Demand and income. Income and Substitution Effects. How demand rises with income. How demand rises with income. The Shape of the Engel Curve

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1 Demand and income Engel Curves and the Slutsky Equation If your income is initially 1, you buy 1 apples When your income rises to 2, you buy 2 apples. To make the obvious point, demand is a function of income How demand rises with income How demand rises with income Lets plot the combinations of apples and income () from the previous graph Lets plot the combinations of apples and income () from the previous graph. Connecting all possible points, we get the Engel curve, giving demand as a function of income The Shape of the Engel Curve The Shape of the Engel Curve The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve is a straight line, the income elasticity is 1.0 The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve has increasing slope the elasticity is greater than 1.0 1

2 The Shape of the Engel Curve The Shape of the Engel Curve The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve has decreasing slope the elasticity is less than 1.0 Of course the Engel Curve need not be so well behaved This Engel Curve corresponds to a good that is both inferior and superior, depending on income We know that both price and income influence demand. We know that both price and income influence demand. price change means an income change. We know that both price and income influence demand. price change, means an income change. You are purchasing 10 apples at 1 each. If the price falls to 50, you effectively get 5 more income Let s draw the indifference curves between money and apples. /p 2

3 Let s draw the indifference curves between money and apples. Your income is ; pples initially cost p a Let s draw the indifference curves between money and apples. Your income is ; pples initially cost p a You are are on indifference curve. /p /p Suppose the price of apples drops to p* a Suppose the price of apples drops to p* a The budget line rotates out and you move to indifference curve. /p /p* /p /p* Suppose the price of apples drops to p* a The budget line rotates out and you move to indifference curve. Two things have occurred: a price cut and an increase in income. /p /p* /p /p* 3

4 To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve. To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve. The move to the red point on shows the substitution effect. /p /p* /p /p* is always negative Diminishing MRS guarantees it is always negative The income effect Of course, income has gone up as well, and the movement from the red point to the green point reflects that. /p /p* /p /p* We effectively break the price change down into its two components. The substitution effect The income effect. We effectively break the price change down into its two components. The substitution effect The income effect. While the substitution effect is always negative, the income effect may or not be positive /p /p* /p /p* 4

5 Summary Table The Slutsky Equation Ch ange in Quantity Demanded for Normal and Inferior Goods Normal Good Inferior Good Price Price Price Price Increase Decrease Increase Decrease Change in quantity demanded due to (-) (+) (-) (+) substitution effect (holding utility constant) Change due to income effect (holding prices (-) (+) (+) (-) constant) Combined Effect (-) (+)?? These effects are often summarized in the Slutsky equation The Slutsky Equation The Slutsky Equation These effects are often summarized in the Slutsky equation shows the change in demand from a movement along the indifference curve. These effects are often summarized in the Slutsky equation The income effect shows the change in demand from the effective increase in income. n pplication n pplication pples Cost 50 pples Cost 50 pples Cost 45 5

6 n pplication n pplication pples Cost 50 pples Cost 45 pples Cost 50 Income of 101 pples Cost 50 pples Cost 45 pples Cost 50 Income of 101 n pplication n pplication pples Cost 50 pples Cost 45 pples Cost 50 Income of 101 pples Cost 50 pples Cost 45 pples Cost 50 Income of 101 (/) = 3/(-0.05) = - 60 (/) = - 60 Q(/ I) = 50 (1) = 50 pples Cost 50 n pplication pples Cost 45 pples Cost 50 Income of 101 pples Cost 50 n pplication pples Cost 45 pples Cost 50 Income of 101 (/) = - 60 Q(/ I) = (/) U=Constant (/) U=Constant 50 (/) U=Constant = -10 6

7 Caution The version of the Slutsky equation we use is only an approximation. Caution The version of the Slutsky equation we use is only an approximation. We are assuming discrete changes in price and income; the correct equation assumes infinitesimal changes. s wage rates increase, the cost of an hour of leisure increases Demand goes up because the income effect dominates the substitution effect. Different Slopes. 7

8 Different Slopes Changes in the price of one brand versus changes in the prices of all brands.. Different Slopes Changes in the price of one brand versus changes in the prices of all brands. Heavily purchased goods versus lightly purchased goods. Final Point Final Point The slope of the Marshallian, or uncompensated demand function Final Point The slope of the Marshallian, or uncompensated demand function The slope of the Hicksian, or compensated demand function Charles W. Upton 8