BUDGET CONSTRAIT.ppt

1
Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd
Chapter 2: The Straight Line and Applications
 How to plot a budget constraint. Worked Example 2.22, Figure 2.39:
Slides 2 -5
 The effect of a price change in good X (on the horizontal). Worked
Example 2.23, Figure 2.40:
Slides 6 - 10
 The effect of price change in good Y (on the vertical). Worked
Example 2.23, Figure 2.41:
Slides 11 - 14
 The effect of a change in the budget limit. Worked Example 2.23,
Figure 2.42:
Slides 15 - 18
 Plot an Isocost constraint: Slide 19
 Effect of change in the price of labour: Slide 20

2
How to plot any Linear Budget Constraint
 Rearrange the equation in the form y = mx + c (see above)
 Plot y on the vertical axis, against x on the horizontal axis
 Calculate and plot the vertical and horizontal intercepts
 Join the points and label the graph
xP yP M y
M
P
P
P
x
X Y
Y
X
Y
    






M
PX
M
PY
Quantity of good Y, y
Quantity of good X, x
0
10
20
30
40
0 30 60 90

3
Example: Budget Constraint:
 Example: PX =£2: PY = £6: M = 180:

 (units of X) (price per unit) + (units of Y )(price per unit) = budget limit
 This is the budget equation:
 For plotting, rearrange the equation into the form y = mx + c:
 Hence, 2x + 6y = 180 is rearranged as: y = 30 - 0.33x
 In this form, it is easy to read off intercepts
 Vertical intercept = 30 (from the equation above):
 Horizontal intercept = 90 since -c/m = -(30)/(-0.33) = 90
x P y P M
X Y
( ) ( )
 
x P y P M
x y
X Y
2 6 180
   
   

4
Plot the Budget Constraint: 2x + 6y = 180
where PX =£2: PY = £6: M = 180: x(2) + y(6) = 180
 Plot the horizontal intercept: x = 90
 Plot the vertical intercept: y = 30
 Join these points
0
10
20
30
40
0 30 60 90
y = 30 - 0.33 x
M
PX
M
PY
Slope = 
P
P
X
Y
Figure 2.39

5
xP yP M
X Y
 
 Substitute the prices and budget limit into the general equation:
 Rearrange the equation into the form y = mx + c: y = 30 - 0.5x
 Hence, vertical intercept = 30; horizontal intercept = 60.
 Plot, then join, the vertical and horizontal intercepts
Another Example : Plot the Budget Constraint
given PX =£3: PY = £6: M = 180: x(3) + y(6) = 180.
30
60
Budget constraint for
M = 180

6
Adjust the equation of the Budget Constraint: y= 30 -0.5x
when the price of good X decreases
 PX changes from 3 to 1.5
 The original budget constraint, PX =£3: PY = £6: M = 180,
had the equation: 3x + 6y = 180 (or y = 30 - 0.5x)
 To obtain the equation of the new budget constraint
Substitute PX = 1.5 into the original budget constraint (nothing else changes)
Hence, the equation ofthe new budget constraint is: (1.5)x + 6y = 180:
Rearrange this equation (for plotting later) to the form y = mx + c:
y = 30 - 0.25x. This is the equation of the budget constraint when P has
decreased from £3 to £1.5
 Intercept is the same: slope has changed from -0.5 to -0.25

7
Adjust the graph of the Budget Constraint: y=30 - 0.5x
 When PX changes from 3 to 1.5
 Equation of new budget constraint becomes: y = 30 - 0.25x
 Plot the vertical intercept = 30 (this is the same as before)
 Plot the horizontal intercept = 120 (this is different from before)
0
10
20
30
0 20 40 60 80 100 120
x
y

8
Adjust the graph of the Budget Constraint: y = 30 - 0.5x when
the price of good X decreases:
 Join the vertical intercept = 30 and the horizontal intercept = 120
0
10
20
30
0 20 40 60 80 100 120
x
y
Original Constraint
Constraint with PX changed
Figure 2.40

9
Adjust the graph of the Budget Constraint: y = 30 - 0.5x
 Label the graphs
Figure 2.40 PX and its effect on the Budget constraint
0
10
20
30
0 20 40 60 80 100 120
y = 30 - 0.5x
x
y
y = 30 - 0.25x

10
When PX decreases from 3 to 1.5
 The adjusted budget constraint pivots out from the unchanged vertical
intercept (see Figure 2.40)
(note:as X decreases in price, more units of X are affordable, so x increases)
Figure 2.40 PX and its effect on the budget constraint
0
10
20
30
40
0 20 40 60 80 100 120
y = 30 - 0.5x
y = 30 - 0.25x
x
y
Summary: Change in the equation and graph of the Budget
Constraint: y = 30 - 0.5x when the price of good X
decreases

11
Adjust the equation of the original Budget Constraint:
y = 30 - 0.5x,
when the price of good Y decreases from £6 to £3
 PY changes from 6 to 3
 In the original budget constraint, where PX =£3: PY = £6: M = 180,
the equation is : 3x + 6y = 180 ( or y = 30 - 0.5x)
 Substitute 3 for PY in the original equation (nothing else changes)
 The equation of new budget constraint is:
 3x + (3) y = 180:
 Rearrange the equation into the form y = mx + c ( for plotting):
 Hence, the equation of the new budget constraint is y = 60 - x:
 Intercept is the same: slope has changed from -0.5 to -1

12
when the price of good Y decreases
 When PY changes from 6 to 3
 The equation of the budget constraint becomes: y = 60 - x
 Read off the intercepts;
 Plot the vertical intercept = 60
 Plot the horizontal intercept = 60
0
10
20
30
40
50
60
70
0 20 40 60
x

13
when the per unit price of good Y decreases from 6 to 3
 Equation of the new budget constraint becomes: y = 60 - x
y
0
10
20
30
40
50
60
70
0 20 40 60
x
Adjusted for change in PY
Original Constraint

14
when the per unit price of good Y decreases from 6 to 3
 The adjusted constraint pivots upwards from the unchanged horizontal
intercept (see Figure 2.41)
 Comment: When Y decreases in price, more units of Y are affordable
Figure 2.41 P
y and its effect on the budget constraint
0
10
20
30
40
50
60
70
0 20 40 60
y = 30 - 0.5 x
y = 60 - x
x
y

15
Adjust the equation of the Budget Constraint:
y = 30 - 0.5x when the budget limit increases
 M changes from 180 to 240
 The original budget constraint, where PX =£3: PY = £6: M = 180,
was given by the equation was: 3x + 6y = 180 ( or y = 30 - 0.5x)
 replace M by 240 (nothing else changes)
 The equation of the new budget constraint becomes: 3x + 6y = 240:
 Rearrange this equation into the form y = mx + c ( for plotting later):
 The equation of the budget constraint, when the budget limit increases
from 180 to 240
 is y = 40 - 0.5x.
 Slope is the same: intercept has changed from 30 to 40

16
Change in the graph of the Budget Constraint:
 M changes from 180 to 240
 Equation of budget constraint becomes: y = 40 - 0.5x
 Plot the vertical intercept = 40
 Plot the horizontal intercept = 80
0
10
20
30
40
50
0 20 40 60 80
x
y

17
Change in the graph of the Budget Constraint:
 This is the graph of the adjusted budget constraint is: y = 40 - 0.5x
0
10
20
30
40
50
0 20 40 60 80
x
y
Budget = 240
Budget = 180

18
Summary: Change in the graph of the Budget Constraint:
 When the budget limit increases, the constraint moves upwards,
parallel to the original constraint
 Comment: When the budget limit increases, more units of both X and
Y are affordable
Figure 2.42 Y and its effect on the Budget constraint
0
10
20
30
40
50
0 20 40 60 80
x
y
Budget = 240
Budget = 180

19
Isocost line:4K + 5L = 8000, hence K = 2000 - 1.25L
Method:
 Plot K on the vertical axis, L on the horizontal axis.
 Calculate and plot the horizontal and vertical intercepts.
 A and B are simply two extra points.
 It is a safeguard (against arithmetic errors) to plot at least one extra
point when plotting lines
 Join the points
0
500
1000
1500
2000
2500
0 400 800 1200 1600
K = 2000 - 1.25L
L
K
A
B
C
r
C
w

20
Isocost line:4K + 5L = 8000, hence K = 2000 - 1.25L
 Labour increases from £5 to £8 per hour: K = 2000 -2L
 (Show how the last equation was derived)
 The horizontal intercept moves towards the origin, along the
horizontal axis
 Comment: when the price of labour increases, fewer units are
affordable
0
500
1000
1500
2000
2500
0
200
400
600
800
1000
1200
1400
1600
Effect of change in price of labour on the isocost line
K = 2000 - 1.25 L
L
K
K = 2000 - 2 L

BUDGET CONSTRAIT.ppt

Recommended

Recommended

More Related Content

Similar to BUDGET CONSTRAIT.ppt

Similar to BUDGET CONSTRAIT.ppt (18)

Recently uploaded

Recently uploaded (20)

BUDGET CONSTRAIT.ppt