1. Indifference Analysis

2. Shape of ‘Clive’s’ an indifference curve
Notice that this curve is downward sloping
Why is this and does it have any economic meaning? b c
Pears d e f g
Oranges

3. INDIFFERENCE ANALYSIS
To see the special significance of its shape we need to look at a concept known as the
diminishing marginal rate of substitution 6

4. INDIFFERENCE ANALYSIS
The rate of Substitution is the rate we are prepared to exchange Pears (Y) for Oranges (X).
Or: If I give ‘Clive’ one more orange how many pears must I take away to leave him just as happy… 6

5. The MRS of Y for X is: Pears 30 24 20 14 10 8 6 Oranges 7 13 15 Pointb c d e f g

6. Deriving the marginal rate of substitution (MRS)24 b
Units of good Y 6 7
Units of good X

7. Deriving the marginal rate of substitution (MRS)
MRS = DY/ DX= - 6
DY = - 6 24 b
DX = 1
Units of good Y 6 7
Units of good X

8. Consider instead the MRS at 13 oranges
MRS = DY/ DX= - 6
DY = - 6 24 b
DX = 1
Pears 30 24 20 14 10 9 6
Oranges 7 8 13
Point a b c d e f g
Units of good Y 6 7
Units of good X

9. Deriving the marginal rate of substitution (MRS)
Pears 30 24 20 14 10 9 6
Oranges 7 8 13
Point a b c d e f g
MRS = - 6
DY = - 6 24 b
DX = 1
Units of good Y
MRS = - 1 c
DY = - 1 d 9
DX = 1 6 7 13 14
Units of good X

10. INDIFFERENCE ANALYSIS
From an Indifference curves to an indifference Map
An indifference curve tells us the bundles which give Clive the same happiness as 13 pears and 10 oranges.
An indifference map shows us a whole series of different curves showing which bundles give different levels of happiness 6

11. An indifference map
Units of good Y I1 I1
Units of good X

12. An indifference map
Units of good Y I2 I1
Units of good X

13. An indifference map
Units of good Y I3 I2 I1
Units of good X

14. An indifference map
Units of good Y I4 I3 I2 I1
Units of good X

15. An indifference map
Units of good Y I5 I4 I3 I2 I1
Units of good X

16. This is basically a map of the happiness mountain
An indifference map
This is basically a map of the happiness mountain
The further up we are, the happier we are
Units of good Y I5 I4 I3 I2 I1
Units of good X

17. ‘We’re Climbing up the Sunshine Mountain’
We can think of picking bundles of goods as an attempt to climb the happiness mountain.

18. ‘We’re Climbing up the Sunshine Mountain’
A mountain of course is three dimensional and it is difficult to view on a screen.This might be a side view.

19. Putting in contours the mountain looks like this:

20. Putting in contours the mountain looks like this:

21. Gradually rotating and looking down from above it looks like this:

22. Gradually rotating and looking down from above it looks like this:

23. Gradually rotating and looking down from above it looks like this:

24. Gradually rotating and looking down from above it looks like this:

25. Gradually rotating and looking down from above it looks like this:

26. Looking down from above the mountasin looks like this:

27. Gradually rotating and looking down from above it looks like this:

28. So from above the happiness mountain looks like this

29. Putting two axes in: Y X

30. For a given Y, the more X we have the happier we are:

31. Similarly, for a given X, the more Y we have the happier we are:

32. So the more X and Y we have the happier we are :

33. Of course the issue about the happiness mountain is that we never get thereY Y0 X

34. This is basically the indifference map we started with a while ago
Of course the issue about the happiness mountain is that we never get there. So we are interested in just one corner of the mountain Y0
This is basically the indifference map we started with a while ago X X0

35. An indifference map
Units of good Y I5 I4 I3 I2 I1
Units of good X

36. An indifference map
Note for a given quantity of x, a rise in y increases our utility, from I1 to I4
Units of good Y I5 I4 I3 I2 I1
Units of good X

37. An indifference map
Similarly, for a given quantity of y, a rise in x increases our utility, from I2 to I5
Units of good Y I5 I4 I3 I2 I1
Units of good X

38. Down and left decreases it
An indifference map
So to labour the point, anything to the right an upwards increases our utility
Down and left decreases it
Units of good Y I5 I4 I3 I2 I1
Units of good X

39. Could two indifference curves ever cross?
Units of good Y I1
Units of good X

40. Could two indifference curves ever cross?
Could we get this?
Units of good Y I1
Units of good X

41. Could two indifference curves ever cross?
Could we get this? I2
Consider points a,b and c
Point a is indifferent to b
And point a is indifferent to c
Units of good Y
=> b is indifferent to c a b I1 c
Units of good X

42. Could two indifference curves ever cross?
Could we get this? I2
Consider points a,b and c
But point b has more X and Y than c so b is preferred to C
Contradiction, so indifference curves can never cross
Units of good Y a b I1 c
Units of good X

43. An indifference map
So just like the map of a mountain, our contours of happiness (the indifference curves) never cross.
Units of good Y I5 I4 I3 I2 I1
Units of good X

44. INDIFFERENCE ANALYSIS
We now have a map which represents peoples’ choices. What else do we need to make an economic decision about what to consume?
Answer: Information on prices and Income
The budget line:
Suppose the Price of X is Px
And the Price of Y is Py
And Income is represented by I 6

45. Budget Line
Our expenditure on X (PxX) and Y (PyY) must sum to our total income:

46. Budget Line
Our expenditure on X and Y must sum to our total income:
If Y =0, then
2X = 30
and
Max Consumption of X = 15

47. Budget Line
Our expenditure on X and Y must sum to our total income:
If X= 0, then 1Y =30
and
Max Consumption of Y = 30

48. A budget line a Units of good Y Units of good X Units of good X 1515
good Y 30
Point on
budget line
Units of
good X 15
Units of
good Y 30
Point on
budget line a b
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

49. We join these two points to get the budget linea
Units of
good X 15
good Y 30
Point on
budget line
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

50. A budget line a Units of good Y Units of good X Units of good X 1515
good Y 30
Point on
budget line
Point on
budget line a
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

51. A budget line a Units of good Y Units of good X Units of good X 5 105 10 15
Units of
good Y 30 20 10
Point on
budget line a
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

52. A budget line a b Units of good Y Units of good X Units of good X 5 105 10 15
Units of
good Y 30 20 10
Point on
budget line a b b
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

53. A budget line a b Units of good Y c Units of good X Units of good X 55 10 15
Units of
good Y 30 20 10
Point on
budget line a b c b
Units of good Y c
Assumptions
PX = £2
PY = £1
Budget = £30
Units of good X

54. A budget line a b Units of good Y c d Units of good X Units of good X5 10 15
Units of
good Y 30 20 10
Point on
budget line a b c d b
Units of good Y c
Assumptions
PX = £2
PY = £1
Budget = £30 d
Units of good X

55. Budget Line
So all these points satisfy the equation:

56. Note the Maximum x we can consume is 30/Px
A budget line a
Units of
good X 15
Units of
good Y 30
Point on
budget line a d b
Units of good Y
Note the Maximum x we can consume is 30/Px c d
Units of good X
=30/Px=30/2

57. And the maximum Y we can consume is 30/PY = 30/1
A budget line a
Units of
good X 15
Units of
good Y 30
Point on
budget line a d b
Units of good Y
And the maximum Y we can consume is 30/PY = 30/1 c d
=30/Px=30/2

58. 30/PY = A budget line So Height is 30/Py And length is 30/Px a b
Units of good Y
And length is 30/Px c d
=30/Px=30/2

59. So (minus) the slope of the curve is Height / Length
A budget line
30/PY = a
So (minus) the slope of the curve is Height / Length b
Units of good Y c d
=30/Px=30/2

60. So (minus) the slope of the curve is Height / Length
A budget line
30/PY = a
So (minus) the slope of the curve is Height / Length b
Units of good Y c d
=30/Px=30/2

61. So (minus) the slope of the curve is Height / Length
30/PY =
A budget line a
So (minus) the slope of the curve is Height / Length b X
Units of good Y X c d
=30/Px=30/2

62. So (minus) the slope of the curve is Height / Length
A budget line
30/PY = a
So (minus) the slope of the curve is Height / Length b
Units of good Y c
Which is the relative price of x in terms of good y d
=30/Px=30/2

63. A budget line
30/PY = a
Actually the slope is a negative number since we must GIVE UP X to get Y. b
Units of good Y c d
=30/Px=30/2

64. A budget line
30/PY = a
So the slope of the budget constraint is the relative price of X in terms of Y b
Units of good Y c d
=30/Px=30/2

65. INDIFFERENCE ANALYSIS
We now combine the indifference curve we found before and the budget constraint to find:
The optimum consumption point 7

66. Finding the optimum consumption
Units of good Y I5 I4 I3 I2 I1 O
Units of good X

67. Finding the optimum consumption
Units of good Y
Budget line I5 I4 I3 I2 I1 O
Units of good X

68. Finding the optimum consumption
Consider the Points r and v
What indifference curve are they on?
Could we do better? r
Units of good Y I5 I4 v I3 I2 I1 O
Units of good X

69. Finding the optimum consumption
Clearly s and u are better.
They are on I2 r s
Units of good Y u I5 I4 v I3 I2 I1 O
Units of good X

70. Finding the optimum consumption
At point t we have reached the highest point possible and this is our optimum consumption point r s
Units of good Y t u I5 I4 v I3 I2 I1 O
Units of good X

71. Finding the optimum consumption
Utility is maximised at the point of tangency between the indifference map and the budget constraint. r s
Units of good Y t Y1 u I5 I4 v I3 I2 I1 O X1
Units of good X

72. INDIFFERENCE ANALYSIS
The optimum consumption point
Recall that the slope of the indifference curve is
the marginal rate of substitution
While the slope of the budget constraint is:
(Minus) the relative price of X and Y 7

73. Same slope at t of indifference curve and budget line
So when the consumer chooses optimally: r s
Units of good Y t Y1 u I5 I4 v I3 I2 I1 O X1
Units of good X

74. Same slope at t of indifference curve and budget line
At s MRS is above the market price. ‘Clive’ is prepared to give up more Y than market requires to get X – so he does.
Units of good Y t Y1 u I5 I4 v I3 I2 I1 O X1
Units of good X

75. Same slope at t of indifference curve and budget line
At u MRS is below the market price. ‘Clive’ is prepared to give up more X than market requires to get Y – so he does.
Units of good Y t Y1 u I5 I4 v I3 I2 I1 O X1
Units of good X

76. Same slope at t of indifference curve and budget line
The optimum must therefore satisfy: r s
Units of good Y t Y1 u I5 I4 v I3 I2 I1 O X1
Units of good X

77. INDIFFERENCE ANALYSIS
So now we have established what Clive will choose to consume IF the price of X is 2, the price of Y is 1 and his income is 30.
So XD = f(px,py,I) = f(2,1,30) = x1
What can we say about X1? 7

78. We have found the demand for X at particular set of prices and Income
Good Y Y1 I3 I2 I1 B1 B2 B3 X1
Good X

79. We have found the demand for X at particular set of prices and Income
Good Y Y1 I3 I2 I1 B1 B2 B3 X1
Good X
Suppose we draw a diagram below with Price on one axis and quantity on the other
Price of X
Good X X1

80. We have found the demand for X at particular set of prices and Income
Good Y Y1 I3 I2 I1 B1 B2 B3 X1
Good X
And now we project the demand for x downwards at the Price, Px=2
PX=2
Price of X
Good X X1

81. We have found the demand for X at particular set of prices and Income
Good Y Y1 I3 I2 I1 B1 B2 B3 X1
Good X
What does this point represent?
Ans: A point on the demand curve!
PX=2
Price of X
Good X X1

82. INDIFFERENCE ANALYSIS
So now we have established what Clive will choose to consume IF the price of X is 2, the price of Y is 1 and his income is 30.
So XD = f(px,py,I) = f(2,1,30) = x1
What can we say about X1?
What would happen if Px were to change?
or Py
Or I
It is to these issues we now turn. 7