2. The Demand Curves Graphical Derivation

3. x x y pxpx In this part of the diagram we have drawn the choice between x on the horizontal axis and y on the vertical axis. Soon we will draw an indifference curve in here Down below we have drawn the relationship between x and its price P x. This is effectively the space in which we draw the demand curve. We start with the following diagram

4. x y pxpx Next we draw in the indifference curves showing the consumers tastes for x and y. Then we draw in the budget constraint and find the initial equilibrium x0x0 y0y0

5. x y pxpx x0x0 y0y0 Recall the slope of the budget constraint is:

6. x y pxpx x0x0 y0y0 From the initial equilibrium we can find the first point on the demand curve Projecting x 0 into the diagram below, we map the demand for x at p 0 x x0x0 px0px0

7. x y pxpx x0x0 y0y0 x0x0 px0px0 Next consider a rise in the price of x, to p x 1,. This causes the budget constraint to swing in as -p x 1 /p y 0 is greater To find the demand for x at the new price we locate the new equilibrium quantity of x demanded. x1x1 x1x1 px1px1 Then we drop a line down from this point to the lower diagram. This shows us the new level of demand at p 1 x

8. We are now in a position to draw the ordinary Demand Curve x y pxpx x0x0 y0y0 x0x0 px0px0 x1x1 x1x1 px1px1 First we highlight the the p x and x combinations we have found in the lower diagram. DxDx And then connect them with a line. This is the Marshallian demand curve for x

9. In the diagrams above we have drawn our demand curve as a nice downward sloping curve. Will this always be the case? Consider the case of perfect Complements - (Leontief Indifference Curve) e.g. Left and Right Shoes

10. x y pxpx x0x0 y0y0 Leontief Indifference Curves- Perfect Complements Again projecting x 0 into the diagram below, we map the demand for x at p 0 x x0x0 px0px0

11. x y pxpx x0x0 y0y0 x0x0 px0px0 Again considering a rise in the price of x, to p x 1 the budget constraint swings in. We locate the new equilibrium quantity of x demanded and then drop a line down from this point to the lower diagram. x1x1 x1x1 px1px1 This shows us the new level of demand at p 1 x

12. x y pxpx x0x0 y0y0 x0x0 px0px0 x1x1 x1x1 px1px1 Again we highlight the the p x and x combinations we have found in the lower diagram and derive the demand curve.

13. In the diagrams above we have drawn our demand curve as a nice downward sloping curve. Will this always be the case? Consider the case of perfect Complements - (Leontief Indifference Curve) e.g. Left and Right Shoes

14. x y pxpx x0x0 y0y0 Perfect Substitutes x0x0 px0px0

15. x y pxpx x0x0 y0y0 Putting in the Budget constraint we get: x0x0 px0px0

16. x y pxpx x0x0 y0y0 x0x0 px0px0 Where is the utility maximising point here? And hence the demand for x = 0

17. x y pxpx x0x0 y0y0 x0x0 px0px0 Suppose now that the price of x was to fall The budget constraint would swing out What is the best point now?

18. x y pxpx x0x0 y0y0 x0x0 px0px0 Suppose now that the price of x was to fall The budget constraint would swing out What is the best point now? Ans: Anywhere on the whole line

19. x y pxpx x0x0 y0y0 x0x0 px0px0 px1px1 And the demand curve is just a straight line

20. x y pxpx x0x0 y0y0 x0x0 px0px0 px1px1 At price below p x 1 what will happen?

21. x y pxpx x0x0 y0y0 x0x0 px0px0 px1px1 Now budget constraint swings down from y axis And the best consumption point is X max

22. x y pxpx x0x0 y0y0 x0x0 px0px0 px1px1 At price below p x 1 what will happen? Now budget constraint swings down from y axis And the best consumption point is x max So at all prices less than p x 1 demand is x max

23. x y pxpx x0x0 y0y0 x0x0 px0px0 px1px1 At price below p x 1 what will happen? Now budget constraint swings down from y axis And x max (the best consumption point) moves out as price falls

24. So here the demand curve does not take the usual nice smooth downward sloping shape. What determines the shape of the demand curve Ans: The shape of the indifference curves. Q: What properties must indifference curve have to give us sensible looking demand curves