income and substitution effects engel curves and the slutsky equation
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![Page 1: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/1.jpg)
Income and Substitution Effects
Engel Curves and the Slutsky Equation
![Page 2: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/2.jpg)
Demand and income
• If your income is initially X1, you buy A1 apples
• When your income rises to X2, you buy A2 apples.
• To make the obvious point, demand is a function of income
X
A1
I1
X1
A2
X2
I2
![Page 3: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/3.jpg)
How demand rises with income
• Lets plot the combinations of apples and income (X) from the previous graph.
A1
A2
X1 X2
![Page 4: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/4.jpg)
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.
A1
A2
X1 X2
![Page 5: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/5.jpg)
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
![Page 6: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/6.jpg)
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
![Page 7: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/7.jpg)
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
![Page 8: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/8.jpg)
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
![Page 9: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/9.jpg)
Income and Substitution Effects
• We know that both price and income influence demand.
![Page 10: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/10.jpg)
Income and Substitution Effects
• We know that both price and income influence demand.
• A price change means an income change.
![Page 11: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/11.jpg)
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
![Page 12: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/12.jpg)
Income and Substitution Effects
• Let’s draw the indifference curves between money and apples.
$
A
Yo
Yo/pA
I1
![Page 13: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/13.jpg)
Income and Substitution Effects
• Let’s draw the indifference curves between money and apples.
• Your income is Yo; Apples initially cost pa
$
A
Yo
Yo/pA
I1
![Page 14: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/14.jpg)
Income and Substitution Effects
• Let’s draw the indifference curves between money and apples.
• Your income is Yo; Apples initially cost pa
• You are are on indifference curve I1.
$
A
Yo
Yo/pA
I1
![Page 15: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/15.jpg)
Income and Substitution Effects
• Suppose the price of apples drops to p*a
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 16: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/16.jpg)
Income and Substitution Effects
• Suppose the price of apples drops to p*a
• The budget line rotates out and you move to indifference curve I2.
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 17: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/17.jpg)
Income and Substitution Effects
• Suppose the price of apples drops to p*a
• The budget line rotates out and you move to indifference curve I2.
• Two things have occurred: a price cut and an increase in income.
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 18: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/18.jpg)
Income and Substitution Effects
• The substitution effect $
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 19: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/19.jpg)
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
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 20: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/20.jpg)
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 I1 shows the substitution effect.
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 21: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/21.jpg)
Income and Substitution Effects
• The substitution effect is always negative– Diminishing MRS
guarantees it
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 22: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/22.jpg)
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
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 23: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/23.jpg)
Income and Substitution Effects
• We effectively break the price change down into its two components.– The substitution effect
– The income effect.
$
A
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 24: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/24.jpg)
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
Yo
Yo/pA
Yo/p*A
I1
I2
![Page 25: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/25.jpg)
A Summary Table
Change in Quantity Demanded for Normal and Inferior Goods
Normal Good Inferior Good
Price Increase
Price Decrease
Price Increase
Price Decrease
Change in quantity demanded due to substitution effect (holding utility constant)
(-) (+) (-) (+)
Change due to income effect (holding prices constant)
(-) (+) (+) (-)
Combined Effect (-) (+) ? ?
![Page 26: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/26.jpg)
The Slutsky Equation
• These effects are often summarized in the Slutsky equation
I
P
Q
P
Q
tConsU tan
![Page 27: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/27.jpg)
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.
I
P
Q
P
Q
tConsU tan
![Page 28: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/28.jpg)
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.
I
P
Q
P
Q
tConsU tan
![Page 29: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/29.jpg)
An Application
Apples Cost 50¢ Income of $100 50 Demanded
![Page 30: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/30.jpg)
An Application
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
![Page 31: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/31.jpg)
An Application
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
![Page 32: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/32.jpg)
An Application
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
I
P
Q
P
Q
tConsU tan
![Page 33: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/33.jpg)
An Application
(Q/P) = 3/(-0.05) = - 60
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
I
P
Q
P
Q
tConsU tan
![Page 34: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/34.jpg)
An Application
(Q/P) = - 60Q(Q/I) = 50 (1) = 50
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
I
P
Q
P
Q
tConsU tan
![Page 35: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/35.jpg)
An Application
(Q/P) = - 60Q(Q/I) = 50
-60 (Q/P)U=Constant –50
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
I
P
Q
P
Q
tConsU tan
![Page 36: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/36.jpg)
An Application
-60 (Q/P)U=Constant –50
(Q/P)U=Constant = -10
Apples Cost 50¢ Income of $100 50 Demanded
Apples Cost 45¢ Income of $100 53 Demanded
Apples Cost 50¢ Income of $101 51 Demanded
I
P
Q
P
Q
tConsU tan
![Page 37: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/37.jpg)
A Caution
• The version of the Slutsky equation we use is only an approximation.
![Page 38: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/38.jpg)
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.
![Page 39: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/39.jpg)
Why spend time on this topic?
• Giffin Goods
![Page 40: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/40.jpg)
Why spend time on this topic?
• Giffin Goods
• The Demand for Leisure
![Page 41: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/41.jpg)
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.
![Page 42: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/42.jpg)
Why spend time on this topic?
• Giffin Goods
• The Demand for Leisure
• Different Slopes.
![Page 43: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/43.jpg)
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.
.
![Page 44: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/44.jpg)
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.
![Page 45: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/45.jpg)
A Final Point
I
P
Q
P
Q
tConsU tan
![Page 46: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/46.jpg)
A Final Point
• The slope of the Marshallian, or uncompensated demand function
I
P
Q
P
Q
tConsU tan
![Page 47: Income and Substitution Effects Engel Curves and the Slutsky Equation](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649d7e5503460f94a61263/html5/thumbnails/47.jpg)
A Final Point
• The slope of the Marshallian, or uncompensated demand function
• The slope of the Hicksian, or compensated demand function.
I
P
Q
P
Q
tConsU tan
©2003 Charles W. Upton