Utility This slideshow is to help you –Visualize the utility function as a three dimensional...
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Utility • This slideshow is to help you – Visualize the utility function as a three dimensional object – Relate the two dimensional indifference curves to the utility function
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Transcript of Utility This slideshow is to help you –Visualize the utility function as a three dimensional...
Utility
• This slideshow is to help you – Visualize the utility function as a three
dimensional object– Relate the two dimensional indifference
curves to the utility function
space
• First, we need to set up a way of representing utility as a function of consumption and leisure.– the vertical axis (up-down) denotes the level
of utility• Higher = greater utility
– the axis that points into the screen denotes consumption
• “deeper” = more consumption
– the axis that points to the right denotes leisure• Further to the right = more leisure
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Consu
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Leisure
Utility
the space
function
• We know utility is an increasing function of both consumption and leisure:– U(C,Leisure)
• Lets assume a specific functional form:
• What does this function look like?
2/12/1, LeisureCLeisureCU
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Utility
2/12/1, LeisureCLeisureCU
The Function
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Consu
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Leisure
Utility
Let’s rotate the graph in a few directions to understand it’s shape better:
View 1
View 2
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1Consumption
Leisure
Utility
View 1
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Consumption
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Utility
View 2
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Consu
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Leisure
Utility
Now let’s find the indifference curves:Put lines on the surface of the curve for specific levels of utility
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Consu
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Leisure
Utility
Now let’s find the indifference curves:Put lines on the surface of the curve for specific levels of utility – every line traces out all the combinations of consumption and leisure that give a fixed level of utility
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Consu
mpt
ion
Leisure
Utility
Now let’s find the indifference curves:Put lines on the surface of the curve for specific levels of utility – every line traces out all the combinations of consumption and leisure that give a fixed level of utility
U=1/12
U=6/12
U=9/12
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Consu
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Leisure
Utility
U=1/12
U=6/12
U=9/12
Removing the rest of the curve, leaving only these lines
00.25
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Consu
mpt
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Leisure
Utility
Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between themIf we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curve
U=1/12
U=6/12
U=9/12
00.25
0.5
0.75
1
0
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0.751
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1
0
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0.751
Consu
mpt
ion
Leisure
Utility
Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between themIf we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curve
U=1/12
U=6/12
U=9/12
00.25
0.5
0.75
1
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0.751
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Consu
mpt
ion
Leisure
Utility
Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between themIf we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curveSo we need only look at theTwo dimensional versionsIndifference Curves!
U=1/12
U=6/12
U=9/12
0 0.2 0.4 0.6 0.8 1
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Consumption
Leisure
U=1/12
U=6/12
U=9/12
Indifference Curves
