# Income and Substitution Effects Engel Curves and the Slutsky Equation

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- Slide 1
- Income and Substitution Effects Engel Curves and the Slutsky Equation
- Slide 2
- Demand and income If your income is initially X 1, you buy A 1 apples When your income rises to X 2, you buy A 2 apples. To make the obvious point, demand is a function of income X A1A1 I1I1 X1X1 A2A2 X2X2 I2I2
- Slide 3
- How demand rises with income Lets plot the combinations of apples and income (X) from the previous graph. A1A1 A2A2 X1X1 X2X2
- Slide 4
- How demand rises with income Lets plot the combinations of apples and income (X) from the previous graph. Connecting all possible points, we get the Engel curve, giving demand as a function of income. A1A1 A2A2 X1X1 X2X2
- Slide 5
- 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 A X
- Slide 6
- 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 increasing slope the elasticity is greater than 1.0 A X
- Slide 7
- 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 A X
- Slide 8
- The Shape of the Engel Curve 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 A X
- Slide 9
- Income and Substitution Effects We know that both price and income influence demand.
- Slide 10
- Income and Substitution Effects We know that both price and income influence demand. A price change means an income change.
- Slide 11
- Income and Substitution Effects We know that both price and income influence demand. A 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
- Slide 12
- Income and Substitution Effects Lets draw the indifference curves between money and apples. $ A YoYo Y o /p A I1I1
- Slide 13
- Income and Substitution Effects Lets draw the indifference curves between money and apples. Your income is Y o ; Apples initially cost p a $ A YoYo Y o /p A I1I1
- Slide 14
- Income and Substitution Effects Lets draw the indifference curves between money and apples. Your income is Y o ; Apples initially cost p a You are are on indifference curve I 1. $ A YoYo Y o /p A I1I1
- Slide 15
- Income and Substitution Effects Suppose the price of apples drops to p* a $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 16
- Income and Substitution Effects Suppose the price of apples drops to p* a The budget line rotates out and you move to indifference curve I 2. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 17
- Income and Substitution Effects Suppose the price of apples drops to p* a The budget line rotates out and you move to indifference curve I 2. Two things have occurred: a price cut and an increase in income. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 18
- Income and Substitution Effects The substitution effect $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 19
- Income and Substitution Effects The substitution effect 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. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 20
- Income and Substitution Effects The substitution effect 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 I 1 shows the substitution effect. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 21
- Income and Substitution Effects The substitution effect is always negative Diminishing MRS guarantees it $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 22
- Income and Substitution Effects The substitution effect 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. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 23
- Income and Substitution Effects We effectively break the price change down into its two components. The substitution effect The income effect. $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 24
- Income and Substitution Effects 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 $ A YoYo Y o /p A Y o /p* A I1I1 I2I2
- Slide 25
- A Summary Table
- Slide 26
- The Slutsky Equation These effects are often summarized in the Slutsky equation
- Slide 27
- The Slutsky Equation These effects are often summarized in the Slutsky equation The substitution effect shows the change in demand from a movement along the indifference curve.
- Slide 28
- The Slutsky Equation These effects are often summarized in the Slutsky equation The income effect shows the change in demand from the effective increase in income.
- Slide 29
- An Application
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- ( Q/ P) = 3/(-0.05) = - 60
- Slide 34
- An Application ( Q/ P) = - 60 Q( Q/ I) = 50 (1) = 50
- Slide 35
- An Application ( Q/ P) = - 60 Q( Q/ I) = 50 -60 ( Q/ P) U=Constant 50
- Slide 36
- An Application -60 ( Q/ P) U=Constant 50 ( Q/ P) U=Constant = -10
- Slide 37
- A Caution The version of the Slutsky equation we use is only an approximation.
- Slide 38
- A 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.
- Slide 39
- Why spend time on this topic? Giffin Goods
- Slide 40
- Why spend time on this topic? Giffin Goods The Demand for Leisure
- Slide 41
- Why spend time on this topic? Giffin Goods The Demand for Leisure As wage rates increase, the cost of an hour of leisure increases Demand goes up because the income effect dominates the substitution effect.
- Slide 42
- Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes.
- Slide 43
- Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes Changes in the price of one brand versus changes in the prices of all brands..
- Slide 44
- Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes Changes in the price of one brand versus changes in the prices of all brands. Heavily purchased goods versus lightly purchased goods.
- Slide 45
- A Final Point
- Slide 46
- The slope of the Marshallian, or uncompensated demand function
- Slide 47
- A Final Point The slope of the Marshallian, or uncompensated demand function The slope of the Hicksian, or compensated demand function. 2003 Charles W. Upton

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