 220 = $30
$150
                                                               Total CS = $110
$100
 $50
  $0                                                Q
       0     1      2           3            4                                   9
                   Copyright © 2011 Nelson Education Limited
CS and the Demand Curve
       P
$350                                                     The lesson:
                                                      Total CS equals
$300
                                                       the area under
$250                                                 the demand curve
$200                                                  above the price,
                                                         from 0 to Q.
$150
$100
 $50
  $0                                              Q
       0     1    2           3            4                             10
                 Copyright © 2011 Nelson Education Limited
CS with Lots of Buyers & a Smooth D Curve
               Price                 P           The demand for shoes
              per pair
                            $ 60
At Q = 5(thousand),            50
the marginal buyer             40
is willing to pay $50
for pair of shoes.             30
                                                              1000s of pairs
Suppose P = $30.               20                               of shoes
Then his consumer              10
                                                                     D
surplus = $20.                   0                                        Q
                                       0       5 10 15 20 25 30
                  Copyright © 2011 Nelson Education Limited              11
CS with Lots of Buyers & a Smooth D Curve
CS is the area b/w                               The demand for shoes
P and the D curve,                   P
from 0 to Q.                $ 60

Recall: area of               50
                              h
a triangle equals             40
½ x base x height
                               30
Height =
                               20
$60 – 30 = $30.
                               10
So,                                                             D
CS = ½ x 15 x $30                0                                   Q
    = $225.                            0       5 10 15 20 25 30
                  Copyright © 2011 Nelson Education Limited         12
How a Higher Price Reduces CS
If P rises to $40,
                                        P
CS = ½ x 10 x $20                                                1. Fall in CS
                                  60
   = $100.                                                          due to buyers
                                  50                                leaving market
Two reasons for the
fall in CS.                       40
                                  30

  2. Fall in CS due to            20
     remaining buyers             10
     paying higher P                                                         D
                                    0                                                Q
                                          0       5 10 15 20 25 30
                     Copyright © 2011 Nelson Education Limited                   13
ACTIVE LEARNING 1
 Consumer surplusP
                 50
                    demand curve
A. Find marginal         $ 45
   buyer’s WTP at
                           40
   Q = 10.
                           35
B. Find CS for
   P = $30.                30
Suppose P falls to $20.
                           25
How much will CS           20
increase due to…           15
C. buyers entering         10
    the market              5
D. existing buyers paying 0
    lower price
                                             0          5       10   15   20        Q
                                                                                    25
                    Copyright © 2011 Nelson Education Limited                  14
ACTIVE LEARNING 1
 Answers      demand curve
                                      P
                                     50
A. At Q = 10, marginal $ 45
   buyer’s WTP is $30.
                                     40
B. CS = ½ x 10 x $10                 35
   = $50                             30
P falls to $20.                      25
C. CS for the                        20
   additional buyers                 15
   = ½ x 10 x $10 = $50 10
D. Increase in CS                      5
   on initial 10 units                 0
   = 10 x $10 = $100                        0          5       10   15   20        Q
                                                                                   25
                   Copyright © 2011 Nelson Education Limited                  15
Cost and the Supply Curve

                                                               P       Qs
 Derive the supply schedule
 from the cost data:                                          $0 – 9   0

                                                             10 – 19   1
 name     cost
                                                             20 – 34   2
Jack      $10
                                                             35 & up   3
Janet      20
Chrissy    35


                 Copyright © 2011 Nelson Education Limited              16
Producer Surplus and the S Curve
      P                                          PS = P – cost
$40                                                       Suppose P = $25.
                                Chrissy’s
                                  cost                    Jack’s PS = $15
$30
                       Janet’s                            Janet’s PS = $5
$20                     cost                              Chrissy’s PS = $0

$10           Jack’s cost                                 Total PS = $20
                                                    Total PS equals the
                                                   area above the supply
 $0                              Q
                                                   curve under the price,
      0   1   2        3                                from 0 to Q.
              Copyright © 2011 Nelson Education Limited                    17
ACTIVE LEARNING 2
Producer surplus P
                 50 supply curve
A. Find marginal                      45
   seller’s cost
                                      40
   at Q = 10.
                                      35
B. Find total PS for
   P = $20.                           30
                                      25
Suppose P rises to $30.
Find the increase                     20
in PS due to…                         15
C. selling 5                          10
   additional units                    5
D. getting a higher price              0
   on the initial 10 units                    0          5     10   15   20      25
                                                                              18
                                                                                 Q
                   Copyright © 2011 Nelson Education Limited
ACTIVE LEARNING 2
Answers   P
          50
             supply curve
A. At Q = 10,                       45
   marginal cost = $20
                                    40
B. PS = ½ x 10 x $20
                                    35
    = $100
                                    30
P rises to $30.                     25
C. PS on                            20
   additional units                 15
   = ½ x 5 x $10 = $25
                                    10
D. Increase in PS
                                     5
   on initial 10 units
   = 10 x $10 = $100                 0
                                            0          5      10   15   20   19
                                                                                  Q
                                                                                  25
                  Copyright © 2011 Nelson Education Limited
Evaluating the Market Equilibrium
Market eq’m:
                                    P
 P = $30
                              60
 Q = 15,000
                              50                                  S
Total surplus
 = CS + PS                    40           CS
Is the market eq’m            30
efficient?                                 PS
                              20
                              10
                                                             D
                                0                                 Q
                                      0       5 10 15 20 25 30
                 Copyright © 2011 Nelson Education Limited       20
Which Buyers Consume the Good?
Every buyer
                                     P
whose WTP is
                               60
≥ $30 will buy.
                               50                                  S
Every buyer
whose WTP is                   40
< $30 will not.                30
So, the buyers                 20
who value the
                               10
good most highly                                              D
are the ones who                 0                                 Q
consume it.                            0       5 10 15 20 25 30
                  Copyright © 2011 Nelson Education Limited       21
Which Sellers Produce the Good?
Every seller whose
                                    P
cost is ≤ $30 will
                              60
produce the good.
                              50                                  S
Every seller whose
cost is > $30 will            40
not.
                              30
So, the sellers with
                              20
the lowest cost
produce the good.             10
                                                             D
                                0                                 Q
                                      0       5 10 15 20 25 30
                 Copyright © 2011 Nelson Education Limited       22
Does Eq’m Q Maximize Total Surplus?
At Q = 20,
                                       P
cost of producing
the marginal unit                60
is $35                           50                                  S
value to consumers               40
of the marginal unit
is only $20                      30
Hence, can increase              20
total surplus
                                 10
by reducing Q.                                                  D
This is true at any Q              0                                 Q
greater than 15.                         0       5 10 15 20 25 30
                    Copyright © 2011 Nelson Education Limited       23
Does Eq’m Q Maximize Total Surplus?
At Q = 10,
                                       P
cost of producing
the marginal unit                60
is $25                           50                                  S
value to consumers               40
of the marginal unit
is $40                           30
Hence, can increase              20
total surplus
                                 10
by increasing Q.                                                D
This is true at any Q              0                                 Q
less than 15.                            0       5 10 15 20 25 30
                    Copyright © 2011 Nelson Education Limited       24
Does Eq’m Q Maximize Total Surplus?
The market                       P
eq’m quantity              60
maximizes                                                      S
                           50
total surplus:
At any other               40
quantity,                  30
can increase
                           20
total surplus by
moving toward              10
                                                          D
the market eq’m              0                                 Q
quantity.
                                   0       5 10 15 20 25 30
              Copyright © 2011 Nelson Education Limited       25
Adam Smith and the Invisible Hand
  Passages from The Wealth of Nations, 1776
                “Man has almost constant occasion
                for the help of his brethren, and it is
                vain for him to expect it from their
                benevolence only. He will be more
                likely to prevail if he can interest their
                self-love in his favor, and show them
                that it is for their own advantage to do
                for him what he requires of them…
                It is not from the benevolence of the
                butcher, the brewer, or the baker that
Adam Smith,
                we expect our dinner, but from their
 1723-1790
                regard to their own interest….
              Copyright © 2011 Nelson Education Limited   26
Adam Smith and the Invisible Hand
  Passages from The Wealth of Nations, 1776
              “Every individual…neither intends to
              promote the public interest, nor knows
              how much he is promoting it….
              He intends only his own gain, and he is
              in this, as in many other cases, led by
              an invisible hand to promote an end
              which was no part of his intention.
              Nor is it always the worse for the society
              that it was no part of it. By pursuing his
              own interest he frequently promotes
Adam Smith,   that of the society more effectually than
 1723-1790
              when he really intends to promote it.”
              Copyright © 2011 Nelson Education Limited   27
The Free Market vs. Govt Intervention
 The market equilibrium is efficient. No other
  outcome achieves higher total surplus.
 Govt cannot raise total surplus by changing the
  market’s allocation of resources.
 Laissez faire (French for “allow them to do”):
  the notion that govt should not interfere with the
  market.




                 Copyright © 2011 Nelson Education Limited   28

More Related Content

More from abanki

Ch 19 Microeconomics
Ch 19 MicroeconomicsCh 19 Microeconomics
Ch 19 Microeconomicsabanki
 
Economic Systems & Schools of Thought
Economic Systems & Schools of ThoughtEconomic Systems & Schools of Thought
Economic Systems & Schools of Thoughtabanki
 
Money and Banking
Money and BankingMoney and Banking
Money and Bankingabanki
 
Oligopoly & Game Theory
Oligopoly & Game TheoryOligopoly & Game Theory
Oligopoly & Game Theoryabanki
 
Ch 12: Business Cycle
Ch 12: Business CycleCh 12: Business Cycle
Ch 12: Business Cycleabanki
 
Ch 15 micro 1
Ch 15 micro 1Ch 15 micro 1
Ch 15 micro 1abanki
 
Ch 6: Unemployment and Inflation
Ch 6: Unemployment and InflationCh 6: Unemployment and Inflation
Ch 6: Unemployment and Inflationabanki
 
Price Controls
Price ControlsPrice Controls
Price Controlsabanki
 
Price Controls
Price ControlsPrice Controls
Price Controlsabanki
 
Microeconomics Ch 1
Microeconomics Ch 1Microeconomics Ch 1
Microeconomics Ch 1abanki
 
Ppt2 style
Ppt2 stylePpt2 style
Ppt2 styleabanki
 
Macroeconomics, ch 1-2
Macroeconomics, ch 1-2Macroeconomics, ch 1-2
Macroeconomics, ch 1-2abanki
 
Ppt1 thesis
Ppt1 thesisPpt1 thesis
Ppt1 thesisabanki
 

More from abanki (13)

Ch 19 Microeconomics
Ch 19 MicroeconomicsCh 19 Microeconomics
Ch 19 Microeconomics
 
Economic Systems & Schools of Thought
Economic Systems & Schools of ThoughtEconomic Systems & Schools of Thought
Economic Systems & Schools of Thought
 
Money and Banking
Money and BankingMoney and Banking
Money and Banking
 
Oligopoly & Game Theory
Oligopoly & Game TheoryOligopoly & Game Theory
Oligopoly & Game Theory
 
Ch 12: Business Cycle
Ch 12: Business CycleCh 12: Business Cycle
Ch 12: Business Cycle
 
Ch 15 micro 1
Ch 15 micro 1Ch 15 micro 1
Ch 15 micro 1
 
Ch 6: Unemployment and Inflation
Ch 6: Unemployment and InflationCh 6: Unemployment and Inflation
Ch 6: Unemployment and Inflation
 
Price Controls
Price ControlsPrice Controls
Price Controls
 
Price Controls
Price ControlsPrice Controls
Price Controls
 
Microeconomics Ch 1
Microeconomics Ch 1Microeconomics Ch 1
Microeconomics Ch 1
 
Ppt2 style
Ppt2 stylePpt2 style
Ppt2 style
 
Macroeconomics, ch 1-2
Macroeconomics, ch 1-2Macroeconomics, ch 1-2
Macroeconomics, ch 1-2
 
Ppt1 thesis
Ppt1 thesisPpt1 thesis
Ppt1 thesis
 

Ch 07 micro 1

  • 1. Lecture PowerPoint® Slides to accompany Prepared by Marc Prud‘Homme, University of Ottawa 1
  • 2. Chapter 7 Consumers, Producers, and the Efficiency of Markets Copyright © 2011 Nelson Education Limited 2
  • 3. WTP and the Demand Curve Q: If price of iPod is $200, who will buy an iPod, and what is quantity demanded? A: Anthony & Flea will buy an iPod, Chad & John will not. name WTP Hence, Qd = 2 Anthony $250 when P = $200. Chad 175 Flea 300 John 125 Copyright © 2011 Nelson Education Limited 3
  • 4. WTP and the Demand Curve Derive the P (price demand who buys Qd of iPod) schedule: $301 & up nobody 0 name WTP 251 – 300 Flea 1 Anthony $250 176 – 250 Anthony, Flea 2 Chad 175 Chad, Anthony, 126 – 175 3 Flea 300 Flea John, Chad, John 125 0 – 125 4 Anthony, Flea Copyright © 2011 Nelson Education Limited 4
  • 5. WTP and the Demand Curve P $350 P Qd $300 $250 $301 & up 0 $200 251 – 300 1 $150 176 – 250 2 $100 126 – 175 3 $50 0 – 125 4 $0 Q 0 1 2 3 4 Copyright © 2011 Nelson Education Limited 5
  • 6. About the Staircase Shape… P This D curve looks like a staircase $350 with 4 steps – one per buyer. $300 If there were a huge # of buyers, as in a competitive market, $250 there would be a huge # $200 of very tiny steps, $150 and it would look $100 more like a smooth curve. $50 $0 Q 0 1 2 3 4 6 Copyright © 2011 Nelson Education Limited
  • 7. Consumer Surplus (CS) Consumer surplus is the amount a buyer is willing to pay minus the amount the buyer actually pays: CS = WTP – P name WTP Suppose P = $260. Anthony $250 Flea’s CS = $300 – 260 = $40. Chad 175 The others get no CS because they do not buy an iPod at this Flea 300 price. John 125 Total CS = $40. Copyright © 2011 Nelson Education Limited 7
  • 8. CS and the Demand Curve P Flea’s WTP P = $260 $350 Flea’s CS = $300 $300 – 260 = $40 $250 Total CS = $40 $200 $150 $100 $50 $0 Q 0 1 2 3 4 8 Copyright © 2011 Nelson Education Limited
  • 9. CS and the Demand Curve P Flea’s WTP Instead, suppose $350 P = $220 $300 Anthony’s WTP Flea’s CS = $250 $300 – 220 = $80 $200 Anthony’s CS = $250 – 220 = $30 $150 Total CS = $110 $100 $50 $0 Q 0 1 2 3 4 9 Copyright © 2011 Nelson Education Limited
  • 10. CS and the Demand Curve P $350 The lesson: Total CS equals $300 the area under $250 the demand curve $200 above the price, from 0 to Q. $150 $100 $50 $0 Q 0 1 2 3 4 10 Copyright © 2011 Nelson Education Limited
  • 11. CS with Lots of Buyers & a Smooth D Curve Price P The demand for shoes per pair $ 60 At Q = 5(thousand), 50 the marginal buyer 40 is willing to pay $50 for pair of shoes. 30 1000s of pairs Suppose P = $30. 20 of shoes Then his consumer 10 D surplus = $20. 0 Q 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 11
  • 12. CS with Lots of Buyers & a Smooth D Curve CS is the area b/w The demand for shoes P and the D curve, P from 0 to Q. $ 60 Recall: area of 50 h a triangle equals 40 ½ x base x height 30 Height = 20 $60 – 30 = $30. 10 So, D CS = ½ x 15 x $30 0 Q = $225. 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 12
  • 13. How a Higher Price Reduces CS If P rises to $40, P CS = ½ x 10 x $20 1. Fall in CS 60 = $100. due to buyers 50 leaving market Two reasons for the fall in CS. 40 30 2. Fall in CS due to 20 remaining buyers 10 paying higher P D 0 Q 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 13
  • 14. ACTIVE LEARNING 1 Consumer surplusP 50 demand curve A. Find marginal $ 45 buyer’s WTP at 40 Q = 10. 35 B. Find CS for P = $30. 30 Suppose P falls to $20. 25 How much will CS 20 increase due to… 15 C. buyers entering 10 the market 5 D. existing buyers paying 0 lower price 0 5 10 15 20 Q 25 Copyright © 2011 Nelson Education Limited 14
  • 15. ACTIVE LEARNING 1 Answers demand curve P 50 A. At Q = 10, marginal $ 45 buyer’s WTP is $30. 40 B. CS = ½ x 10 x $10 35 = $50 30 P falls to $20. 25 C. CS for the 20 additional buyers 15 = ½ x 10 x $10 = $50 10 D. Increase in CS 5 on initial 10 units 0 = 10 x $10 = $100 0 5 10 15 20 Q 25 Copyright © 2011 Nelson Education Limited 15
  • 16. Cost and the Supply Curve P Qs Derive the supply schedule from the cost data: $0 – 9 0 10 – 19 1 name cost 20 – 34 2 Jack $10 35 & up 3 Janet 20 Chrissy 35 Copyright © 2011 Nelson Education Limited 16
  • 17. Producer Surplus and the S Curve P PS = P – cost $40 Suppose P = $25. Chrissy’s cost Jack’s PS = $15 $30 Janet’s Janet’s PS = $5 $20 cost Chrissy’s PS = $0 $10 Jack’s cost Total PS = $20 Total PS equals the area above the supply $0 Q curve under the price, 0 1 2 3 from 0 to Q. Copyright © 2011 Nelson Education Limited 17
  • 18. ACTIVE LEARNING 2 Producer surplus P 50 supply curve A. Find marginal 45 seller’s cost 40 at Q = 10. 35 B. Find total PS for P = $20. 30 25 Suppose P rises to $30. Find the increase 20 in PS due to… 15 C. selling 5 10 additional units 5 D. getting a higher price 0 on the initial 10 units 0 5 10 15 20 25 18 Q Copyright © 2011 Nelson Education Limited
  • 19. ACTIVE LEARNING 2 Answers P 50 supply curve A. At Q = 10, 45 marginal cost = $20 40 B. PS = ½ x 10 x $20 35 = $100 30 P rises to $30. 25 C. PS on 20 additional units 15 = ½ x 5 x $10 = $25 10 D. Increase in PS 5 on initial 10 units = 10 x $10 = $100 0 0 5 10 15 20 19 Q 25 Copyright © 2011 Nelson Education Limited
  • 20. Evaluating the Market Equilibrium Market eq’m: P P = $30 60 Q = 15,000 50 S Total surplus = CS + PS 40 CS Is the market eq’m 30 efficient? PS 20 10 D 0 Q 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 20
  • 21. Which Buyers Consume the Good? Every buyer P whose WTP is 60 ≥ $30 will buy. 50 S Every buyer whose WTP is 40 < $30 will not. 30 So, the buyers 20 who value the 10 good most highly D are the ones who 0 Q consume it. 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 21
  • 22. Which Sellers Produce the Good? Every seller whose P cost is ≤ $30 will 60 produce the good. 50 S Every seller whose cost is > $30 will 40 not. 30 So, the sellers with 20 the lowest cost produce the good. 10 D 0 Q 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 22
  • 23. Does Eq’m Q Maximize Total Surplus? At Q = 20, P cost of producing the marginal unit 60 is $35 50 S value to consumers 40 of the marginal unit is only $20 30 Hence, can increase 20 total surplus 10 by reducing Q. D This is true at any Q 0 Q greater than 15. 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 23
  • 24. Does Eq’m Q Maximize Total Surplus? At Q = 10, P cost of producing the marginal unit 60 is $25 50 S value to consumers 40 of the marginal unit is $40 30 Hence, can increase 20 total surplus 10 by increasing Q. D This is true at any Q 0 Q less than 15. 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 24
  • 25. Does Eq’m Q Maximize Total Surplus? The market P eq’m quantity 60 maximizes S 50 total surplus: At any other 40 quantity, 30 can increase 20 total surplus by moving toward 10 D the market eq’m 0 Q quantity. 0 5 10 15 20 25 30 Copyright © 2011 Nelson Education Limited 25
  • 26. Adam Smith and the Invisible Hand Passages from The Wealth of Nations, 1776 “Man has almost constant occasion for the help of his brethren, and it is vain for him to expect it from their benevolence only. He will be more likely to prevail if he can interest their self-love in his favor, and show them that it is for their own advantage to do for him what he requires of them… It is not from the benevolence of the butcher, the brewer, or the baker that Adam Smith, we expect our dinner, but from their 1723-1790 regard to their own interest…. Copyright © 2011 Nelson Education Limited 26
  • 27. Adam Smith and the Invisible Hand Passages from The Wealth of Nations, 1776 “Every individual…neither intends to promote the public interest, nor knows how much he is promoting it…. He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes Adam Smith, that of the society more effectually than 1723-1790 when he really intends to promote it.” Copyright © 2011 Nelson Education Limited 27
  • 28. The Free Market vs. Govt Intervention  The market equilibrium is efficient. No other outcome achieves higher total surplus.  Govt cannot raise total surplus by changing the market’s allocation of resources.  Laissez faire (French for “allow them to do”): the notion that govt should not interfere with the market. Copyright © 2011 Nelson Education Limited 28