w6sol - Economics 11: Microeconomic Theory 1 Professor...

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Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Exercises Week 6 ANSWERS 1) In a two period world, Mark has an income of $50 today and $20 tomorrow. He has the following production technology: Q 2 =20*I 1 1/2 . Where I 1 is the investment today and Q is the gross return of the investment. a) Suppose that Mark wants to consume $60 tomorrow. How much is his consumption and investment today?. Answer If 40 60 2 = = Q C F , I need to invest today: I Q = = 20 40 2 then 4 2 20 40 = = = I I I b) Suppose that the interest rate is 100% and his utility function is U(C 1 , C 2 )=C 1 1/2 C 2 1/2 . Find the optimal investment and consumption. Answer Initial situation (A) Wealth without investment 60 60 10 50 1 1 20 50 1 min 2 1 min = = + = + + = + + = W r C C W A A first stage: Optimal Investment r C C W Max + + = 1 2 1 I I C C I I f C C a s A A = = + = + = 50 20 20 ) ( : . . 1 1 2 2 r I I r I f C I C MaxW A A + + + = + + + = 1 20 20 50 1 ) ( 2 1 Solving for the optimal I
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2 / 1 2 / 1 2 / 1 ' 10 1 1 10 1 0 1 20 2 1 1 1 ) ( 1 ) 1 ( = + + = = + + = + + = I r r I r I r I f I W () 1 10 1 () / 10 1 10 1 2 2 / 1 2 2 2 / 1 2 / 1 = =
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This note was uploaded on 04/05/2009 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.

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w6sol - Economics 11: Microeconomic Theory 1 Professor...

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