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Demand Curves Graphical Derivation

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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 x y pxpx x

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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 x pxpx x y

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

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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 x 0 x0x0 y0y0 x pxpx x y px0px0

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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. 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 x0x0 y0y0 x pxpx x y px0px0 x1x1 px1px1 x1x1

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We are now in a position to draw the ordinary Demand Curve 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 x y pxpx x

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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

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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

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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 x y pxpx x

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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. x y pxpx x

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Perfect Substitutes x y pxpx x

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Putting in the Budget constraint we get: Where is the utility maximising point here? x y pxpx x And hence the demand for x = 0 px0px0

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The budget constraint would swing out x0x0 y0y0 x0x0 Suppose now that the price of x were to fall Q: What is the best point now? The demand curve is just a straight line px1px1 A: Anywhere on the whole line x y pxpx x px0px0

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

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x max (the best consumption point) moves out as price falls As price decreases further, what will happen? x0x0 y0y0 x0x0 px1px1 x y pxpx x px0px0

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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?

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Indifference Curves and Utility Maximization

Indifference Curves and Utility Maximization

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