Presentation on theme: "The Marshall, Hicks and Slutsky Demand Curves"— Presentation transcript:
1The Marshall, Hicks and Slutsky Demand Curves Graphical Derivation
2We start with the following diagram: xypxIn 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.
3xpxyNext we draw in the indifference curves showing the consumers’ tastes for x and y.y0x0Then we draw in the budget constraint and find the initial equilibrium.
4Recall the slope of the budget constraint is: xpxyy0x0
5Projecting x0 into the diagram below, we map the demand for x at px0 yFrom the initial equilibrium we can find the first point on the demand curvey0Projecting x0 into the diagram below, we map the demand for x at px0px0x0
6Then we drop a line down from this point to the lower diagram. Next consider a rise in the price of x, to px1. This causes the budget constraint to swing in as – px1/py0 is greater.yTo find the demand for x at the new price we locate the new equilibrium quantity of x demanded.y0x1xpxThen we drop a line down from this point to the lower diagram.px1px0This shows us the new level of demand at p1xx1x0x
7This is the Marshallian demand curve for x. yWe 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 and then connect them with a line.y0xpxpx1This is the Marshallian demand curve for x.Dxpx0x1x0x
8Our next exercise involves giving the consumer enough income so that they can reach their original level of utility U2.yTo do this we take the new budget constraint and gradually increase the agent’s income, moving the budget constraint out until we reach the indifference curve U2y0U2U1xx1x0pxpx1px0Dxx1x0x
9This is called the Hicksian demand for x and we will label it xH. The new point of tangency tells us the demand for x when the consumer had been compensated so they can still achieve utility level U2, but the relative price of x and y has risen to px1/py0.yy0U2U1xHxx1x0The level of demand for x represents the pure substitution effect of the increase in the price of x.pxpx1px0DxThis is called the Hicksian demand for x and we will label it xH.xx1x0
10Notice this is the compensated demand for x when the price is px1. We derive the Hicksian demand curve by projecting the demand for x downwards into the demand curve diagram.yy0U2Notice this is the compensated demand for x when the price is px1.U1xHxx1x0pxpx1To get the Hicksian demand curve we connect the new point to the original demand x0px0px0Dxxx1xHx0
11y0 U2 U1 xH x1 x0 px1 px0 Dx Hx x1 xH x0 We label the curve Hx Notice that the Hicksian demand curve is steeper than the Marshallian demand curve when the good is a normal good.px1px0DxHxxx1xHx0
12Notice that an alternative compensation scheme would be to give the consumer enough income to buy their original bundle of goods x0yoyy0U2U1xHxx1x0pxIn this case the budget constraint has to move out even further until it goes through the point x0y0px1px0DxHxxx1xHx0
13But now the consumer doesn’t have to consume x0y0 pxSo they will choose a new equilibrium point on a higher indifference curve.px1px0DxHxxx1xHx0
14y0 U3 U2 U1 x1 xs x0 px1 px0 Dx Hx xs x1 xH x0 Once again we find the demand for x at this new higher level of income by dropping a line down from the new equilibrium point to the x axis.yy0U3We call this xs . It is the Slutsky demand.U2U1xx1xsx0pxOnce again this income compensated demand is measured at the price px1px1px0DxHxxsxx1xHx0
15U3 y0 U2 U1 x1 x0 xs px1 px0 Dx Hx Sx xs Finally, once again we can draw the Slutsky compensated demand curve through this new point xspx1 and the original x0px0y0U3U2U1xx1xsx0pxThe new demand curve Sx is steeper than either the Marshallian or the Hicksian curve when the good is normal.px1px0DxHxSxxsx
161. The normal Marshallian demand curve SummarySWe can derive three demand curves on the basis of our indifference curve analysis.1. The normal Marshallian demand curve2. The Hicksian compensated demand curve where agents are given sufficient income to maintain them on their original utility curve.H3. The Slutsky income compensated demand curve where agents have sufficient income to purchase their original bundle.Finally, for a normal good the Marshallian demand curve is flatter than the Hicksian, which in turn is flatter than the Slutsky demand curve.pxMx
17Problems to considerConsider the shape of the curves if X is an inferior good.Consider the shape of each of the curves if X is a Giffen good.Will it matter if Y is a Giffen or an inferior good?