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

2. 2 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd How to plot any Linear Budget Constraint u Rearrange the equation in the form y = mx + c (see above) u Plot y on the vertical axis, against x on the horizontal axis u Calculate and plot the vertical and horizontal intercepts u Join the points and label the graph M P X M P Y Quantity of good Y, y Quantity of goodX, x 0 10 20 30 40 0306090

3. 3 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Example: Budget Constraint: u Example: P X =£2: P Y = £6: M = 180: u u (units of X) (price per unit) + (units of Y )(price per unit) = budget limit u This is the budget equation: u For plotting, rearrange the equation into the form y = mx + c: u Hence, 2x + 6y = 180 is rearranged as: y = 30 - 0.33x u In this form, it is easy to read off intercepts u Vertical intercept = 30 (from the equation above): u Horizontal intercept = 90 since -c/m = -(30)/(-0.33) = 90

4. 4 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Plot the Budget Constraint: 2x + 6y = 180 where P X =£2: P Y = £6: M = 180: x(2) + y(6) = 180 u Plot the horizontal intercept: x = 90 u Plot the vertical intercept: y = 30 u Join these points Quantity of good Y, y Quantity of goodX, x y = 30 - 0.33 x M P X M P Y Slope =  P P X Y Figure 2.39

5. 5 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd u Substitute the prices and budget limit into the general equation: u Rearrange the equation into the form y = mx + c: y = 30 - 0.5x u Hence, vertical intercept = 30; horizontal intercept = 60. u Plot, then join, the vertical and horizontal intercepts Another Example : Plot the Budget Constraint given P X =£3: P Y = £6: M = 180: x(3) + y(6) = 180. Quantity of good Y, y 30 60 Quantity of good X, x Budget constraint for M = 180

6. 6 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the equation of the Budget Constraint: y= 30 -0.5x when the price of good X decreases u P X changes from 3 to 1.5 u The original budget constraint, P X =£3: P Y = £6: M = 180, had the equation: 3x + 6y = 180 (or y = 30 - 0.5x) u To obtain the equation of the new budget constraint Substitute P X = 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 u Intercept is the same: slope has changed from -0.5 to -0.25

7. 7 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y=30 - 0.5x when the price of good X decreases u When P X changes from 3 to 1.5 u Equation of new budget constraint becomes: y = 30 - 0.25x u Plot the vertical intercept = 30 (this is the same as before) u Plot the horizontal intercept = 120 (this is different from before) 0 10 20 30 020406080100120 x y

8. 8 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y = 30 - 0.5x when the price of good X decreases: u Join the vertical intercept = 30 and the horizontal intercept = 120 0 10 20 30 020406080100120 x y Original Constraint Constraint with P X changed Figure 2.40

9. 9 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y = 30 - 0.5x when the price of good X decreases u Label the graphs Figure 2.40  P X and its effect on the Budget constraint 0 10 20 30 020406080100120 y = 30 - 0.5x x y y = 30 - 0.25x

10. 10 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd When P X decreases from 3 to 1.5 u 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  P X and its effect on the budget constraint 0 10 20 30 40 020406080100120 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. 11 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the equation of the original Budget Constraint: y = 30 - 0.5x, when the price of good Y decreases from £6 to £3 u P Y changes from 6 to 3 u In the original budget constraint, where P X =£3: P Y = £6: M = 180, the equation is : 3x + 6y = 180 ( or y = 30 - 0.5x) u To obtain the equation of the new budget constraint u Substitute 3 for P Y in the original equation (nothing else changes) u The equation of new budget constraint is: u 3x + (3) y = 180: u Rearrange the equation into the form y = mx + c ( for plotting): u Hence, the equation of the new budget constraint is y = 60 - x: u Intercept is the same: slope has changed from -0.5 to -1

12. 12 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y = 30 - 0.5x when the price of good Y decreases u When P Y changes from 6 to 3 u The equation of the budget constraint becomes: y = 60 - x u Read off the intercepts; u Plot the vertical intercept = 60 u Plot the horizontal intercept = 60 0 10 20 30 40 50 60 70 0204060 x

13. 13 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y = 30 - 0.5x when the per unit price of good Y decreases from 6 to 3 u Equation of the new budget constraint becomes: y = 60 - x u Join the vertical intercept = 60 and the horizontal intercept = 60 y 0 10 20 30 40 50 60 70 0204060 x Adjusted for change in P Y Original Constraint

14. 14 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the graph of the Budget Constraint: y = 30 - 0.5x when the per unit price of good Y decreases from 6 to 3 u The adjusted constraint pivots upwards from the unchanged horizontal intercept (see Figure 2.41) u 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 0204060 y = 30 - 0.5x y = 60 -x x y

15. 15 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Adjust the equation of the Budget Constraint: y = 30 - 0.5x when the budget limit increases u M changes from 180 to 240 u The original budget constraint, where P X =£3: P Y = £6: M = 180, was given by the equation was: 3x + 6y = 180 ( or y = 30 - 0.5x) u To obtain the equation of the new budget constraint u replace M by 240 (nothing else changes) u The equation of the new budget constraint becomes: 3x + 6y = 240: u Rearrange this equation into the form y = mx + c ( for plotting later): u The equation of the budget constraint, when the budget limit increases from 180 to 240 u is y = 40 - 0.5x. u Slope is the same: intercept has changed from 30 to 40

16. 16 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Change in the graph of the Budget Constraint: y = 30 - 0.5x when the budget limit increases u M changes from 180 to 240 u Equation of budget constraint becomes: y = 40 - 0.5x u Plot the vertical intercept = 40 u Plot the horizontal intercept = 80 0 10 20 30 40 50 020406080 x y

17. 17 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Change in the graph of the Budget Constraint: y = 30 - 0.5x when the budget limit increases u Join the vertical intercept = 40 and the horizontal intercept = 80 u This is the graph of the adjusted budget constraint is: y = 40 - 0.5x 0 10 20 30 40 50 020406080 x y Budget = 240 Budget = 180

18. 18 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Summary: Change in the graph of the Budget Constraint: y = 30 - 0.5x when the budget limit increases u When the budget limit increases, the constraint moves upwards, parallel to the original constraint u 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 020406080 x y Budget = 240 Budget = 180

19. 19 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Isocost line:4K + 5L = 8000, hence K = 2000 - 1.25L Method: u Plot K on the vertical axis, L on the horizontal axis. u Calculate and plot the horizontal and vertical intercepts. u A and B are simply two extra points. u It is a safeguard (against arithmetic errors) to plot at least one extra point when plotting lines u Join the points 0 500 1000 1500 2000 2500 040080012001600 K = 2000 - 1.25L L K A B C r C w

20. 20 Copyright©2001 Teresa Bradley and John Wiley & Sons Ltd Isocost line:4K + 5L = 8000, hence K = 2000 - 1.25L u Labour increases from £5 to £8 per hour: K = 2000 -2L u (Show how the last equation was derived) u The horizontal intercept moves towards the origin, along the horizontal axis u Comment: when the price of labour increases, fewer units are affordable Figure 2.48 Effect of change in price of labor on the isocost line 0 500 1000 1500 2000 2500 0 200400600800 1000120014001600 Effect of change in price of labour on the isocost line K = 2000 - 1.25L L K K = 2000 - 2L