ECON10A_4 (3)

ECON10A_4 (3) - Studentswithoutregisteredclickers 3108479...

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Students without registered clickers 1/4/2008 1 3108479 3947959 4217956 4950077 6126890 3158532 3955804 4251971 4982104 6131866 3231958 3964582 4255121 5041702 6135115 3237278 4001095 4271961 5055231 6141857 3240173 4037941 4276655 5085725 6152912 3332913 4060984 4279584 5094420 6154199 3346871 4074399 4292124 5125489 6157333 3411998 4089884 4348900 5129358 6161848 3463627 4105680 4351805 5150115 6162986 3477205 4115184 4381984 5162755 6164560 3513272 4115226 4398004 5171020 6183883 3561248 4116901 4443909 5183199 6188098 3561370 4169884 4455663 5222336 6192694 3589066 4172151 4482071 5252143 6192900 3650751 4177143 4499877 5255948 6195812 3700549 4179636 4581542 5370457 6198790 3761293 4180501 4583084 5405865 6199194 3866746 4181285 4641841 5573142 6203202 3880333 4188611 4658787 5719737 6212294 3883816 4201398 4729596 5865639 6231815 3886652 4201521 4732236 6055776 8458184 3919784 4204673 4807160 6098354 8727885 3933082 4205522 4847737 6098826 3935731 4214177 4913455 6116925 3936622 4214847 4933974 6122261
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1/4/2008 2 REVIEW –  3 IMPORTANT UTILITY  FUNCTIONS Linear: U(x 1 ,x 2 )=ax 1 +bx 2 Cobb-Douglass: U(x 1 ,x 2 )=ax 1 α x 2 β Leontief: U(x 1 ,x 2 )=min[x 1 /a, x 2 /b]
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1/4/2008 3 Linear: U(x 1 ,x 2 )=ax 1 +bx 2 Perfect Substitutes MRS constant X 1 X 2 c/b c/a Slope=-a/b U(x 1 ,x 2 )=c
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1/4/2008 4 Cobb-Douglass: U(x 1 ,x 2 )=ax 1 α x 2 β Diminishing MRS Willingness to trade depends on how much of each good is possessed X 1 X 2 U(x 1 ,x 2 )=c
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1/4/2008 5 Leontief: U(x 1 ,x 2 )=min[x 1 /a, x 2 /b] Perfect Complements Goods must be used in fixed preportions MRS = 0 or undefined X T X M 1 4 (1,4) (2,8)
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1/4/2008 6 MATH REVIEW Constrained Optimization
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1/4/2008 7 Example 1 Unconstrained–one independent variable max x f(x) We assume nice properties (continuity, second order conditions) F.O.C. for interior solution: A. f(x)=0 B. f’(x)=0 C. f”(x)=0 X f(x) X*
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1/4/2008 8 Example 1a Unconstrained–one independent variable max x 2x-4x 2 X*= A. 4 B. 2 C. ¼ F.O.C.: 2-8x=0 X f(x) X*
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1/4/2008 9 Example 2 Unconstrained–Two independent variables We assume nice properties (continuity, second order conditions) F.O.C. s for interior solution: A. B. f’(x)=o X f(x) ) , ( max 2 1 , 2 1 x x f x x 1 2 1 2 1 2 ( , ) ( , ) 0, 0 f x x f x x x x = =
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1/4/2008 10 Example 2a Unconstrained–Two independent variables F.O.C. s for interior solution: 8+y-2x=0 x-2y=0 X f(x) 2 2 , 8 max 2 1 y x xy x x x - - +
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1/4/2008 11 Example 3 - Constrained Optimization Optimum is where these are equal: slope of level curve of function x
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This note was uploaded on 12/20/2011 for the course ECON 10a taught by Professor Babcock during the Fall '11 term at UCSB.

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ECON10A_4 (3) - Studentswithoutregisteredclickers 3108479...

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