Demand Curves

1. Demand Curves Graphical Derivation

2. We start with the following diagram y x px x 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 Px. This is effectively the space in which we draw the demand curve.

3. y y0 x0 x px x 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

4. y x px x Recall the slope of the budget constraint is: y0 x0

5. y y0 x px x From the initial equilibrium we can find the first point on the demand curve Projecting x0 into the diagram below, we map the demand for x at px0 px0 x0

6. Next consider a rise in the price of x, to px1. This causes the budget constraint to swing in as –px1/py0 is greater y To find the demand for x at the new price we locate the new equilibrium quantity of x demanded. y0 x1 x px Then we drop a line down from this point to the lower diagram. px1 px0 This shows us the new level of demand at p1x x x1 x0

7. y We are now in a position to draw the ordinary Demand Curve First we highlight the the px and x combinations we have found in the lower diagram. y0 x x0 x1 px And then connect them with a line. px1 This is the Marshallian demand curve for x px0 Dx x x1 x0

8. 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

9. Leontief Indifference Curves- Perfect Complements y y0 x px x0 Again projecting x0 into the diagram below, we map the demand for x at p0x px0 x0

10. y x px x Again considering a rise in the price of x, to px1 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. y0 x0 x1 px1 px0 This shows us the new level of demand at p1x x1 x0

11. y x px x Again we highlight the the px and x combinations we have found in the lower diagram and derive the demand curve. y0 x0 x1 px1 px0 x0 x1

12. y x px x Perfect Substitutes

13. y x px And hence the demand for x = 0 px0 x Putting in the Budget constraint we get: Where is the utility maximising point here?

14. y The budget constraint would swing out x px A: Anywhere on the whole line px1 The demand curve is just a straight line x Suppose now that the price of x were to fall y0 Q: What is the best point now? x0 px0 x0

15. y Now budget constraint pivots out from y axis And the best consumption point is x max x px So at all prices less than px1 demand is x max x At price below px1 what will happen? y0 x0 px0 px1 x0

16. x max (the best consumption point) moves out as price falls y As price decreases further, what will happen? y0 x x0 px px0 px1 x0 x

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