Econ 302 (Inter Micro)- Lesson 04a- Individual and Market Demand.pdf

# Econ 302 (Inter Micro)- Lesson 04a- Individual and Market Demand.pdf

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Lesson 4.0 Individual and Market Demand Pindyck 4.0-4.4

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Budget Constraint X-Axis: Apples P X = \$2 Y-Axis: Cookies P Y = \$2 Money: \$8 Preferences 𝑼𝑼 = 𝑿𝑿𝑿𝑿
Utility maximization occurs when: 𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 = 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 𝑴𝑴𝑼𝑼 𝑿𝑿 𝑴𝑴𝑼𝑼 𝑿𝑿 = 𝑷𝑷 𝑿𝑿 𝑷𝑷 𝑿𝑿

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Cobb-Douglas Short Cut 𝑼𝑼 = 𝒂𝒂𝑿𝑿 𝒄𝒄 𝑿𝑿 𝒅𝒅 𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 = 𝒄𝒄 𝒅𝒅 𝑿𝑿 𝑿𝑿
Cobb-Douglas Short Cut 𝑼𝑼 = 𝑿𝑿 𝟏𝟏 𝑿𝑿 𝟏𝟏 𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 = 𝟏𝟏 𝟏𝟏 𝑿𝑿 𝑿𝑿 = 𝑿𝑿 𝑿𝑿

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Utility maximization occurs when: 𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 = 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 𝑿𝑿 𝑿𝑿 = 𝟐𝟐 𝟐𝟐
For this example the optimization condition is: 𝑿𝑿 = 𝑿𝑿

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Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝑿𝑿 𝟖𝟖 = 𝟐𝟐𝑿𝑿 + 𝟐𝟐𝑿𝑿
Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝑿𝑿 𝟖𝟖 = 𝟐𝟐𝑿𝑿 + 𝟐𝟐 ( 𝑿𝑿 )

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Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝑿𝑿 𝟖𝟖 = 𝟒𝟒𝑿𝑿
Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝑿𝑿 𝑿𝑿 = 𝟐𝟐 𝑿𝑿 = 𝟐𝟐

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Cookies (Y) Apples (X) 2 1 2 4 6 3 8 4 U=4 U = X*Y
Cookies (Y) Apples (X) 2 1 2 4 6 3 8 4 U=4 MRS XY = MktS XY U = X*Y

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Budget Constraint X-Axis: Apples P X = \$1 Y-Axis: Cookies P Y = \$2 Money: \$8 Preferences 𝑼𝑼 = 𝑿𝑿𝑿𝑿
Utility maximization occurs when: 𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 = 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝑿𝑿𝑿𝑿 𝑿𝑿 𝑿𝑿 = 𝟏𝟏 𝟐𝟐

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For this example the optimization condition is: 𝑿𝑿 = 𝟎𝟎 . 𝟓𝟓𝑿𝑿
Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝟎𝟎 . 𝟓𝟓𝑿𝑿 𝟖𝟖 = 𝟏𝟏𝑿𝑿 + 𝟐𝟐𝑿𝑿

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Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝟎𝟎 . 𝟓𝟓𝑿𝑿 𝟖𝟖 = 𝟏𝟏𝑿𝑿 + 𝟐𝟐 ( 𝟎𝟎 . 𝟓𝟓𝑿𝑿 )
Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝟎𝟎 . 𝟓𝟓𝑿𝑿 𝟖𝟖 = 𝟐𝟐𝑿𝑿

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Substitute the optimization condition into the budget constraint: 𝑿𝑿 = 𝟎𝟎 . 𝟓𝟓𝑿𝑿 𝑿𝑿 = 𝟒𝟒 𝑿𝑿 = 𝟐𝟐
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