Demand Curves Graphical Derivation We start with the

Demand Curves Graphical Derivation

We start with the following diagram y 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. x px 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. x

Next we draw in the indifference curves showing the consumers tastes for x and y. y y 0 x px x Then we draw in the budget constraint and find the initial equilibrium

y Recall the slope of the budget constraint is: y 0 x px x

y From the initial equilibrium we can find the first point on the demand curve y 0 x px Projecting x 0 into the diagram below, we map the demand for x at px 0 x 0 x

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

y We are now in a position to draw the ordinary Demand Curve First we highlight the px and x combinations we have found in the lower diagram. y 0 px x 1 x x 0 And then connect them with a line. p x 1 p x 0 This is the Marshallian demand curve for x Dx x 1 x 0 x

• 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

Leontief Indifference Curves. Perfect Complements y y 0 px x 0 x Again projecting x 0 into the diagram below, we map the demand for x at p 0 x p x 0

Again considering a rise in the price of x, to px 1 the budget constraint swings in. y y 0 px x 1 x 0 x We locate the new equilibrium quantity of x demanded and then drop a line down from this point to the lower diagram. p x 1 p x 0 This shows us the new level of demand at p 1 x x 1 x 0 x

y y 0 px x 1 x 0 x p x 1 p x 0 x 1 x 0 x Again we highlight the px and x combinations we have found in the lower diagram and derive the demand curve.

y Perfect Substitutes x px x

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

y Suppose now that the price of x were to fall The budget constraint would swing out y 0 px x 0 x Q: What is the best point now? A: Anywhere on the whole line p x 0 p x 1 The demand curve is just a straight line x 0 x

y At price below px 1 what will happen? Now budget constraint pivots out from y axis y 0 px x 0 x p x 0 px And the best consumption point is x max So at all prices less than px 1 demand is x max 1 x 0 x

y As price decreases further, what will happen? y 0 px x 0 x x max (the best consumption point) moves out as price falls p x 0 p x 1

• 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?